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thoughts on SoDOS

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Nick Wedd

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Feb 19, 2007, 6:35:42 AM2/19/07
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SoDOS, Sum of defeated Opponents' McMahon Scores, is often used as a
tiebreak in McMahon tournaments.

Its use is deprecated, for the reason explained at
http://www.britgo.org/organisers/mcmahonpairing.html#sodos. The
ordering of the SoDOS values depends on the zero of the mapping from the
players' ratings to their initial McMahon scores, making it arbitrary
and unsatisfactory.

However, this dependence on the zero only arises when the numbers of
Defeated Opponents vary. If we are breaking a tie between two players
who have the same number of wins, then there is no problem, SoDOS is a
satisfactory measure.

Therefore, I suggest that the use of SoDOS should be regarded as
acceptable, if the number of wins has been used as a higher-priority
tiebreak. I have never noticed number of wins used as a tiebreak in a
McMahon tournament, but I can think of no objection to it.

Nick
--
Nick Wedd ni...@maproom.co.uk

Robert Jasiek

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Feb 19, 2007, 7:54:06 AM2/19/07
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On Mon, 19 Feb 2007 11:35:42 +0000, Nick Wedd <ni...@maproom.co.uk>
wrote:

>If we are breaking a tie between two players
>who have the same number of wins, then there is no problem, SoDOS is a
>satisfactory measure.

Already the basic idea of SODOS is doubtful: It values a player's wins
more than his losses. With the same right, one might use SOLOS instead
of SODOS. Rather all games of a player in the same stage of a
tournament should be considered of equal importance. In each game, in
principle the player has to exercise the same go skill to attempt
winning. SODOS violates this basic principle. Therefore it should not
even be used in a Round-Robin.

--
robert jasiek

-

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Feb 19, 2007, 8:33:58 AM2/19/07
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> Nick Wedd <ni...@maproom.co.uk> wrote:
>> If we are breaking a tie between two players who have the same number
>> of wins, then there is no problem, SoDOS is a satisfactory measure.


The various tiebreaking methods may be mathematically evaluated.
I regret only not yet having time to build an implementation for such.
Nick Wedd is fundamentally correct on this point.

Robert Jasiek <jas...@snafu.de> wrote:
> Already the basic idea of SODOS is doubtful: It values a player's wins
> more than his losses. With the same right, one might use SOLOS instead
> of SODOS.


Well ... no. Losing to a greater than great opponent indicates no
additional special privileges. However defeating a greater than great
opponent indicates a rare ability, so information to be made use of.

> Rather all games of a player in the same stage of a tournament should be
> considered of equal importance. In each game, in principle the player has
> to exercise the same go skill to attempt winning. SODOS violates this basic
> principle. Therefore it should not even be used in a Round-Robin.


Robert's assumptions were seriously flawed. To develop criteria for
what games of a tournament represent, examine notions of convergence
upon Maximum Entropy, or Maximum Likelihood. The purpose of any
ratings shuffle is to determine the most likely candidate who is winner.
If McMahon Score is all we need, of course that is most likely winner.
The game results are interpreted as information. Not all game results
offer the same amount of information, because some game results are
more significant than others. That's the whole idea of understanding
what tiebreaking does. There's no need for uninformed opinion because
we may build mathematical models for tournaments and develop statistics
on which tiebreaking methods are most likely to produce the winners.

I have stated earlier that SODOS can be expanded to SODOSODOS, etc.
We have computers that easily arrive at proper recursive computations.
The purpose of fair tiebreaking is to converge upon Maximum Likelihood.
If your criteria are otherwise you have not obtained any concept of fair.
And I would like to reiterate that there's no opportunity for opinionated
argument here. These discussions may be resolved with mathematical
modelling using statistics from many high-speed tournament simluations.


- regards
- jb

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Traviesties in the methods Europeans Use for Pairing Algorithms ...
Mon, Sep 5 2005
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http://groups.google.com/group/rec.games.go/msg/628fad4c49e770ee
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Robert Jasiek

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Feb 19, 2007, 9:23:22 AM2/19/07
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On Mon, 19 Feb 2007 13:33:58 GMT, jazze...@hotmail.com (-) wrote:
> Losing to a greater than great opponent indicates no
> additional special privileges.

With SODOS, a player is not punished for losing to a more doubtful
than doubtful opponent. Why should winner against a greater than great
opponent be more important than losing to a more doubtful than
doubtful opponent? Why not vice versa? There is no a priory reason to
decide which of the two is more important, i.e. they should be
considered equally important. SODOS does the contrary.

> examine notions of convergence
> upon Maximum Entropy, or Maximum Likelihood.

ML is a tool for evaluating a player population, not for evaluating a
single player.

> I have stated earlier that SODOS can be expanded to SODOSODOS, etc.
> We have computers that easily arrive at proper recursive computations.

Some claim it is even possible to count elections by means of
computers :)

> The purpose of fair tiebreaking is to converge upon Maximum Likelihood.

The only purpose? Is evaluation of a player population the only aim?

> These discussions may be resolved with mathematical
> modelling using statistics from many high-speed tournament simluations.

Resolved is a bit of an exaggeration, ALA axioms are not agree upon.

--
robert jasiek

Ben Finney

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Feb 19, 2007, 4:00:53 PM2/19/07
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Nick Wedd <ni...@maproom.co.uk> writes:

> Therefore, I suggest that the use of SoDOS should be regarded as
> acceptable, if the number of wins has been used as a higher-priority
> tiebreak. I have never noticed number of wins used as a tiebreak in
> a McMahon tournament, but I can think of no objection to it.

I know that the annual NEC Cup tournament in Australia uses these tie
breakers in sequence: points (from wins), SOS, SoDOS. Whether that's
run as a McMahon tournament I'm not entirely sure, but I think so.

--
\ "If nature has made any one thing less susceptible than all |
`\ others of exclusive property, it is the action of the thinking |
_o__) power called an idea" -- Thomas Jefferson |
Ben Finney

Ben Finney

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Feb 19, 2007, 4:05:31 PM2/19/07
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Robert Jasiek <jas...@snafu.de> writes:

> Nick Wedd <ni...@maproom.co.uk> wrote:
> >If we are breaking a tie between two players who have the same
> >number of wins, then there is no problem, SoDOS is a satisfactory
> >measure.
>
> Already the basic idea of SODOS is doubtful: It values a player's
> wins more than his losses.

The proposal is to use SoDOS only in cases where comparing other
information about the games has not yielded a difference between the
players.

> With the same right, one might use SOLOS instead of SODOS.

What would be the expansion of SOLOS?

What is your reasoning for presenting SOLOS instead of SoDOS?

> Rather all games of a player in the same stage of a tournament
> should be considered of equal importance.

The proposal is to use all the available information about all the
player's games first, and only to use SoDOS to break ties that still
exist after that.

--
\ "All my life I've had one dream: to achieve my many goals." -- |
`\ Homer, _The Simpsons_ |
_o__) |
Ben Finney

Robert Jasiek

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Feb 20, 2007, 12:40:24 AM2/20/07
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On Tue, 20 Feb 2007 08:05:31 +1100, Ben Finney
<bignose+h...@benfinney.id.au> wrote:
>The proposal is to use SoDOS only in cases where comparing other
>information about the games has not yielded a difference between the
>players.

Sure, I am aware of this.

>What would be the expansion of SOLOS?

Expansion?

>What is your reasoning for presenting SOLOS instead of SoDOS?

It is as doubtful as SODOS. Since it is unclear why to consider wins
intead of losses (or vice versa), it is also unclear which of SODOS or
SOLOS should be used if and of these two had to be used at all.

>The proposal is to use all the available information about all the
>player's games first, and only to use SoDOS to break ties that still
>exist after that.

Sure, I am aware of this.

It does not alter the fundamental weakness of SODOS (why wins but not
losses should be considered for more information).

--
robert jasiek

henricb...@gmail.com

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Feb 21, 2007, 4:21:49 AM2/21/07
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On 19 Feb, 13:54, Robert Jasiek <jas...@snafu.de> wrote:
> On Mon, 19 Feb 2007 11:35:42 +0000, Nick Wedd <n...@maproom.co.uk>

I think it's obvious that you are right on this point, Robert.
I don't understand why anyone came up with SODOS in the first place.
SODOS does not respect the symmetry of the problem.
SOSOS does, so it may be more justifiable.

As we have discussed before, none of these tiebreakers can be
worse than toss up anyway, and toss up is not unfair.
For fairness the important things are that the rules should be made
clear beforehand and that nobody is discriminated apriori.

best regards,
Henric

-

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Feb 21, 2007, 12:37:23 PM2/21/07
to

> jazze...@hotmail.com (-) wrote:
>> Losing to a greater than great opponent indicates no
>> additional special privileges.

Robert Jasiek <jas...@snafu.de> wrote:
> With SODOS, a player is not punished for losing to a more doubtful
> than doubtful opponent. Why should winner against a greater than
> great opponent be more important than losing to a more doubtful
> than doubtful opponent? Why not vice versa? There is no a priory
> reason to decide which of the two is more important, i.e. they should
> be considered equally important. SODOS does the contrary.


The "punishment" part is unnecessary, because McMahon Score
is sufficient. Nor should a "punishment" component be required, as
the player continuing to place high in SODOS (pairing for Round 3),
then SODOSODOS (pairing for Round 4), etc., deserves to hold high
in standing for maintaining competitive SODOS's, at that MMS level.

Difficult to understand the nature of Robert's questions when
considering contextual parameters: we agreed this was a tournament.
The tournament purpose is going to hold a "winner against a greater
than great opponent" more importantly than a "loser to a more doubtful
than doubtful opponent."

At the end of a tournament we will agree that the players do not
have equal standing in Go Ability, as Go Players. That unequal position
was -latent- at the start of the tournament, so the player positions were
not equal even when they entered the tournament. There's nothing
unfair about acknowledging that the players were not equal when we
began the tournament. The notion that different ideas should obtain
an equality is unsubstantiated, and unwarranted. Robert has not told
us why "this" and "that" should be considered equally important.
Strangely enough, Robert wants to insist that unequal ideas are equal.

I digress just a bit to relate a story about skiing, which could be
just a popular in Germany as it is for Nordic countries. The old method
for teaching ski turns was "stem christie" which consists of placing the
ski opposite to the turn uphill in a kind of temporary snow plow, then
shifting weight to that ski to make it an outside ski to the turn and
then bringing the inside ski back into parallel for the traverse once
into the turn. Unfortunately this method slows down the skiier too
much (for racing) and is actually less safe, because many ski accidents
happen as the result of snowplow or snowplow-related forms. This is
the sort of thinking, perhaps, which results from "equality minded"
people who want their weight transferred onto both skis equally for
making turns. Skiers need to be capable of making turns under all
sorts of conditions and not be relying upon one method, nor even
use "stem christie" as a method. So we teach the opposite way: to
"walk" down the hill herringbone fashion by opening up the downhill
ski and pushing off through the turn. Move the ski tips away from
each other. The weight has already been transferred to the outside
ski once picking up the downhill ski. There's never any "equality"
involved during turns or traverses because the only "equality" in
skiing is directly down the hill. The skier's fundamental position is
down the hill with knees and fists forward. Beginners and novices
are just afraid of speed because they clutch to equality for turns,
but speed was one of the finer points of skiing, wasn't it ?

>> ... examine notions of convergence


>> upon Maximum Entropy, or Maximum Likelihood.

> ML is a tool for evaluating a player population, not for evaluating a
> single player.


ROTFL. At this late date, to be having this discussion.... :-)
All that concerns us is the relationship between the single player and
the player population of a tournament. The tournament is not purposed
for showering accolades upon players who obtain some N-dan diplomas.

>> I have stated earlier that SODOS can be expanded to SODOSODOS, etc.
>> We have computers that easily arrive at proper recursive computations.

> Some claim it is even possible to count elections by means of computers :)


Computer are being used before, during, and after, elections, even
to assess validity of "computer elections." The people's attitude, by
accepting the results from computers, is found in their hearts and minds
concerning their "spiritual condition" (or lack of it) to acceed to forms
of social stratification. The problem there was lack of transparency,
however there is no lack of transparency when analyzing tournaments.
Each calculation step may be verified by other computers and the code
be made open for public inspection.

There are very good reasons to distrust computers when we have no
access to the code. By the same token there are very good reasons to
trust the results of computations when the mathematics is made clear and
the experiments may be repeated as often as you please.

>> The purpose of fair tiebreaking is to converge upon Maximum Likelihood.

> The only purpose? Is evaluation of a player population the only aim?


ML neither evaluates the population nor the individuals. It merely
obtains a "spread" among the individuals of a population according to
selectable criteria. We are interested only in the -relationship- among
players of a tournament for producing a rank ordering. No players, nor
any player population, are being "evaluated" by the tournament, nor by
the tiebreaking. Tiebreaking methods that converge upon ML are just
those which indicate the more likely rank ordering among the players.

>> These discussions may be resolved with mathematical modelling
>> using statistics from many high-speed tournament simluations.

> Resolved is a bit of an exaggeration, ALA axioms are not agree upon.


Why don't you explain exactly what these are so we can shine
some daylight on your obscurantist muddling ?

<henricb...@gmail.com> wrote:
> I don't understand why anyone came up with SODOS in the first place.
> SODOS does not respect the symmetry of the problem.


There's no symmetry in this problem. Are losers going to be
awarded prizes, or opportunities to compete in easier tournaments?



> As we have discussed before, none of these tiebreakers can be
> worse than toss up anyway, and toss up is not unfair.


Anything less fair than Maximum Likelihood is unfair.

> For fairness the important things are that the rules should be made
> clear beforehand and that nobody is discriminated apriori.


There is no particular pairing scheme for Round One, so
much of it is arbitrary and anybody could claim "discrimination."
Yet Henric did well with "the Italian Go Problem" excepting the plot
which attempts to correlate "democracy" and "lack of corruption"
with how well those Go Organizations matched "the Swedish motion."
If Rafella just admitted to an abortion at age 14 (even if never having
one) then much of "the Italian Go Problem" might have been solved.

- regards
- jb

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spectators attended the traditional street carnival parade in the state
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henricb...@gmail.com

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Feb 22, 2007, 11:27:48 AM2/22/07
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On 21 Feb, 18:37, jazzerci...@hotmail.com (-) wrote:

>
> <henricbergsa...@gmail.com> wrote:
> > I don't understand why anyone came up with SODOS in the first place.
> > SODOS does not respect the symmetry of the problem.
>
> There's no symmetry in this problem. Are losers going to be
> awarded prizes, or opportunities to compete in easier tournaments?

The symmetry is the following:
If two players have equal SOS and one has higher SODOS, this
may suggest that he has beaten stronger players, but if so
it equally well suggests that he lost against weaker players.
Winning against stronger players and losing against weaker
players cancels, by symmetry. My quess is that SODOS may
have its origin in chess, where there are many draws, in go
it is completely pointless, as far as I can see.

> > As we have discussed before, none of these tiebreakers can be
> > worse than toss up anyway, and toss up is not unfair.
>
> Anything less fair than Maximum Likelihood is unfair.

Are loteries unfair in your opinion?

> > For fairness the important things are that the rules should be made
> > clear beforehand and that nobody is discriminated apriori.
>
> There is no particular pairing scheme for Round One, so
> much of it is arbitrary and anybody could claim "discrimination."
> Yet Henric did well with "the Italian Go Problem" excepting the plot
> which attempts to correlate "democracy" and "lack of corruption"
> with how well those Go Organizations matched "the Swedish motion."
> If Rafella just admitted to an abortion at age 14 (even if never having
> one) then much of "the Italian Go Problem" might have been solved.
>
> - regards
> - jb
>

I think you were a lot sharper and more rational a couple of months
ago,
jb. Are you changing medication now and then or something? If that's
the case I think you should go back to what you were using then.

best regards,
Henric

-

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Feb 22, 2007, 11:58:42 AM2/22/07
to

>> <henricbergsa...@gmail.com> wrote:
>>> I don't understand why anyone came up with SODOS in the first place.
>>> SODOS does not respect the symmetry of the problem.

> jazzerci...@hotmail.com (-) wrote:
>> There's no symmetry in this problem. Are losers going to be
>> awarded prizes, or opportunities to compete in easier tournaments?

henricb...@gmail.com wrote:
> The symmetry is the following:
> If two players have equal SOS and one has higher SODOS, this
> may suggest that he has beaten stronger players, but if so
> it equally well suggests that he lost against weaker players.
> Winning against stronger players and losing against weaker
> players cancels, by symmetry. My quess is that SODOS may
> have its origin in chess, where there are many draws, in go
> it is completely pointless, as far as I can see.


First, it begins this way: two players have equal MMS. Then you
may talk about SODOS and SOS. The SOS only reports who they met.
Why should somebody obtain points in a tournament only for shaking
an opponent's hand? The SODOS reports how much effort a player
has expended, to obtain the `win' conditions. Second, you are wrong
to presume that "winning against stronger players and losing against
weaker players cancels, by symmetry." The Maximum Likelihood deltas
among all players are not necessarily equal. Third, you are absolutely
wrong to suppose that `draw' is impossible in Go. Tournament Rules
may offer an integer _komi_, or there might be a game annullment, or
there might be a `bye' marked as a `draw' instead of a `win' (by some
improper variation of tournament scoring).

Examine Regulation #3 in the upcoming European Ing Memorial 2007:

"3. The first two rounds the pairing will be forced according to the
results of the first round draw. The other four rounds the pairing
will be done with the program MacMahon, using SODOS as first
and SOS as second tiebreaker."

>>> As we have discussed before, none of these tiebreakers can be
>>> worse than toss up anyway, and toss up is not unfair.

>> Anything less fair than Maximum Likelihood is unfair.

> Are loteries unfair in your opinion?


What is the purpose of lotteries?

>>> For fairness the important things are that the rules should be made
>>> clear beforehand and that nobody is discriminated apriori.

>> There is no particular pairing scheme for Round One, so
>> much of it is arbitrary and anybody could claim "discrimination."
>> Yet Henric did well with "the Italian Go Problem" excepting the plot
>> which attempts to correlate "democracy" and "lack of corruption"
>> with how well those Go Organizations matched "the Swedish motion."
>> If Rafella just admitted to an abortion at age 14 (even if never having
>> one) then much of "the Italian Go Problem" might have been solved.

> I think you were a lot sharper and more rational a couple of months ago,


> jb. Are you changing medication now and then or something? If that's
> the case I think you should go back to what you were using then.


Perhaps the Europeans are arguing over medications instead of
resolving their Italian Go Problems. It's downright embarassing that
Kung Fu techniques have not yet been brought to bear. Much of this
occurs from people exercising turfdom in a vacuum of their own making.


- regards
- jb

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-----------------------------------------------------------------------------

Robert Jasiek

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Feb 22, 2007, 12:25:40 PM2/22/07
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On Thu, 22 Feb 2007 16:58:42 GMT, jazze...@hotmail.com (-) wrote:
> MacMahon, using SODOS as first and SOS as second tiebreaker."

This was Ing Chang-ki's second bad invention.

> What is the purpose of lotteries?

To be entertained for payment?

--
robert jasiek

henricb...@gmail.com

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Feb 22, 2007, 12:43:12 PM2/22/07
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On 22 Feb, 17:58, jazzerci...@hotmail.com (-) wrote:

> What is the purpose of lotteries?

I don't know, I don't participate in any, but many do, so I suppose
they like them. You are changing the subject though, the relevant
question was if loteries are fair, not what their purpose is.

best regards,
H.

-

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Feb 22, 2007, 1:05:20 PM2/22/07
to

> jazze...@hotmail.com (-) wrote:
>> Examine Regulation #3 in the upcoming European Ing Memorial 2007:
>> "3. The first two rounds the pairing will be forced according to the
>> results of the first round draw. The other four rounds the pairing
>> will be done with the program MacMahon, using SODOS as first
>> and SOS as second tiebreaker."

Robert Jasiek <jas...@snafu.de> wrote:
> This was Ing Chang-ki's second bad invention.


Much worse is Robert's absense of any explanation why he says this.

------------------------------------------------------------


> jazzerci...@hotmail.com (-) wrote:
>> What is the purpose of lotteries?

<henricb...@gmail.com> wrote in message

> I don't know, I don't participate in any, but many do, so I suppose
> they like them. You are changing the subject though, the relevant
> question was if loteries are fair, not what their purpose is.


You cannot evaluate them for fairness without a statement of purpose.
Some may say it is unfair to apply national testing standards on students
while others justify use of tests according to purposes being advanced.
The preliminary discussion needs to address goals, criteria and purpose.
If the group cannot agree on its goals then you may as well abandon any
attempt to discuss whether a given example offers fairness and justice.


e.g. "Lotteries are fair because everyone has an equal chance..."
or "Lotteries are unfair because they do not reward by merit..."


In the Shirley Jackson short story _The_Lottery_, the winner was the
one chosen for killing by stoning. Such lotteries are manifestly unfair.
Yet, townspeople agreed to their tradition, so they thought it was fair.

- regards
- jb

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henricb...@gmail.com

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Feb 22, 2007, 2:26:23 PM2/22/07
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"-":

> You cannot evaluate them for fairness without a statement of purpose.
(....)

> If the group cannot agree on its goals then you may as well abandon > any attempt to discuss whether a given example offers fairness and
> justice.
>

I'm aware that fairness is a problematic concept.
Allow me to remind you that you were making claims on what
was supposed to be fair/unfair before I did. My claim is actually
just that there is no rational ground for arguing that tiebreakers
which
are equivalent to throwing dice or "better" are "unfair".
In my opinion we should either leave fair/unfair out of it or accept
that tiebreakers with aleatory properties are fair.

Robert is digging himself down in peculiar fairness arguments
too, it's a bit amusing to observe this.

Why not analyse fairness along these lines:

Fairness is a vague concept and there is no consensus on what it
means.
One fairness criterion is to give equal chances to everybody
(loterie).
Another is to give more (maybe even everything) to the guy who
performs best. Since there will never be any consensus, let's accept
the widest
possible definition and say that anything between the two extremes is
fair: lotteries as well as the best performer takes all. If we accept
this, then
all the common tiebreakers are equally fair. By contrast it would be
unfair to discriminate e.g. males or females, people with surname
beginning in "B", red haired people, americans or whatever. This
solution has many
advantages. The most obvious advantage is that, in the frequently
occurring
situations where it is not practically possible to determine who is
really
the best performer, it is fair to resort to more or less aleatory
tiebreakers.
We don't even need to torment ourselves too much with elaborate
investigations of the exact performance related properties of
tiebreakers,
as long as we are confident that they are either 100% aleatory or
somewhat
more performance related, we can feel free to use them. We don't
refrain
from organising tournaments and brood instead over impossible fairness/
unfairness issues.

cheers,
Henric

Robert Jasiek

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Feb 22, 2007, 3:19:48 PM2/22/07
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On Thu, 22 Feb 2007 18:05:20 GMT, jazze...@hotmail.com (-) wrote:
>> This was Ing Chang-ki's second bad invention.
> Much worse is Robert's absense of any explanation why he says this.

His first bad invention was the Ing ko rules. Why I consider SODOS to
be bad: see my earlier mails.

> You cannot evaluate them for fairness without a statement of purpose.

Now this an interesting claim that fairness could not exist without a
context of purpose. Why do you think so? Can't it exist on the basis
of criteria that are not purposes?

--
robert jasiek

-

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Feb 22, 2007, 3:53:34 PM2/22/07
to

> "-":
>> You cannot evaluate them for fairness without a statement of purpose.
>> (....)
>> If the group cannot agree on its goals then you may as well abandon
>> any attempt to discuss whether a given example offers fairness and
>> justice.

henricb...@gmail.com wrote:
> I'm aware that fairness is a problematic concept.
> Allow me to remind you that you were making claims on what
> was supposed to be fair/unfair before I did. My claim is actually
> just that there is no rational ground for arguing that tiebreakers
> which are equivalent to throwing dice or "better" are "unfair".


There's the sort of discussion about fairness which proceeds
from what any group might define as fair. Another type of discussion
proceeds from acknowledgment of Maximum Likelihood as offering
that definition. If there are many games on record to work from then
Maximum Likelihood is about as fair as possible. The tournament
does not offer a sufficient number of games however we can still
speak of convergence to Maximum Likelihood even from the scanty
information available. AcceleRat is one means for improving on the
convergence to Maximum Likelihood where the provisional rating is
added into MMS via polynomial coefficients to obtain a sorting score:

End of Round Two:
(say) Tournament Points = 1,000 * MMS + k * AcceleRat + SoDoS

End of Round Three:
(say) Tournament Points = 10,000 * MMS + k * AcceleRat + SoDoSoDoS

etc.


Or, one may leave off AcceleRat, by k=0, with a field of evenly-matched
strong contenders. The problem with throwing dice, or coins, is that the
situations with slight detectable difference would be ignored. Resorting
to coin toss is effectively throwing away information useful for Maximum
Likelihood. So coin toss as tiebreaking method is potentially less fair
than mathematical focus on methods which illusterate convergence to ML.
One analogy is the problem of imprecise clock which records the same
racing score for two contenders in 10ths of a second. The Olympics has
long ago improved on imprecise clocks to obtain 100ths and 1000ths, so
there is no sharing of medals among the finalists.

> In my opinion we should either leave fair/unfair out of it or accept
> that tiebreakers with aleatory properties are fair.


I don't believe we ought to "leave fair/unfair out of it." I don't
anticipate that groups who operate Tournaments are going to agree
on leaving "fair/unfair out of it." When we speak of Go as a game of
complete information we have agreed not to introduce dice or chance.

> Fairness is a vague concept and there is no consensus on what it
> means. One fairness criterion is to give equal chances to everybody
> (loterie). Another is to give more (maybe even everything) to the guy
> who performs best. Since there will never be any consensus, let's
> accept the widest possible definition and say that anything between the
> two extremes is fair: lotteries as well as the best performer takes all.
> If we accept this, then all the common tiebreakers are equally fair.


Which, if I may say so, might typify "Scandanavian thinking" and
why all countries are not jumping on the bandwagon to sign on with
"the Swedish motion." As says Arianna Huffington, fourth dimension
political columnist: "the truth is not always in the middle." Simply
bracketing the problem with crude calipers isn't going to satisfy those
who wish to obtain accuracy with their precision. Proposing to end a
discussion with "somewhere therein lies `fairness'" does not satisfy the
ongoing philosophic inquiry. We have already the notion of fairness in
the form of Maximum Likelihood because its cousin Minimum Entropy is
suggesting that "least amount of argument" against it, is being obtained.
Tiebreaking methods which tend toward ML are to be preferred over the
methods that do not tend toward ML. Do you recall Computer Roshambo
competitions? It is a fact that some programs perform better at Roshambo
than others. Given enough iterations they will -always- perform better.

Programs that apply only "random guessing" (sic!) lose out to programs
which apply some sophisticated A.I.

> By contrast it would be unfair to discriminate e.g. males or females, people
> with surname beginning in "B", red haired people, americans or whatever.
> This solution has many advantages. The most obvious advantage is that, in
> the frequently occurring situations where it is not practically possible to
> determine who is really the best performer, it is fair to resort to more or less
> aleatory tiebreakers.


It is rather that cultural predisposition which marks "aleatory" as
"fair." In no sense are cases for jurisprudence decided by coin toss.
Football games might begin from a coin toss only because there is no
other basis by which to proceed. Similarly, Round One may proceed
from coin toss or lottery because there is no information at inception.
Once acquiring information, ignoring that information will not be fair.

> We don't even need to torment ourselves too much with elaborate
> investigations of the exact performance related properties of
> tiebreakers, as long as we are confident that they are either 100% aleatory
> or somewhat more performance related, we can feel free to use them.
> We don't refrain from organising tournaments and brood instead over
> impossible fairness/unfairness issues.


There is a straightforward mathematical procedure for evaluating
the fairness of various tiebreaking methods, given large numbers of
tournament simulations. Confronted by that straightforward mathematical
method, the issues of "torment" or "elaborate" or complaints of "exact
performance related properties" are somewhat moot. The computers
do all the work, the programs may be sanity checked, the trial runs may
be repeated on different workstations in different countries of Earth.
Those not wishing to participate with the research are welcome to
watch from the sidelines. Aleatory methods are just one of many
categories of tiebreaking for obtaining an ordering according to how
accurately matched are "the actual standings." This is not too much
different from Computer Roshambo competitions which can rank the
various approaches. Aleatory methods are less fair than many others.

-------------------------------------------------------------------------------


>>> This was Ing Chang-ki's second bad invention.

> jazze...@hotmail.com (-) wrote:
>> Much worse is Robert's absense of any explanation why he says this.

"Robert Jasiek" <jas...@snafu.de> wrote in message

> His first bad invention was the Ing ko rules. Why I consider SODOS to
> be bad: see my earlier mails.


Not acceptible, Robert. You have too many earlier posts to search
through. You can simply type up your "reasons" in a few short lines.
I don't suppose you have a leg to stand on. Will you play in the Ing?



>> You cannot evaluate them for fairness without a statement of purpose.

> Now this an interesting claim that fairness could not exist without a


> context of purpose. Why do you think so? Can't it exist on the basis
> of criteria that are not purposes?


We have not mentioned the use of Official State Lotteries as a
method of revenue generation. Surely there's an argument of fairness
involved in preferring to "tax" gamblers, or those with ability to pay,
over those who cannot afford to be "taxed" and thereby do not play.
But, then, there's also an argument against State Lotteries when the
State involves itself with an attitude that money is to become aleatory.

Perhaps Robert would be willing to share with us some examples
of criteria that are not purposes. Maximum Likelihood has purposes.

- regards
- jb

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New Red Cross logo paves way for Israel to join
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Robert Jasiek

unread,
Feb 22, 2007, 4:39:19 PM2/22/07
to
On Thu, 22 Feb 2007 20:53:34 GMT, jazze...@hotmail.com (-) wrote:
> Perhaps Robert would be willing to share with us some examples
> of criteria that are not purposes.

All human beings are equal or all go players at the start of the
tournament have equal rights are criteria of fairness without purposes
in themselves, although they might be made on purpose.

--
robert jasiek

henricb...@gmail.com

unread,
Feb 22, 2007, 5:04:49 PM2/22/07
to
On 22 Feb, 21:53, jazzerci...@hotmail.com (-) wrote:

> There's the sort of discussion about fairness which proceeds
> from what any group might define as fair.

(...)

> There is a straightforward mathematical procedure for evaluating
> the fairness

I'm afraid you are a victim of a very fundamental and probably
potentially
dangerous misconception, jb. There is no way that fair/unfair, good/
bad,
beautiful/ugly and similar things can be derived as mathematical
theorems.
Fortunately, I'm tempted to add.

H.

henricb...@gmail.com

unread,
Feb 22, 2007, 5:50:26 PM2/22/07
to
On 22 Feb, 21:53, jazzerci...@hotmail.com (-) wrote:

> > two extremes is fair: lotteries as well as the best performer takes all.
> > If we accept this, then all the common tiebreakers are equally fair.
>
> Which, if I may say so, might typify "Scandanavian thinking"

Actually I suspect that you are missing the point. I'm not advocating
any global compromise philosophy. Let me try and explain better, let's
make a Gedankenexperiment:

Suppose a sponsor has given a new Mercedes to a tournament.To attract
people, the organisers decide to arrange a lottery, with equal chances
for all participants to win the car. Would you claim that this is
"unfair"? I don't think you would and I think most people wouldn't,
maybe not necessarily sensible, but hardly unfair. Compare this to the
situation where they decide to make it a knock out tournament, where
the winner takes the car. I should think that nobody would say that's
unfair either. Now imagine various situations inbetween these two
extremes. You may feel whatever you like of course, but I put to you
that it would be a bit odd at least if any mix somewhere between the
two extremes were to be considered "unfair", if none of the extreme
cases is "unfair".

Compare these cases with setups where the lottery is rigged in favor
of the organisers cousin, or where that Boscole guy is not allowed
into the lottery because the organiser is a nasty killfiler who
doesn't like Boscole, or where the rules are changed according to how
the tournament is going. Most people would agree that these examples
are indeed "unfair".

H.

-

unread,
Feb 23, 2007, 12:58:10 AM2/23/07
to

> jazze...@hotmail.com (-) wrote:
>> Perhaps Robert would be willing to share with us some examples
>> of criteria that are not purposes.

Robert Jasiek <jas...@snafu.de> wrote:
> All human beings are equal or all go players at the start of the
> tournament have equal rights are criteria of fairness without purposes
> in themselves, although they might be made on purpose.


"All human beings are equal ..." in WHAT WAY ? We do not suppose that
Go Players have equal ability before, during, nor after, the tournament.
Fairness has purpose: it is designed to minimize arguments / complaints.
Robert entertains a myth that ONE TOURNAMENT could determine a World
Champion. Instead our reality consists of several feeder tournaments by
which winners qualify to compete in successively harder tournaments until
reaching a title match with their unsullied winning streak. Tournaments
occur by relationship to other tournaments: do not exist in isolation.

Seeding occurs in tournaments as a fair method for implementing
rapid convergence upon Maximum Likelihood. Strongest players have
already "paid their dues" in past performances to obtain good seeding.


-------------------------------------------------------------------------


> jazzerci...@hotmail.com (-) wrote:
>> There's the sort of discussion about fairness which proceeds
>> from what any group might define as fair.

>> (...)
>> ... a straightforward mathematical procedure for evaluating the fairness



<henricb...@gmail.com> wrote:
> I'm afraid you are a victim of a very fundamental and probably potentially
> dangerous misconception, jb. There is no way that fair/unfair, good/bad,
> beautiful/ugly and similar things can be derived as mathematical theorems.
> Fortunately, I'm tempted to add.


I am not claiming anything about good/bad or beautiful/ugly. Several
times we have asked this newsgroup (and innumerable other sources)
whether there was any aesthetic fairer than Maximum Likelihood. The
ratings systems on the competitive Go Servers popular in the Western
World utilize Maximum Likelihood. The American Go Association sets
its player rankings from collected results by use of Maximum Likelihood.
If Henric wants to propose an alternative aesthetic then show why some
alternative is fairer than Maximum Likelihood. I suspect that the Asian
Go Servers also apply Maximum Likelihood for setting player ratings.
There is a straightforward procedure for evaluating convergence upon
Maximum Likelihood, given each of the tiebreaking proposals, and then
determining which of the tiebreaking proposals yield better convergence.

-----------------------------------------------------------------------------


>> <henricb...@gmail.com> wrote:
>>> Fairness is a vague concept and there is no consensus on what it
>>> means. One fairness criterion is to give equal chances to everybody
>>> (loterie). Another is to give more (maybe even everything) to the guy
>>> who performs best. Since there will never be any consensus, let's
>>> accept the widest possible definition and say that anything between the
>>> two extremes is fair: lotteries as well as the best performer takes all.
>>> If we accept this, then all the common tiebreakers are equally fair.

> jazzerci...@hotmail.com (-) wrote:
>> Which, if I may say so, might typify "Scandanavian thinking" ...



<henricb...@gmail.com> wrote:
> Actually I suspect that you are missing the point. I'm not advocating
> any global compromise philosophy. Let me try and explain better, let's
> make a Gedankenexperiment:
>
> Suppose a sponsor has given a new Mercedes to a tournament. To
> attract people, the organisers decide to arrange a lottery, with equal
> chances for all participants to win the car. Would you claim that this
> is "unfair"? I don't think you would and I think most people wouldn't,
> maybe not necessarily sensible, but hardly unfair. Compare this to the
> situation where they decide to make it a knock out tournament, where
> the winner takes the car. I should think that nobody would say that's
> unfair either.


There are some complaints about knock out tournaments. Players
could instead decide whether they wish to render their participation as
"knock out" by withdrawing from future round pairing. Else, they could
decide to continue and hope nobody goes undefeated. Yet to decide
this for players in advance, and then to encounter no undefeated set,
might present an embarassment for the organizers and sponsors.

> Now imagine various situations inbetween these two extremes. You
> may feel whatever you like of course, but I put to you that it would be a
> bit odd at least if any mix somewhere between the two extremes were
> to be considered "unfair", if none of the extreme cases is "unfair".


In practice this is likely to occur: the organizers attract more
players than they had anticipated. They advertise six rounds, the
prize incentive, and a registration deadline. Instead they attract
80 participants for a six round tournament. There is strong likelihood
of a tie among undefeated players. They will need the security of the
most reliable tiebreaking method which exhibits the best convergence
upon Maximum Likelihood if they are to minimize arguments/complaints.
Because many of the players are aware of the abstruse mathematical
theories there will be arguments/complaints if coin tossing is used.
I am not aware of any major tournaments among the strongest players
that accept coin tossing as a fair method for tiebreaking.

- regards
- jb

-------------------------------------------------------------------------
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Jens

unread,
Feb 23, 2007, 12:56:19 PM2/23/07
to
When we are talking about the top of the results table, we
have players with many wins and few losses. For these it
seems to be appropriate to look at their wins rather than
their losses. For these players SODOS is based on more
data than SOLOS. For the bottom of the table it should imo
be the other way around.

Jens

Robert Jasiek

unread,
Feb 23, 2007, 1:19:16 PM2/23/07
to
On Fri, 23 Feb 2007 18:56:19 +0100, Jens
<not-a-val...@onlinehome.de> wrote:
>When we are talking about the top of the results table, we
>have players with many wins and few losses.

And since we are talking about a tiebreaker, we have players with
exactly the same number of wins.

>For these it
>seems to be appropriate to look at their wins rather than
>their losses. For these players SODOS is based on more
>data than SOLOS.

"More data" does not imply "better data". If more data is all you
want, then calculate

SOS
SOSOS
SOSOSOS
SOSOSOSOS
SOSOSOSOSOS
SOSOSOSOSOSOS
SOSOSOSOSOSOSOS
SOSOSOSOSOSOSOSOS
SOSOSOSOSOSOSOSOSOS
SOSOSOSOSOSOSOSOSOSOS
etc.

or follow Jeff's advice to use ratings and maximal likelihood (you get
abundant more data) or use the board score as tiebreaker (I do not
know whether you would prefer greater or smaller scores) and prohibit
resignation or divide the board score by the used thinking time
difference...

--
robert jasiek

-

unread,
Feb 23, 2007, 1:51:19 PM2/23/07
to

Robert Jasiek <jas...@snafu.de> wrote:
> "More data" does not imply "better data".


We have a "better chance" of finding "better data" among
"more data" than among "less data."

> or follow Jeff's advice to use ratings and maximal likelihood


I have not claimed that we are using Maximal Likelihood. I
said tiebreaking methods which converge upon ML are to be preferred
as "more fair" than the tiebreaking methods with less convergence.
In all of our discussions concerning ML, nobody has ever indicated
a means "more fair" for defining what the term "fairness" means.

> ... or use the board score as tiebreaker


Which may not correlate very well to a player's ability to defeat
stronger players.

> ... and prohibit resignation


Perhaps a relic of World War II ?

> ... or divide the board score by the used thinking time difference...


Bzzzt ! Clocks do not measure "thinking time."

- regards
- jb

-----------------------------------------------------------------------
PRISONER OF ZIONISM
http://www.rense.com/general75/SSPW.HTM
http://www.rense.com/general75/plax.htm
http://www.rense.com/general75/formltry.htm
http://www.rense.com/general75/zzn.htm
http://www.rense.com/Datapages/zunddata.htm
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Robert Jasiek

unread,
Feb 23, 2007, 2:11:02 PM2/23/07
to
On Fri, 23 Feb 2007 18:51:19 GMT, jazze...@hotmail.com (-) wrote:
> We have a "better chance" of finding "better data" among
> "more data" than among "less data."

Quite contrarily. The more data we have the more useless information
must be sorted out.

>> ... and prohibit resignation
> Perhaps a relic of World War II ?

Of the Anglo-French War, which lasted some 116 years?

--
robert jasiek

-

unread,
Feb 23, 2007, 2:47:50 PM2/23/07
to

> jazze...@hotmail.com (-) wrote:
>> We have a "better chance" of finding "better data" among
>> "more data" than among "less data."

Robert Jasiek <jas...@snafu.de> wrote:
> Quite contrarily. The more data we have the more useless information
> must be sorted out.


Mr. Jasiek's notion must be challenged thoroughly. The time
cost for obtaining potentially useful data is far less than the time cost
for sorting out extraneous information.


- regards
- jb

------------------------------------------------------------------------------------
British children: poorer, at greater risk and more insecure
http://www.nationalvanguard.org/story.php?id=11722
------------------------------------------------------------------------------------

Robert Jasiek

unread,
Feb 24, 2007, 1:41:08 AM2/24/07
to
On Fri, 23 Feb 2007 19:47:50 GMT, jazze...@hotmail.com (-) wrote:
> The time
> cost for obtaining potentially useful data is far less than the time cost
> for sorting out extraneous information.

Not time is the problem but understanding how to separate useful from
useless data.

--
robert jasiek

-

unread,
Feb 27, 2007, 4:19:46 AM2/27/07
to

> jazze...@hotmail.com (-) wrote:
>> We have a "better chance" of finding "better data" among
>> "more data" than among "less data."

Robert Jasiek <jas...@snafu.de> wrote:
> Quite contrarily. The more data we have the more useless
> information must be sorted out.

Investigation of various procedures for tournament tiebreaking:

Program `tourney.ub' examines average tournament entropy measures
for rounds 3 through 8 of 500,000 tournament simulations using
16, 24, 32, 40, 48, 56, 64, 72, or any reasonable number of players.
Each table represents approximately 14 computing hours on a 1.4 Ghz
machine. I suppose there are techniques for program speed-up at
cost of clarity. Confidence for these tournament entropy measures
appears to be certain, within 0.5% , with successive trials.

First two Rounds are paired randomly and successive Rounds 3-8
are paired pairwise according to the sort order given by the
method chosen, i.e. MMS & SOS = MMS * 2^11 + SOS. Players are
not prohibited from multiple game encounters for this simulation.
For SODOS, sort order given by MMS & SOSDOS = MMS * 2^11 + SODOS.

For two players with ranks p1 & p2, the "win probability" for each
is defined as: w1 = p1/(p1+p2), and w2 = p2/(p1+p2). It does
not matter which is chosen to determine the outcome of a match.
Player ranks are random integers from 7 <-> 32767 given by the
assignment bitor(irnd,7). There is some probability that two
players may have the same rank, i.e. 1/(2^12) which can cause
some confusion at attempting to measure zero entropy convergence.
The ranks must be positive to avoid division by zero in the formula.

There is an "expected outcome" for Final Rounds which corresponds
to the original sort order of player ranks. If a tournament
continues indefinitely the sort order of tournament play is
considered to converge upon that player rank sort order. Among
these simulations, then, there is no assumption that one player
is going to "learn" more than another during the tournament play.
The square of tournament entropy is defined as a derangement from
"expected outcome" in the sort order: sum of squares of the index
in the present tournament sort order displaced from its expected
location. It is an interesting question that, given a certain
number of players, how many Rounds would be necessary to expect
zero entropy (with probability > 1/2), yet once reaching zero the
tournament entropy (non-negative) would not remain there but drift
away and continue bouncing >= zero. The tournament entropy numbers
are not much comparable for different numbers of players, however
with the number of players held fixed they may be made comparable.
These entropy numbers correspond to the condition -after- a Round;
after Round 3, two (tiebreaking) sorts have already been applied.

It might seem unsatisfying for the "usurper" players that we are
expecting no upset surprises for a tournament simulation, however
it is more likely that upsets do not occur. In practice player
ranks are modified by the outcome of a tournament, owing to some
slight variation by the tournament results, yet for these purposes
we are not expecting to modify player ranks but to obtain some
estimates of "fairness" for the "competing" tiebreaking methods.

The "fairness" of a pairing method is defined as minimal entropy,
given a certain number of players and a certain number of Rounds.
In practice the tournament pairing attempts to accomplish certain
other aesthetic goals such as no players matched twice, and/or no
players from the same club or region matched, no players matched
whose ranks are far apart, and no players matched whose MacMahon
Scores are wildly different. After the first two Random Rounds
we are here considering only the latter condition (MacMahon Score
with its slight adjustments) for successive match pairings.


There are some surprising results. It turns out that tiebreaking
methods which portend rapid convergence toward zero entropy can also
tend to be "hotter" and can lead away from zero entropy once inside
a margin. The SODOS offers more rapid convergence after Round 3
(applied twice) but then loses out just slightly to the more sedate
(and subtle) SOS method in Rounds 4 through 8. The conclusion is
that there is something for everybody in this "debate" concerning
which to use. In general tournaments tiebreaking methods might not
be used at all until Final Round, or before and after Final Round.
If that is the case then SODOS appears slightly better than SOS.
However if the tiebreaking methods are applied for pairing during
all Last Four Rounds then SOS is better by about 2%.

There are many other ways to construe "improvements" for pairing
procedures, such as a succession of SODOS and SOS, or mixing them,
or other recursive methods, and other tiebreaking theories. These
may each be put to the test via machine tournament simulations and
we can locate a means to steer a navigable path through opinionated
forests so that we do not get mislead by the various trees within.
Is "coin-toss" different from arbitrary assignment based only on
MacMahon Score? If so, the "coin-toss" table is also less fair. :-)


Tournament Entropy^2 Scores:
First column is # players. Entropy^2 numbers given for Rounds 3-8.

MMS * 2^11 + SOS:
16 3 to 8 344.48 312.92 286.41 264.50 246.52 231.85
24 3 to 8 1168.94 1070.93 975.98 897.44 833.24 780.61
32 3 to 8 2785.32 2552.26 2319.69 2129.87 1973.74 1845.05
40 3 to 8 5460.82 5025.48 4559.79 4181.34 3869.42 3612.15
48 3 to 8 9463.33 8707.58 7907.34 7241.99 6694.66 6244.48
56 3 to 8 15052.99 13854.94 12582.74 11508.37 10631.19 9908.26
64 3 to 8 22498.93 20745.55 18831.60 17214.64 15886.25 14794.97
72 3 to 8 32067.31 29647.78 26915.19 24576.17 22676.49 21107.55

MMS * 2^11 + SODOS:
16 3 to 8 332.08 316.00 288.38 266.98 250.70 236.65
24 3 to 8 1137.72 1073.80 997.55 918.41 854.82 802.22
32 3 to 8 2723.63 2582.70 2385.85 2192.75 2036.16 1910.44
40 3 to 8 5352.54 5084.93 4658.46 4293.99 3992.23 3741.17
48 3 to 8 9292.36 8845.63 8102.47 7479.90 6947.26 6497.91
56 3 to 8 14816.75 14126.69 12993.50 11980.14 11121.38 10390.49
64 3 to 8 22175.93 21181.88 19444.78 17928.04 16611.25 15511.98
72 3 to 8 31656.85 30260.36 27726.38 25543.06 23704.19 22154.64


Note that the first column (after Round 3) Entropy^2 Scores is -less- for
SODOS adjustments than for SOS adjustments. Thereafter, SOS is better.
So perhaps there is a mixed form which improves upon both tables.


- regards
- jb

------------------------------------------------------------

10 F=18:D=72:dim P%(D,F),E(F),G%(D),Q%(D):' -- tourney.ub tourn. sim.
20 Rank=1:Num=2:Ord=3:MMS=4:SOS=5:SODOS=6:MMSOS=7:MMSODOS=8:SODOSODOS=9
22 MMSODOSODOS=10:Test=MMSOS:L=11:for Pl=16 to D step 8:randomize
30 print "MMSOS";Pl;" 4 to";F+1-L;:clr block E(*)
40 for W=0 to 499999:clr block P%(*,*):' 500,000 tournaments each
50 for I=1 to D:P%(I,Rank)=bitor(irnd,7):P%(I,0)=irnd:P%(I,Num)=I:G%(I)=I
60 Q%(I)=I*I:next:R=L+1:K=fnPairPlay(L)+fnSort(0)+fnPairPlay(L+1)
70 K=fnSort(Rank):for I=1 to D:P%(G%(I),Ord)=I:next:K=fnSort(Test)
80 for R=L+2 to F:K=fnPairPlay(R)+fnSort(Test):E(R)+=fnEntropy(0):next
90 :' for I=1 to Pl:print using(3),P%(G%(I),Ord);:next:print
100 next W:for I=L+2 to F:K=E(I)/W:print using(7,2),K;:next:print:next Pl
110 fnSort(I):' -------- sort rows of P% based on column index `I'
120 local J,K:for J=1 to Pl-1:for K=J+1 to Pl:' sort low-to-high
130 if P%(G%(J),I)>P%(G%(K),I) then swap block G%(J),G%(K)
140 next:next:return(I)
150 fnPairPlay(R):' ------------- pairing, play and scores for Round `R'
160 local J:for J=1 to Pl step 2
170 if sft(P%(G%(J),Rank),15)\(P%(G%(J),Rank)+P%(G%(J+1),Rank))>irnd
180 :then P%(G%(J),R)=P%(G%(J+1),Num):P%(G%(J+1),R)=-P%(G%(J),Num)
190 :inc P%(G%(J),MMS):P%(G%(J),SODOS)+=P%(G%(J+1),MMS)
200 :else P%(G%(J),R)=-P%(G%(J+1),Num):P%(G%(J+1),R)=P%(G%(J),Num)
210 :inc P%(G%(J+1),MMS):P%(G%(J+1),SODOS)+=P%(G%(J),MMS)
220 P%(G%(J),SOS)+=P%(G%(J+1),MMS):P%(G%(J+1),SOS)+=P%(G%(J),MMS)
230 P%(G%(J),MMSOS)=sft(P%(G%(J),MMS),11)+P%(G%(J),SOS)
240 P%(G%(J+1),MMSOS)=sft(P%(G%(J+1),MMS),11)+P%(G%(J+1),SOS)
250 :' P%(G%(J+1),MMSODOS)=sft(P%(G%(J+1),MMS),11)+P%(G%(J+1),SODOS)
260 :' P%(G%(J),MMSODOS)=sft(P%(G%(J),MMS),11)+P%(G%(J),SODOS)
265 next:return(R)
270 fnEntropy(K):' -- calculate degree of derangement from expectation
280 local J:for J=1 to Pl:K+=Q%(abs(P%(G%(J),Ord)-J)):next:return(K)

------------------------------------------------------------

Robert Jasiek

unread,
Feb 27, 2007, 5:30:50 AM2/27/07
to
On Tue, 27 Feb 2007 09:19:46 GMT, jazze...@hotmail.com (-) wrote:
> The "fairness" of a pairing method is defined as minimal entropy

Thanks for stating your definition. However, I wonder if you want to
apply it only to the making of the pairings or also to the final
results list.

--
robert jasiek

-

unread,
Feb 27, 2007, 2:50:02 PM2/27/07
to

> jazze...@hotmail.com (-) wrote:
>> The "fairness" of a pairing method is defined as minimal entropy

Robert Jasiek <jas...@snafu.de> wrote:
> Thanks for stating your definition. However, I wonder if you want
> to apply it only to the making of the pairings or also to the final
> results list.


All tiebreaking methods being tested so far keep reducing
tournament entropy^2 with additional Rounds. A "fall-off" for SOS or
SODOS seems gain of about 9% with each additional Round. Condition
of tournament pairing has much to do with the proper selection
on which method to use for the next Round. Use of random pairing
in the first two Rounds introduces some need for correction. It
turns out that straight MMS pairing (effective "coin flip") appears
as a better approach than SODOS or SOS for Round 3. Strict MMS
was not better for subsequent Rounds 4 to 8. Round 4 showed gain
in typical entropy^2 "fall-off" of less than 3%, though Round 5 shows
gain in reduced entropy^2 by approximately 7%. Perhaps techniques
for random pairing should be avoided altogether? Yet, if random
pairing is not used for initial Rounds then on what basis is pairing
made? Though pairing based on initial rank might reduce entropy
significantly we considered not seeding the tournament that way...

Tournament Entropy^2 Scores:
First column is # players. Entropy^2 numbers given for Rounds 3-8.

MMS only:
16 3 to 8 328.76 323.05 299.14 277.77 259.53 244.13
24 3 to 8 1117.34 1093.69 1018.90 939.98 870.90 815.89
32 3 to 8 2660.28 2621.51 2420.15 2234.10 2066.37 1932.05
40 3 to 8 5212.93 5129.04 4742.44 4393.28 4068.92 3791.29
48 3 to 8 9026.14 8895.87 8219.36 7612.39 7050.92 6559.32
56 3 to 8 14361.39 14184.26 13111.45 12153.86 11241.17 10442.67
64 3 to 8 21453.24 21189.41 19571.39 18167.93 16797.21 15601.41
72 3 to 8 .....

Recall that the first column for MMS & SOS was:

MMS * 2^11 + SOS:

16 3 to 8 344.48 ...
24 3 to 8 1168.94 ...
32 3 to 8 2785.32 ...
40 3 to 8 5460.82 ...
48 3 to 8 9463.33 ...
56 3 to 8 15052.99 ...
64 3 to 8 22498.93 ...
72 3 to 8 32067.31 ...


What's our explanation for why strict MMS does better, when recovering
from two Rounds of random pairing? Apparently, SOS (or SODOS) data
is disinformative at that point (for Round 3) and should not be used.
Once past a point of disinformation (after a few rounds of recovery from
random pairing) the tournament entropy appears to reduce a bit faster
when applying some assortment of fine-tuning tiebreaking adjustments.


- regards
- jb

-----------------------------------------------------------
Japanese card trick
http://www.glumbert.com/media/cyril
-----------------------------------------------------------

-

unread,
Feb 28, 2007, 4:54:26 AM2/28/07
to

>> jazze...@hotmail.com (-) wrote:
>>> The "fairness" of a pairing method is defined as minimal entropy


Upon further examination I realized that my prior calculations
were not using the "complete SOS" numbers. One needs to go
back and sum ALL opponent scores as the tournament progresses,
not merely "partial SOS" numbers on the fly. This implementation
(lines 280-291) is much slower now, but more accurate for entropy
convergence. Compare new MMS & SOS table with previous table:

(New Implementation)
MMS * 2^11 + -complete- SOS:
16 3 to 8 349.49 313.34 285.55 263.02 245.25 230.60
24 3 to 8 1184.22 1060.67 961.50 884.43 821.62 770.58
32 3 to 8 2818.35 2524.60 2284.51 2096.31 1944.06 1820.16
40 3 to 8 5518.09 4941.88 4467.73 4096.49 3797.97 3551.86
48 3 to 8 9555.78 8554.92 7731.85 7082.25 6561.08 6133.26
56 3 to 8 15189.95 13597.38 12284.67 11246.95 10417.20 9734.73
64 3 to 8 ...
72 3 to 8 ...


>> (Old Implementation)
>> MMS * 2^11 + -partial- SOS:


>> 16 3 to 8 344.48 312.92 286.41 264.50 246.52 231.85
>> 24 3 to 8 1168.94 1070.93 975.98 897.44 833.24 780.61
>> 32 3 to 8 2785.32 2552.26 2319.69 2129.87 1973.74 1845.05
>> 40 3 to 8 5460.82 5025.48 4559.79 4181.34 3869.42 3612.15
>> 48 3 to 8 9463.33 8707.58 7907.34 7241.99 6694.66 6244.48
>> 56 3 to 8 15052.99 13854.94 12582.74 11508.37 10631.19 9908.26

>> 64 3 to 8 ...
>> 72 3 to 8 ...


The first column is temporarily worse, entropically, owing to previous
remarks concerning what happens upon recovery from random Rounds
1 & 2. Using "completed SOS" figures there introduces more of the same
"disinformational" quality, if using MMS & SOS tiebreaker pairing for the
recovery Round, so we're not going to do that: strict MMS is still best.

Nevertheless, completed SOS supplies better entropy^2 minimalization
for subsequent Rounds of tiebreaker pairing over partial SOS, illustrated
"even more dramatically" for larger tournaments. More to be said later
concerning mixed tiebreaker pairing forms during tournament Rounds.

Concerning the topic of SODOS, it appears at this point that either we
require a highly informative date source data for tiebreaking, or we do
not. SODOS offers less information than SOS because it is not much
different for players in a winner's circle and tends not to apply at all
for players in the losing bands. The intuition that SODOS might have
been a nicer method was perhaps a recovery relic from random Rounds,
and strict MMS seems to offer less disinformation when avoiding that.

- regards
- jb

-----------------------------------------------------------------------------


10 F=18:D=72:dim P%(D,F),E(F),G%(D),Q%(D):' -- tourney.ub tourn. sim.
20 Rank=1:Num=2:Ord=3:MMS=4:SOS=5:SODOS=6:MMSOS=7:MMSODOS=8:SODOSODOS=9

30 MMSODOSODOS=10:Test=MMSOS:L=11:for Pl=16 to D step 8:randomize
40 print "MMSOS";Pl;" 3 to";F+1-L;:clr block E(*)
50 for W=0 to 499999:clr block P%(*,*):' 500,000 tournaments each
60 for I=1 to D:P%(I,Rank)=bitor(irnd,7):P%(I,0)=irnd:P%(I,Num)=I:G%(I)=I
70 Q%(I)=I*I:next:R=L+1:K=fnPairPlay(L)+fnSort(0)+fnPairPlay(L+1)
80 K=fnSort(Rank):for I=1 to D:P%(G%(I),Ord)=I:next:K=fnSort(Test)
90 for R=L+2 to F:K=fnPairPlay(R)+fnSort(Test):E(R)+=fnEntropy(0):next
100 :' for I=1 to Pl:print using(3),P%(G%(I),Ord);:next:print
110 next W:for I=L+2 to F:K=E(I)/W:print using(7,2),K;:next:print:next Pl
120 fnSort(I):' -------- sort rows of P% based on column index `I'
130 local J,K:for J=1 to Pl-1:for K=J+1 to Pl:' sort low-to-high
140 if P%(G%(J),I)>P%(G%(K),I) then swap block G%(J),G%(K)
150 next:next:return(I)
160 fnPairPlay(R):' ------------- pairing, play and scores for Round `R'
170 local J,K,SSOS,SSODOS:for J=1 to Pl step 2
180 if sft(P%(G%(J),Rank),15)\(P%(G%(J),Rank)+P%(G%(J+1),Rank))>irnd
190 :then P%(G%(J),R)=P%(G%(J+1),Num):P%(G%(J+1),R)=-P%(G%(J),Num)
200 :inc P%(G%(J),MMS)
210 :else P%(G%(J),R)=-P%(G%(J+1),Num):P%(G%(J+1),R)=P%(G%(J),Num)
220 :inc P%(G%(J+1),MMS)
280 next J:clr block P%(1..Pl,SOS..SODOS):for J=1 to Pl:for K=L to R
290 P%(J,SOS)+=P%(abs(P%(J,K)),MMS):next K
291 P%(J,MMSOS)=sft(P%(J,MMS),11)+P%(J,SOS):next J
300 :' for J=1 to Pl:for K=L to R
310 :' if P%(J,K)>0 then P%(J,SODOS)+=P%((P%(J,K),SOS)
320 :' next K
321 :' P%(J,MMSODOS)=sft(P%(J,MMS),11)+P%(J,SODOS):next J
322 return(R)
330 fnEntropy(K):' -- calculate degree of derangement from expectation
340 local J:for J=1 to Pl:K+=Q%(abs(P%(G%(J),Ord)-J)):next:return(K)
-----------------------------------------------------------------------------

-

unread,
Mar 1, 2007, 2:26:41 AM3/1/07
to

>> jazze...@hotmail.com (-) wrote:
>>> The "fairness" of a pairing method is defined as minimal entropy


We learn also that the -complete- SODOS is not even quite
so anti-entropic as the -partial- SOS, given sufficient players, and
is certainly less anti-entropic than using the -complete- SOS:


(New Implementation)
MMS * 2^11 + -complete- SODOS:
16 3 to 8 339.64 313.19 286.71 263.76 246.13 231.73
24 3 to 8 1158.55 1067.57 977.37 884.43 821.62 770.58
32 3 to 8 2767.98 2556.23 2320.97 2127.72 1972.31 1843.82
40 3 to 8 5436.96 5034.14 4542.85 4178.25 3868.65 3613.51
48 3 to 8 9425.32 8735.44 7897.49 7252.96 6701.31 6248.11
56 3 to 8 15006.51 13931.58 12651.70 11571.73 10675.88 9937.37
64 3 to 8 22456.49 20862.52 18927.05 17277.03 15940.04 14826.18


72 3 to 8 ...

>>> (Old Implementation)
>>> MMS * 2^11 + -partial- SOS:


>>> 16 3 to 8 344.48 312.92 286.41 264.50 246.52 231.85
>>> 24 3 to 8 1168.94 1070.93 975.98 897.44 833.24 780.61
>>> 32 3 to 8 2785.32 2552.26 2319.69 2129.87 1973.74 1845.05
>>> 40 3 to 8 5460.82 5025.48 4559.79 4181.34 3869.42 3612.15
>>> 48 3 to 8 9463.33 8707.58 7907.34 7241.99 6694.66 6244.48
>>> 56 3 to 8 15052.99 13854.94 12582.74 11508.37 10631.19 9908.26
>>> 64 3 to 8 22498.93 20745.55 18831.60 17214.64 15886.25 14794.97

>>> 72 3 to 8 ...

As previously discussed there is the apparent advantage on Round 3
if following the first two random pairings, but thereafter with repeated
application loses out for tournaments with 40 or more players.

Present order of anti-entropic methods, listed by preferance, best first:

more highly informative --:
[ ... ]
(a) MMS & Complete SOS
(b) MMS & Partial SOS
(c) MMS & Complete SODOS
(d) MMS & Partial SODOS
(e) MMS only
[ ... ]
less highly informative --:


Though, following random rounds, one inverts that list of preferances.

- regards
- jb

----------------------------------------------------------
... good news for old brains
http://www.nwfdailynews.com/article/2230
----------------------------------------------------------
(correction)
[ ... ]


300 for J=1 to Pl:for K=L to R

310 if P%(J,K)>0 then P%(J,SODOS)+=P%((P%(J,K),MMS)
321 next K:P%(J,MMSODOS)=sft(P%(J,MMS),11)+P%(J,SODOS):next J
[ ... ]
----------------------------------------------------------

-

unread,
Mar 2, 2007, 1:53:59 AM3/2/07
to

>>> jazze...@hotmail.com (-) wrote:
>>>> The "fairness" of a pairing method is defined as minimal entropy


Sum of Opponent's Sum of Opponent Scores (SOSOS) performs
slightly worse than Sum of Defeated Opponent Scores (SODOS), in
smaller tournaments, but for tournaments of 56 or more after 6 Rounds
tends to perform slightly better. Apparently there is quite a bit of
context to consider. All studies so far result from adjacency pairing.
Different results could occur from "slaughter pairing" & "slide pairing."

Of course more investigation renders the topic more complicated.
In round-robin SODOS would offer more information than SOS. :-)

MMS * 2^11 + -complete- SOSOS:
16 3 to 8 373.68 330.29 298.65 273.27 252.26 235.95
24 3 to 8 1261.50 1115.31 1003.36 915.04 843.06 784.31
32 3 to 8 2990.83 2645.04 2377.65 2164.28 1990.72 1850.09
40 3 to 8 5843.13 5171.43 4640.00 4218.51 3879.85 3603.81
48 3 to 8 10104.66 8943.52 8026.22 7294.35 6704.39 6225.60
56 3 to 8 16054.14 14218.08 12767.68 11585.01 10638.54 9872.64
64 3 to 8 23955.20 21219.97 19041.65 17286.99 15869.59 14725.13


72 3 to 8 ...

compared with:

> MMS * 2^11 + -complete- SODOS:
> 16 3 to 8 339.64 313.19 286.71 263.76 246.13 231.73
> 24 3 to 8 1158.55 1067.57 977.37 884.43 821.62 770.58
> 32 3 to 8 2767.98 2556.23 2320.97 2127.72 1972.31 1843.82
> 40 3 to 8 5436.96 5034.14 4542.85 4178.25 3868.65 3613.51
> 48 3 to 8 9425.32 8735.44 7897.49 7252.96 6701.31 6248.11
> 56 3 to 8 15006.51 13931.58 12651.70 11571.73 10675.88 9937.37
> 64 3 to 8 22456.49 20862.52 18927.05 17277.03 15940.04 14826.18
> 72 3 to 8 ...

Present order of anti-entropic methods, listed by preferance, best first:

more highly informative --:
[ ... ]
(a) MMS & Complete SOS

(b) MMS & SOSOS (more than 64 players, more than 6 rounds)


(b) MMS & Partial SOS

(c) MMS & SOSOS (more than 56 players, more than 6 rounds)
(d) MMS & Complete SODOS
(e) MMS & SOSOS (more than 40 players, more than 4 rounds)

(d) MMS & Partial SODOS
(e) MMS only
[ ... ]
less highly informative --:


Though, following random rounds, one inverts that list of preferances.

- regards
- jb

--------------------------------------------------------------------
Music Review | Michael Brecker Memorial
Celebrating a Saxophonist’s Art and Heart
http://www.nytimes.com/2007/02/22/arts/music/22brec.html
http://www.youtube.com/watch?v=4RgHYcmK_-g
--------------------------------------------------------------------

-

unread,
Mar 3, 2007, 4:57:43 AM3/3/07
to

>>>> jazze...@hotmail.com (-) wrote:
>>>>> The "fairness" of a pairing method is defined as minimal entropy


Sum of Defeated Opponent's Sum of Defeated Opponent's Scores
(SODOSODOS) does not perform very well in larger tournaments, which
contradicts previous assumptions and intuitions I had stated on this ng.
Initial anti-entropic gains are offset by eventual entropic drifts.

MMS * 2^11 + SODOSODOS:
16 3 to 8 338.68 314.98 287.27 265.10 247.38 233.08
24 3 to 8 1155.31 1073.85 984.98 904.98 838.63 785.53
32 3 to 8 2754.86 2571.01 2343.89 2142.87 1983.93 1855.46
40 3 to 8 5412.88 5062.91 4591.99 4208.23 3896.14 3638.71
48 3 to 8 9387.85 8779.83 7980.16 7315.33 6762.07 6309.14
56 3 to 8 14944.13 14001.99 12793.46 11716.29 10808.69 10056.07
64 3 to 8 22366.27 20996.74 19161.71 17505.70 16133.23 15000.18
72 3 to 8 31901.12 30005.74 27320.97 24932.73 22974.92 21365.42


Present order of anti-entropic methods, listed by preferance, best first:

more highly informative --:
[ ... ]
(a) MMS & Complete SOS
(b) MMS & SOSOS (more than 64 players, more than 6 rounds)

(c) MMS & Partial SOS
(d) MMS & SOSOS (more than 56 players, more than 6 rounds)
(e) MMS & Complete SODOS
(f) MMS & SOSOS (more than 40 players, more than 4 rounds)
*(g) MMS & SODOSODOS ( today's posted table )
(h) MMS & Partial SODOS
(i) MMS only


[ ... ]
less highly informative --:

- regards
- jb

--------------------------------------------------------------------
Thanks for the Memories...a special tribute to Saddam
http://www.bushflash.com/thanks.html
--------------------------------------------------------------------

-

unread,
Mar 4, 2007, 12:54:08 AM3/4/07
to

>>>>> jazze...@hotmail.com (-) wrote:
>>>>>> The "fairness" of a pairing method is defined as minimal entropy


Sum of Defeated Opponent's Sum of Defeated Opponent's Sum of
Defeated Opponent's Scores (SODOSODOSODOS) gets further away
from "informative" measures, as per similar patterns with SOSOS, etc.,
in every respect worse than SODOSODOS except for recovery Round
(in larger tournaments) where "less information" tends to be beneficial:


MMS * 2^11 + SODOSODOSODOS:
16 3 to 8 339.35 318.28 289.18 266.15 249.99 233.51
24 3 to 8 1156.44 1085.43 991.39 908.45 841.20 787.74
32 3 to 8 2757.65 2598.20 2358.90 2155.10 1993.24 1863.77
40 3 to 8 5415.34 5111.97 4639.25 4242.74 3917.28 3653.83
48 3 to 8 9389.47 8880.90 8064.29 7367.49 6800.60 6333.41
56 3 to 8 14949.66 14171.09 12896.03 11786.98 10865.22 10100.82
64 3 to 8 22348.37 21220.99 19308.88 17630.58 16234.57 15089.66
72 3 to 8 31871.11 30296.83 27569.14 25121.51 23121.81 21485.79


-( compare with )-


> MMS * 2^11 + SODOSODOS:
> 16 3 to 8 338.68 314.98 287.27 265.10 247.38 233.08
> 24 3 to 8 1155.31 1073.85 984.98 904.98 838.63 785.53
> 32 3 to 8 2754.86 2571.01 2343.89 2142.87 1983.93 1855.46
> 40 3 to 8 5412.88 5062.91 4591.99 4208.23 3896.14 3638.71
> 48 3 to 8 9387.85 8779.83 7980.16 7315.33 6762.07 6309.14
> 56 3 to 8 14944.13 14001.99 12793.46 11716.29 10808.69 10056.07
> 64 3 to 8 22366.27 20996.74 19161.71 17505.70 16133.23 15000.18
> 72 3 to 8 31901.12 30005.74 27320.97 24932.73 22974.92 21365.42

Present order of anti-entropic methods, listed by preferance, best first:

more highly informative --:
[ ... ]
(a) MMS & Complete SOS
(b) MMS & SOSOS (more than 64 players, more than 6 rounds)
(c) MMS & Partial SOS
(d) MMS & SOSOS (more than 56 players, more than 6 rounds)
(e) MMS & Complete SODOS
(f) MMS & SOSOS (more than 40 players, more than 4 rounds)

(g) MMS & SODOSODOS
*(h) MMS & SODOSODOSODOS ( today's posted table )
(i) MMS & Partial SODOS
(j) MMS only


[ ... ]
less highly informative --:


I conclude that further "derivative methods" other than immediate
measures (SOS, SODOS) are not going to be terribly useful. Next we
will examine various strategies for pairing methods in tournament design.


- regards
- jb

-------------------------------------------------------------------------
Handy Homo Prevention Tips For Concerned Parents With Suspect Toddlers
http://www.landoverbaptist.org/news0704/homoprevention.html
-------------------------------------------------------------------------

-

unread,
Mar 7, 2007, 2:34:23 PM3/7/07
to

>>> jazze...@hotmail.com (-) wrote:
>>>> The "fairness" of a pairing method is defined as minimal entropy


For tournaments of more than 16 players, including both SOS (Sum
of Opponent Scores) and SODOS (Sum of Defeated Opponent Scores)
in tiebreaker info achieves lowest tournament entropy of any measures
tested so far, even better for recovery rounds. Bear in mind ambient
"background entropy level" so what appears as slight improvement is
more significant when subtracting "background entropy level."

MMS * 2^11 + complete SOS + complete SODOS
16 3 to 8 348.59 311.69 284.30 262.22 244.72 230.14
24 3 to 8 1181.28 1055.46 957.53 881.72 819.44 768.95
32 3 to 8 2812.55 2512.99 2274.82 2089.82 1939.88 1817.41
40 3 to 8 5498.60 4910.43 4441.87 4078.39 3784.22 3541.21
48 3 to 8 9514.83 8496.10 7684.01 7044.88 6533.30 6110.86
56 3 to 8 15125.19 13504.67 12208.51 11189.58 10372.22 9700.04
64 3 to 8 ...


72 3 to 8 ...


> MMS * 2^11 + complete SOS:


> 16 3 to 8 349.49 313.34 285.55 263.02 245.25 230.60
> 24 3 to 8 1184.22 1060.67 961.50 884.43 821.62 770.58
> 32 3 to 8 2818.35 2524.60 2284.51 2096.31 1944.06 1820.16
> 40 3 to 8 5518.09 4941.88 4467.73 4096.49 3797.97 3551.86
> 48 3 to 8 9555.78 8554.92 7731.85 7082.25 6561.08 6133.26
> 56 3 to 8 15189.95 13597.38 12284.67 11246.95 10417.20 9734.73
> 64 3 to 8 ...

> 72 3 to 8 ...

Present order of anti-entropic methods, listed by preferance, best first:

more highly informative --:
[ ... ]

*(a) MMS & Complete SOS + Complete SODOS ( today's post )
(b) MMS & Complete SOS
(c) MMS & SOSOS (more than 64 players, more than 6 rounds)
(d) MMS & Partial SOS
(e) MMS & SOSOS (more than 56 players, more than 6 rounds)
(f) MMS & Complete SODOS
(g) MMS & SOSOS (more than 40 players, more than 4 rounds)
(h) MMS & SODOSODOS
(i) MMS & SODOSODOSODOS
(j) MMS & Partial SODOS
(k) MMS only


[ ... ]
less highly informative --:


It's time to recognize that using only SOS for tiebreaking information
is not the fairest method for ordering the results of tournament Rounds.


- regards
- jb

----------------------------------------------------------------------
Super bug kills dozens in hospitals across Israel...
http://www.ynetnews.com/articles/0,7340,L-3373478,00.html
----------------------------------------------------------------------

-

unread,
Mar 15, 2007, 3:37:07 AM3/15/07
to

>>>> jazze...@hotmail.com (-) wrote:
>>>>> The "fairness" of a pairing method is defined as minimal entropy

jazze...@hotmail.com (-) wrote:
> MMS * 2^11 + complete SOS + complete SODOS

> 16 3 to 8 348.59 311.69 284.30 262.22 244.72 230.14 ...
> ....


After Round 193 Tournament Entropy^2 for 16 Players is about 41.12.
"Level of confidence" = 2*log(680)/(log(680) + log(41.12)) -1 = 27.4% .
The "wash out" point (Entropy^2(Round N) < Entropy^2(Round N+1))
was not yet detected. Entropy^2 values leading up to Round 193:

... 41.58 41.51 41.42 41.34 41.27 41.21 41.12

Note how the term differences illustrate a "sawtooth" convergence:

... 0.07 0.09 0.08 0.07 0.06 0.09

Perhaps with sufficient computation there is no "wash out" point nor
reaching of zero. This feature would occur only by insufficient trials.


- regards
- jb

-------------------------------------------------------------
Weapons of Mass De-Population
http://www.rense.com/1.imagesH/hrhe.jpg
-------------------------------------------------------------

-

unread,
Mar 15, 2007, 2:42:52 PM3/15/07
to

>>> jazzerci...@hotmail.com (-) wrote:
>>>> The "fairness" of a pairing method is defined as minimal entropy


As per request from Mr. Jasiek, -successive- tiebreaking for
SOS, and then SODOS, is examined. After some more minimal
entropy calculations, results appear inconclusive though it seems
there is a general trend to be not quite so succussful except for the
analysis with 32 Players, and for Round 8 a slight improvement for
16, 24, 32, & 40 Players but not for 48 or 56 Players...

MMS * 2^11 + (complete SOS) * 128 + (complete SODOS)
16 3 to 8 349.14 312.04 284.60 262.31 244.46 229.42
24 3 to 8 1183.42 1056.43 958.70 882.05 819.22 767.20
32 3 to 8 2810.33 2510.83 2273.29 2089.10 1938.41 1814.19
40 3 to 8 5501.22 4912.83 4444.87 4079.35 3784.06 3536.84
48 3 to 8 9526.48 8506.04 7694.24 7055.28 6543.69 6114.44
56 3 to 8 15156.69 13529.16 12232.52 11212.43 10392.12 9706.04

64 3 to 8 ...
72 3 to 8 ...


> MMS * 2^11 + complete SOS + complete SODOS
> 16 3 to 8 348.59 311.69 284.30 262.22 244.72 230.14
> 24 3 to 8 1181.28 1055.46 957.53 881.72 819.44 768.95
> 32 3 to 8 2812.55 2512.99 2274.82 2089.82 1939.88 1817.41
> 40 3 to 8 5498.60 4910.43 4441.87 4078.39 3784.22 3541.21
> 48 3 to 8 9514.83 8496.10 7684.01 7044.88 6533.30 6110.86
> 56 3 to 8 15125.19 13504.67 12208.51 11189.58 10372.22 9700.04
> 64 3 to 8 ...
> 72 3 to 8 ...

Present order of anti-entropic methods, listed by preferance, best first:


more highly informative --:
[ ... ]

*(a) MMS & (Complete SOS)*128 + (Complete SODOS) ( today )
-or- MMS & Complete SOS + Complete SODOS ( tie? )

(b) MMS & Complete SOS
(c) MMS & SOSOS (more than 64 players, more than 6 rounds)
(d) MMS & Partial SOS
(e) MMS & SOSOS (more than 56 players, more than 6 rounds)
(f) MMS & Complete SODOS
(g) MMS & SOSOS (more than 40 players, more than 4 rounds)
(h) MMS & SODOSODOS
(i) MMS & SODOSODOSODOS
(j) MMS & Partial SODOS
(k) MMS only
[ ... ]
less highly informative --:


- regards
- jb

----------------------------------------------------------------
The Ultimate Con 911 Documentary Trailer 1
http://youtube.com/watch?v=yIgoXQWiSlM
----------------------------------------------------------------

-

unread,
Mar 24, 2007, 7:55:27 AM3/24/07
to

>> jazzerci...@hotmail.com (-) wrote:
>>> The "fairness" of a pairing method is defined as minimal entropy


As per request from Mr. Jasiek, SOS-1 and SOS-2 were examined.
(This notation designates erasure of smallest SOS score or scores.)
Tiebreaking performance is not quite as effective when eliminating
potentially useful sidebar data, so that approach is not recommended.
Further investigation establishes that cascaded tiebreaking on SOS,
and then by SODOS, is only marginally better when number of players
is a power of 2. In all other cases tested: breaking by MMS, and then
simply summing the SOS+SODOS, offers best performance among all
tiebreaking methods examined so far.

Using "full-field Swiss" as a pairing method, which -always- pairs
top half against bottom half (without any banding) is not recommened.
Most of these tests hold constant the "adjacency pairing" approach.
Surprisingly having three initial random Rounds, instead of two, does
rather well overall at the 8th Round however four initial random Rounds
is not quite so effective. Having Round One random, and Round Two
paired on Player Rank, is also not a very effective approach. A proposal
(by Fernando Aguilar) used for the 2005 Iberoamerican Go Tournament
http://senseis.xmp.net/?McMahonPairing/Discussion achieves "dramatic
improvements" for tournaments with more than 16 players. This received
prior announcement on rec.games.go: a tournament field is accorded an
"initial banding" suggestion by increasing initial MMS "appropriately."
For simulation the player field was partitioned into four (equal) groups:
0,1,2,3 extra MMS points awarded respectively, from low-to-high rank.
Because there is no necessary requirement for pairing only by equal
MMS it is difficult to understand a remark there by _Phelan_, i.e. "The
biggest problem was higher level players not playing some rounds."
(A player at the lower end of one MMS band may be matched with a
player at the higher end of next MMS band, under adjacency pairing.)

One "disadvantage" to using preloaded MMS is that we have crossed
over the line between having, or not-having, knowledge of initial player
rank conditions. Obviously a zero entropy measure could be obtained
by awarding all players individually: 0,10,20,30,40,50,60,70 ... MMS.
That "tournament" would occur by appearance only, with none of the
games having any real significance but to establish just same final order
as initial order, producing a difference result of zero entropy. Pairing
strategy appealing to knowledge of initial player rank circumstance tends
slightly into a direction which compromises notions of "fairness" that
there should be no knowledge at all of initial player rank circumstance.
On the other hand, why should Tournament Directors (and other players
in tournaments) pretend knowledge denial of player rank circumstance?
What is "knowledge of player rank circumstance" (in the Italian model)?
Preloaded MMS (under adjacency pairing) tends to assure that strong
players will be matched with other strong players from the getgo, with
many "informative and decisive" game results. This technique dwarfs
prior inquiries about marginal tiebreaking to the degree of rendering
discussions over marginal tiebreaking approaches as almost irrelevant.

Another "disadvantage" addresses what occurs (here) when player
count is greater than 48. Initial "low entropy" results start ballooning
in successive Rounds as preloading gives way to (real-world) "noise"
of tournament statistics. The "fairness" indicator ent^((1-p)/(1+p))
cannot be regarded as reliable during the initial artificial suppression
while statistics are still ballooning. Once statistics start a downward
trend (after Rounds 5,6 for 56 Players; after Rounds 7 for 64 or 72
Players), we may regard "tournament statistics" as gaining a foothold
over the initial artificial suppression. Even with ballooning, however,
once everyone has accepted preloaded MMS as "natural and fair" then
fair tournaments may be conducted with only a few Rounds, already
satisfying the "fairness" indicator. Apparent statistical ballooning is
not particularly worrisome when all tournament entropy^2 numbers
are less than "fairness" indicator, i.e. p>0.05 , level of significance
for finding a winner. For example, 64 players at entropy^2 < 13540 ,
we have a winner and fair rank order for the tournament finalists.
Values much less are already obtained even under this mild MMS
preloading. We need only verify that ballooning procedures do not
exceed "fairness" indicator. Results for 72 players are encouraging:


(preload 0,1,2,3 MMS) -->> MMS*2^10 +(complete SOS)+(complete SODOS)
16 3 to 8 348.74 311.77 284.48 262.35 244.88 229.39
24 3 to 8 753.95 690.02 647.52 613.67 586.01 562.87
32 3 to 8 1606.38 1504.44 1435.53 1378.44 1329.68 1288.10
40 3 to 8 2548.64 2459.99 2397.17 2336.91 2280.98 2230.63
48 3 to 8 3769.15 3736.90 3711.69 3663.95 3607.83 3551.22
56 3 to 8 5311.35 5371.23 5403.44 5382.23 5335.59 5278.34
64 3 to 8 6639.83 6904.01 7074.89 7142.15 7149.84 7125.93
72 3 to 8 8733.96 9210.14 9528.68 9683.24 9741.44 9740.62

> (no preloading) MMS*2^11 +(complete SOS)+(complete SODOS)

> 16 3 to 8 348.59 311.69 284.30 262.22 244.72 230.14
> 24 3 to 8 1181.28 1055.46 957.53 881.72 819.44 768.95

> 32 3 to 8 2812.55 2512.99 2274.82 2089.98 1939.88 1817.41


> 40 3 to 8 5498.60 4910.43 4441.87 4078.39 3784.22 3541.21
> 48 3 to 8 9514.83 8496.10 7684.01 7044.88 6533.30 6110.86
> 56 3 to 8 15125.19 13504.67 12208.51 11189.58 10372.22 9700.04

> 64 3 to 8 22610.09 20178.80 18237.62 16710.89 15487.47 14482.71
> 72 3 to 8 32242.59 28783.38 26009.14 23824.40 22070.24 20626.43


Yet how does a Tournament Director decide where to delineate
the banding "breaks" between preloaded MMS figures among a field
of strong players all very nearly equal in strength and ability ? Even
with equal partitioning an inequality produced between two very nearly
ranked players placed on opposite sides of the banding "break" seems
unfair. I will next examine a progressive gradient scale which works
with the 1024 multiplier anyway that minimizes unfair banding breaks.

- regards
- jb

-------------------------------------------------------------------------
Former V.P. Al Gore at Senate Environment & Public Works Cmte.
Climate Change Hearing (3/21/2007)
rtsp://video.c-span.org/project/energy/energy032107_gore.rm?mode=compact
-------------------------------------------------------------------------

-

unread,
Mar 29, 2007, 9:20:09 PM3/29/07
to

>> jazzerci...@hotmail.com (-) wrote:
>>> The "fairness" of a pairing method is defined as minimal entropy


Methods of pairing are being investigated. Adjacency pairing
is clearly flawed in terms of minimal entropy convergence and can lead
to conditions of trivial result (2005 U.S. Open) where the outcome of a
crucial game did not change who is winner of the tournament. We seek
to understand why that type of result occurred and how to prevent it.

The following tables attempt to compare a lot of apples and oranges
so they are not particularly useful for drawing lots of conclusions. :-)
Table (B) was "adjacency pairing", using integer MMS preload (the
Aguilar suggestion) broken evenly across the candidate field but
based upon the common expectation of 72 players, in all situations.
Table (A) uses "swiss reduction pairing", graduated MMS preload
using as a basis the number of players for that tournament simulation.
"Swiss Reduction Pairing" is defined as splitting the candidate field
according to final round proximity, given by FS = min(2^(F-R),PL\2) ,
where "F" is the Round # of "final round", "R" is the current Round #,
"PL" is number of players in the tournament (16,24,32,40,48, 56,64,72),
and "FS" is the "field size" for the current break in Swiss Pairing. The
remainder of the candidate field is paired and played, based upon the
"chunksize" of FS, so each band is comprised of 2*FS players. Rounds
subsequent then halve bandsize until Final Round, which is adjacency.
The "remainder band" (when player number is not a power of 2) is then
paired according to FS=(1+PL-K)\2 where "K" is the next player to be
paired and played for this Round. In practice a "remainder band" might
occur at the low-end of the ranking scale though choice of where this
"remainder band" ought to occur should not appreciably affect entropy^2.
This is not quite the same as standard "Swiss Pairing" which declares
bands according to common MMS but it suffices to illustrate some gains
toward entropy reduction. If graduated MMS preload is utilized then it
becomes problemmatic to obtain a common MMS for group banding.
I considered also that common MMS group banding in the context of
MMS preload might be unfair to certain individuals nearby the breaks,
so the breaks ought to be the result of pairing method from tournament
results, and not arbitrary whim of tournament director from the outset.

The formula used for graduated MMS preload is 1024*(I-1)\(PL\4)
where each game in the new calculation system is now worth 1024 points,
"I" indexes player's relative ranking position in rank sort low-to-high,
and "PL" is the total number of players in the tournament. The degree
of preload is controlled by the last number "4" which biases the pairing
according to a graduated scale from 0 =< grad.MMS < 4. Increasing this
number reduces the significance of that tournament's anomaly results
and decreasing this number reduces the significance of strong players
who have already "paid their dues" by establishing prior competencies.

> (Previous Post) Table (B):
> Adjacency Pairing, preload = 1024* I \ (72 \ 4)
> (preload 0,1,2,3 MMS\72) -->> MMS*2^10 +(complete SOS)+(complete SODOS)


> 16 3 to 8 348.74 311.77 284.48 262.35 244.88 229.39
> 24 3 to 8 753.95 690.02 647.52 613.67 586.01 562.87
> 32 3 to 8 1606.38 1504.44 1435.53 1378.44 1329.68 1288.10
> 40 3 to 8 2548.64 2459.99 2397.17 2336.91 2280.98 2230.63
> 48 3 to 8 3769.15 3736.90 3711.69 3663.95 3607.83 3551.22
> 56 3 to 8 5311.35 5371.23 5403.44 5382.23 5335.59 5278.34
> 64 3 to 8 6639.83 6904.01 7074.89 7142.15 7149.84 7125.93
> 72 3 to 8 8733.96 9210.14 9528.68 9683.24 9741.44 9740.62


Today -- Table (A)
Swiss Reduction Pairing, preload = 1024* (I-1) \ (PL\4)
(grad.preload 0<-->3.9 MMS\PL) -->> MMS*2^10 +(compl SOS)+(compl SODOS)
16 3 to 8 41.11 58.06 70.22 81.61 90.37 93.15
24 3 to 8 136.87 194.36 252.73 293.43 316.85 325.95
32 3 to 8 322.36 459.09 579.58 680.01 730.94 758.51
40 3 to 8 626.69 972.63 1257.33 1431.27 1534.40 1590.57
48 3 to 8 1079.80 1771.36 2269.26 2553.97 2739.13 2835.97
56 3 to 8 1710.50 2847.00 3633.64 4074.52 4381.26 4541.23
64 3 to 8 2548.75 4229.84 5381.11 6051.73 6521.68 6769.44
72 3 to 8 3691.25 6130.23 7655.69 8630.90 9322.60 9694.21


Note that the only lines strictly comparable are those for 72 players.
Table B's lines for 16-64 players were skewed by using 1024* I \(D\4)
instead of 1024*(I-1)\(PL\4) , where "D=72". This illustrates, however,
how increased MMS preloading dramatically affects minimal entropy^2.
Instead of haggling over trivial stuff like SOS vs. SODOS, which gain
only a few points, we are comparing 229.39 with 93.15 (16 Players) !
For the case of 72 Players we are comparing "Swiss Reduction" vs.
"Adjacency" pairing methods, here shown as a modest improvement.
Yet what of the disturbing trend of "ballooning" consequent to a choice
of Aguilar MMS preloading? Each of the entropy^2 figures are still
climbing out to Round 8. So I ran the simulator out to Round 18 and
found a "hump" occuring near Rounds 14,15 irrespective of number of
players, where ent^((1-p)/(1+p)) can begin to make sense. Round 3
for Table (A) and Table (C) is very much the same, demonstrating how
accurate the average over 500,000 tournament simulations can be.
Then Table (A) and Table (C) diverge for successive Rounds, the
explanation being that "Swiss Reduction" does not go into effect until
approach to Final Rounds. Nevertheless, the "ballooning" hump was
found in Table (C) just 2.3% higher than the entropy^2 figures for
Round 8 in Table (A), for 16 Players, and is -less- than Round 8 for
24-72 Players. This simulation took quite a while so data is published:

Table (C)
Swiss Reduction Pairing, 18 Rounds instead of 8 Rounds:
(grad.preload 0<-->3.9 MMS) -->> MMS*2^10 +(compl SOS)+(compl SODOS)
16 3 to 18 41.13 58.04 70.33 78.80 84.35 87.99
90.48 92.04 93.07 93.72 94.11 95.31 94.47
93.69 92.68 90.53

24 3 to 18 136.94 194.28 234.84 262.38 280.10 291.64
299.15 304.12 307.36 309.39 310.54 310.99 311.56
308.97 304.84 297.69

32 3 to 18 322.33 459.09 554.41 618.14 658.90 685.14
702.25 713.37 720.69 724.94 726.91 727.47 721.07
713.14 701.83 685.97

40 3 to 18 626.61 894.16 1079.46 1202.07 1279.51 1329.90
1362.61 1383,83 1397.57 1405.47 1409.48 1415.34 1406.12
1389.61 1366.94 1337.26

48 3 to 18 1080.15 1542.47 1861.77 2072.38 2205.36 2290.33
2345.82 2381.91 2405.12 2417.79 2424.24 2428.04 2409.25
2377.97 2338.07

56 3 to 18 1710.76 2444.66 2950.87 3283.14 3491.51 3624.74
3714.34 3771.97 3807.68 3827.01 3835.77 3821.12 3784.66
3732.70 3670.22 3597.44

64 3 to 18 2549.63 3647.28 4402.10 4896.13 5205.07 5404.22
5536.73 5621.43 5672.92 5700.96 5711.36 5663.58 5599.10
5514.03 5419.54 5315.48

72 3 to 18 3623.44 5185.73 6258.49 6959.84 7397.38 7679.38
7864.74 7985.85 8055.92 8092.33 8122.37 8075.34 7988.77
7871.26 7740.11 7597.79


A method is sought which obtains the gains of Swiss Pairing
without the temporary setbacks of Adjacency Pairing, so I will next
examine entropy^2 results after implementing Avoidance Pairing.


- regards
- jb

-------------------------------------------------------------
http://en.wikipedia.org/wiki/Solvable_group
-------------------------------------------------------------

-

unread,
Apr 3, 2007, 6:38:33 AM4/3/07
to

>>> jazzerci...@hotmail.com (-) wrote:
>>>> The "fairness" of a pairing method is defined as minimal entropy

> Previous Posting -- Table (A)


> Swiss Reduction Pairing, preload = 1024* (I-1) \ (PL\4)
> (grad.preload 0<-->3.9 MMS\PL) -->> MMS*2^10 +(compl SOS)+(compl SODOS)
> 16 3 to 8 41.11 58.06 70.22 81.61 90.37 93.15
> 24 3 to 8 136.87 194.36 252.73 293.43 316.85 325.95
> 32 3 to 8 322.36 459.09 579.58 680.01 730.94 758.51
> 40 3 to 8 626.69 972.63 1257.33 1431.27 1534.40 1590.57
> 48 3 to 8 1079.80 1771.36 2269.26 2553.97 2739.13 2835.97
> 56 3 to 8 1710.50 2847.00 3633.64 4074.52 4381.26 4541.23
> 64 3 to 8 2548.75 4229.84 5381.11 6051.73 6521.68 6769.44
> 72 3 to 8 3691.25 6130.23 7655.69 8630.90 9322.60 9694.21

Today's Posting -- Table (B)
Loose Swiss Reduction Pairing, preload = 1024* (I-1) \ (PL\4)


(grad.preload 0<-->3.9 MMS\PL) -->> MMS*2^10 +(compl SOS)+(compl SODOS)

16 3 to 8 41.07 58.02 70.18 78.68 85.86 91.45
24 3 to 8 136.05 194.38 235.02 273.16 298.22 313.46
32 3 to 8 322.35 459.06 554.53 626.90 688.43 721.49
40 3 to 8 626.40 893.79 1138.31 1310.88 1418.68 1479.53
48 3 to 8 1079.10 1540.91 1977.10 2268.10 2455.68 2570.96
56 3 to 8 1710.75 2444.43 3077.16 3570.71 3862.08 4063.31
64 3 to 8 2548.48 3643.17 4540.48 5287.19 5715.87 6031.39
72 3 to 8 3624.05 5462.57 6913.31 7933.31 8557.13 9014.68


Only a minor programming difference distinguishes Table (A) from
Table (B) but what a vast improvement for entropy^2 reduction ! The
secret consists in never using Adjacency Pairing. What of the "playoff
concept" between the top contenders? Well, we simply do not pit the
top contenders against each other but rely upon the sidebar data, (SOS
and SoDOS) which returns to offer its level of significance. Table (A)
applies FS=min(PL\2, 2^(F-R)) ; Table (B) applies FS=min(PL\2,2^(F-R+1)):
"Loose Swiss Reduction" is being proposed as a detectable improvement.
As before, here `FS' is the field-size chunk used for "pairing down" or
pair-skipping. In Table (A) the Last Round aims for adjacency pairing
for a higher temperature finale, while in Table (B) the Last Round (and
previous rounds) open up the field-size to provide cooler matches. If
we use "slaughter pairing" then all games would be more predictable.
Nevertheless, predictable games are not perceived as very "fair" so
there's some consideration also to mix up for tighter, hotter matches.
Though a bit of thinking may be required for this, the conclusion today
is that matches between close contenders, or top contenders, are not
very much advised if an overall tournament entropy^2 is to be minimzed.
The notion seems to indicate: pair strong players against weaker players
to provide "less upsetting" tournament results overall. Stronger players
have easier games and weaker players find themselves in a big struggle.
The tournament can tend to match up players who might not ordinarily
meet in their local club, settle ending differences among strong players
with tiebreaker, and still produce less disorder for the general results.

In a handicapped tournament, the overall result tends to be more fair
when using one less or one-half less than normally calculated handicap.
The "tradeoff disadvantage" is that changes in rank resulting from such
tournaments tend to be more "conservative" (slow moving). AcceleRat
techniques actually work by slightly misplacing a player into different
ranking structures to increase slightly a predictability of game results.

Other methods were tried, such as FS=min(PL\2,2^(F-R),2^(R-L)),
which starts with "hot" matches, cools down midway and heats up again.
Some musing, and investigation, with partition theory did not cough up
much: constant field-size divisions into thirds/sixths do not perform.

- regards
- jb

----------------------------------------------------------------------
who distinguishes anti-semitism from holocaust denial:
In Depth: Alexander Cockburn (4/01/2007)
rtsp://video.c-span.org/archive/arc_btv/arc_btv040107_4.rm?mode=compact
----------------------------------------------------------------------
THE APPLETS FOR TRIANGULAR, PENTAGONAL, AND HEXAGONAL CA
(and the game of life) ARE UP AND RUNNING.
http://www.cse.sc.edu/%7Ebays/CAhomePage
----------------------------------------------------------------------

Harry Sigerson

unread,
Apr 4, 2007, 6:08:53 AM4/4/07
to
On Tue, 03 Apr 2007 10:38:33 GMT, jazze...@hotmail.com (-) wrote:

jb,
That was an enjoyable post as far as the wording goes. I'm sure
it would have been even more so if I could understand the mathematics
that drove the piece.
One question -- when you call a match 'hot' you do mean a game
between two highly rated players? It is to be inferred, I suppose.

Where you write...


"Though a bit of thinking may be required for this, the
conclusion today is that matches between close contenders, or top
contenders, are not very much advised if an overall tournament
entropy^2 is to be minimzed.
The notion seems to indicate: pair strong players against
weaker players to provide "less upsetting" tournament results
overall. Stronger players have easier games and weaker players find
themselves in a big struggle."

...that's an ideal to strive for.

Do you have any tips regarding mathematics resources you used in
your work on this?

Harry.

-

unread,
Apr 4, 2007, 10:30:44 AM4/4/07
to

Harry Sigerson <harrys...@ntlworld.com> wrote:
> That was an enjoyable post as far as the wording goes. I'm
> sure it would have been even more so if I could understand
> the mathematics that drove the piece.


See recent comment with AT&T Research for A000292 at:
http://www.research.att.com/~njas/sequences/A000292 . I
don't know if this was something known or highly investigated
however I had difficulty locating any of it in the current literature.
For this context, entropy^2 can assume only discrete values. New
sequence at: http://www.research.att.com/~njas/sequences/A126972 ,
though the formula was misprinted and should be 1+combi(n+3,3) .
For awhile I looked at some possible connection between the "57"
which appears in A126972 , as the number of distinct entropy^2
values for a permutation on seven elements {1,2,3,4,5,6,7} and
the famliar "57" which John Tromp's "legal Go position count"
procedure identifies for the 2x2 board. Note also that this "57"
is unique as a sum of its two predecessor elements, in A126972 ,
occuring after A126972(n)=w^2, i.e. n=1, 3, 6, 9, 23, 25, 64, 13776...
and four of these `n' values are themselves squares. 13776 factors
as: 16*3*7*41. (Perhaps no more to be found: only eight solutions?)
Continued musing about possible connection with a problem of "legal
Go position count" was fruitless. Corresponding values for 'w' are:
2, 6, 11, 45, 51, 209, 660099... /\/\ 209 = 11*19, 660099 = 3*11*83*241 .

> One question -- when you call a match 'hot' you do mean a game
> between two highly rated players? It is to be inferred, I suppose.


No. Matches are 'hot' for games between two -closely- rated
players. Adjacency Pairing is `hot' and Slaughter Pairing is `cold.'



> Where you write...
>
> "Though a bit of thinking may be required for this, the
> conclusion today is that matches between close contenders, or
> top contenders, are not very much advised if an overall tournament
> entropy^2 is to be minimzed. The notion seems to indicate: pair
> strong players against weaker players to provide "less upsetting"
> tournament results overall. Stronger players have easier games
> and weaker players find themselves in a big struggle."
>
> ...that's an ideal to strive for.


Once adopting Aguilar MMS preloading certain other problems
start to present themselves. While entropy^2 values are still reaching
the "normalizing hump" before decreasing (Rounds 14,15 in examples)
'cooler' pairing strategies achieve slightly better performance. A `hot'
Adjacency Pairing does not perform well until passing the "normalizing
hump" where entropy^2 values begin to decrease, with ent^((1-p)/(1+p)).
Tournaments that end prior to the summit on the entropy^2 "normalizing
hump" should not aim for Adjacency Pairing in the Final Round, but may
settle for skip1 or skip2 pairing and apply tiebreaker. Swiss Reduction
certainly appears to offer an improvement over other alternatives tested.



> Do you have any tips regarding mathematics resources you used in
> your work on this?


Most of the "work" was done by tireless computer simulation over
500,000 trial tournaments for each of the averaged entropy^2 data points.
This project has led me toward another crack at Group Theory and the
Theory of Partitions, each of them "rather hairy mathematical animals."
Some "information paradoxes" occur: because ordered permutations are
symmetric with disordered permutations, high entropy^2 values are not
necessarily unmanageable; _Alice_Through_the_Looking_Glass_ effect.
One might have conjectured that average entropy^2 values are also mode
as well as mean, yet that is not the case. The "interior distributions"
(or frequencies) of entropy^2 values display unusual serrated patterns.
Tournament rank ordering is merely one of many possible permutations.
I sought also to show that degree of confidence for placeholder results
is not divorced from level of confidence for candidate field generally.

I began with a general idea of "fairness" yet along the way encountered
many other goals & objectives typical of what participants might prefer.
I "googled" not very successfully for specific items from the literature,
though without a clear understanding of why documentation for this sort
of approach was not more accessible. My simulation assumes hyperbolic
rank distributions though in "the real world" maybe ranks are distributed
according to the error function. UBASIC, AT&T Integer Sequences, lots
of tinkering patience, availability of a reasonably high-speed computer,
surveys of (possibly related) prior literature. One study in progress
concerns the transition states of balanced bits under `xor.' Frequency
distribution of differences among bitcounts bears a resemblance to one
side of symmetric frequency distribution among various entropy^2 values.


- regards
- jb

-----------------------------------------------------------------
10 B=32767:dim P%(7),A%(B+B),B%(B+B),E%(B):Up=2^32:' perm.ub
30 for D=190 to 190:W=!(D):Q=len(W)\32:if Q then R=W@(Q*Up) else R=W

34 Y=Q*16
35 for I=1 to 6000:Z=bitxor(Z,fnBitBal(0,0,fnRand(Q,int(rnd*R),0),0,Q,R))
36 X=bitcount(Z):inc E%(abs(Y-X):Y=X:next I
37 I=B:while E%(I)=0:dec I:wend:for J=0 to I:print E%(J);:next:stop

145 fnBitBal(K,J,I,W,Q,R):J=2*bitcount(I)-Q*32-len(R):K=abs(J):while K>1
147 W=int(rnd*(Q*32+len(R))):if bit(W,I)=(J<0) then 147
148 I=bitreverse(W,I):dec K:dec K:wend
149 if abs((Q*32+len(R)+1)\2-bitcount(I))>1 then stop else return(I)

150 fnRand(Q,R,J):for J=1 to Q:R+=sft(R,32)+int(rnd*Up):next:return(R)
-----------------------------------------------------------------

Harry Sigerson

unread,
Apr 5, 2007, 7:31:03 AM4/5/07
to
On Wed, 04 Apr 2007 14:30:44 GMT, jazze...@hotmail.com (-) wrote:

jb,
Thanks for the post.
You very rapidly lost me wrt to the mathematical tools being used, not
difficult to do. I enjoyed the descriptive text.
The task itself reads as on a par with corralling houseflies <s>.
As where you write...

> A `hot' Adjacency Pairing does not perform well until passing the
> "normalizing hump" where entropy^2 values begin to decrease, with
> ent^((1-> p)/(1+p)).
>

...might indicate.

I wonder if there will be or even to expect that there could ever be a
wholly 'fair' system?
Where you say...



> I began with a general idea of "fairness" yet along the way encountered
> many other goals & objectives typical of what participants might prefer.
>

...paints a picture of a system, which if it did satisfy those goals would
have so many presets to turn on before running it that users might have to be
accredited 'priests' <smile>. Still if there is to be a fairest solution it
will come along the road you and I suppose others are travelling.

Harry.

-

unread,
Apr 5, 2007, 8:35:05 PM4/5/07
to

Harry Sigerson <harrys...@ntlworld.com> wrote:
> You very rapidly lost me wrt to the mathematical tools being used,
> not difficult to do. I enjoyed the descriptive text.
> The task itself reads as on a par with corralling houseflies <s>.
> As where you write...

> jazze...@hotmail.com (-) wrote:
>> A `hot' Adjacency Pairing does not perform well until passing
>> the "normalizing hump" where entropy^2 values begin to
>> decrease, with ent^((1-p)/(1+p)) ...

> ...might indicate.


Thanks for your interest. Perhaps Mr. Jasiek is still lurking out
there, as well. Once introducing Aguilar MMS preloading the nature
of this problem changed drastically. Without biasing the tournament,
(in the previous model) the entropy^2 values resembled a converging
curve, like y = exp(-x) dampening, from thoroughly random conditions
to more semi-ordered states termed an acceptable level of significance.
Helpful to have some diagrams, so I trust you will not object to text:

Inverted Permutation Order
("maximum disorder" measure)
`A007290' in Sloane's Integer Seq.
|
|
[ ... ]
|
|
Expected Initial Entropy
("average disorder" measure) * *
`A000292' in Sloane's Integer Seq. *
| *
| *
| *
| *
|
[ ... ]
| #
| # #
| #
| #
| #
0 | #
Completely Ordered Permutation
("entropy zero" measure)



Initial conditions of the tournament database general converge
around `A000292' values, for entropy^2 . Here be sure to select for
fixed-font. The asterisk markings depict what might be the progress
of a tournament -without- Aguilar MMS preloading, with gradual fall off.
The pound markings beneath depict what might occur for a tournament
-with- Aguilar MMS preloading. Rising from somewhere near zero the
entropy^2 values ascend for several rounds until finally reaching the
"hump" (Rounds 14,15 in my simulation). Even though MMS preloading
might never attain that "hump" for a 6 or 8 Round tournament, its values
of entropy^2 are technically less than would have been the case without
MMS preloading. On the downward side both methods converge on zero.

Throughout the discussions on "fairness" have been two intermingling
themes. One perspective says that dark horse candidates ought to have
a "fair" crack at the (previously known) strong players. The question
being, however, how many dark horse candidates we can entertain here
and whether the few strong players can be tasked to play all of them. So
there's a feasibility problem with accomodating dark horse winner ideas.
Another perspective on "fairness" suggests that players already known to
be strong have "pole position" in the mix and ought to continue playing
other strong players so that they need not be bothered with a lot of dark
horse candidates. The latter is certainly also a good idea however, from
the perspective of reducing tournament entropy^2, the problem posed by
`hot' Adjacency Pairing tends to upset the apple cart more than would be
the case if we simply let dark horse players have a "crack" at potential
tournament winners, via 'cold' Slaughter Pairing. I sought to understand
why there should be a "trivial result" in the 2005 U.S. Open for Final
Round. Ms. Xuefen Lin, a strong pro player, was allowed to compete.
She held off all strong amateurs so well that she could afford to lose
Final Round to Mr. Yongfei Ge, a player already with one loss, yet
she still won the 2005 U.S. Open ... Mr. Yongfei Gei's loss was to a
"weaker" player (they're all strong players) than Ms. Xuefen Lin's loss.

http://www.usgo.org/congress/2005/USopen%20results-05.htm

By necessity this U.S. Open also incorporated MMS preloading,
of a non-graduated variety. I suspect that the high priests of the match
pairing were aiming for `hot' Adjacency Pairing for the Final Round, so
prior rounds were paired away slightly, to produce 'cooler' convergence.
Or, it may be the case that they applied `hot' Adjacency Pairing earlier
in the tournament which then resulted in a situation of "trivial result."
Perhaps the "trivial result" on Board One was compensated by much
nicer results on other Boards? It's difficult to say because opponent
numbers in that list seem jumbled around for deciphering prior rounds.
During the course of a tournament perhaps it's difficult for Tournamet
Directors to justify what appear to be "anomalous methods" in pairing.
One player mentioned to me that he had played three rounds as Black
consecutively; this was a "complaint." Yet, under high Ing Rule komi
he would encounter a slight komi "advange" in later rounds as White.
Having `cooler' pairings under MMS preloading seems counterintuitive
to an expected wisdom. Amount of preloading would factor, as well as
the tournament size. Given parameters for a particular tournament it
seems workable to tailor simulations appropriately, and arrive at breaks.
Well, I was not involved in pairing nor did I wish to engage in arguments
about pairing with the three (independent) teams of high priests there.
Anyway it appears that `cooler' pairing utilizing the tiebreakers is more
entropy reducing than (traditional) methods of directed challenge/fight;
among (initially) surprising results from applied computer simulations.


> I wonder if there will be or even to expect that there could ever
> be a wholly 'fair' system?
> Where you say...


>> I began with a general idea of "fairness" yet along the
>> way encountered many other goals & objectives typical
>> of what participants might prefer.


> ...paints a picture of a system, which if it did satisfy those goals would
> have so many presets to turn on before running it that users might have
> to be accredited 'priests' <smile>. Still if there is to be a fairest solution
> it will come along the road you and I suppose others are travelling.


It is "fair" to keep the discussion about "fairness" alive. I think
that once it is relegated to the means of a mechanical bride then it
is not quite as "fair" as might be with the ongoing human involvement.
We may map out some of the discussion dimensions, as with a pachinko
parlor, to supply authoritative remarks concerning where balls are likely
to go if they are nudged into certain directions. To say that there is
only one optimal path from A to Z ignores a feature of words themselves
and how spelling variants also accomplish other intended conveyances
for meaning. I thought for awhile on a relationship between player rank
distribution and whether pairing should be adjusted to maximize effects
for dynamic distributions. Somewhat akin to finding novel and efficient
methods for (matrix) multiplication, other general algorithmic speedups,
though one guiding precept in computer science has been "there ain't
no such thing as the fastest code" (TANSTATFC). Too often we have
encountered some improvement over prior constructions, however slight.

Rather often it is the -appearance- of "fairness" that persuades the
players that conditions are "fair." Tournament Directors can do a bunch
of little cosmetic things that key upon "fairness perceptions" though
accomplish not much or nothing at all, in terms of entropy^2 reduction.
How things are done or said seems to preoccupy "the way of the world"
rather than what's actually transpiring for factual background. We are
encountering a great shake-out where large numbers of highly qualified
individuals decline to continue their participation. As a consequence
those tournament winners will not necessarily be the best players. :-(


- regards
- jb

-------------------------------------------------------------
Foreigners May Decide French Election
http://www.wvwnews.net/story.php?id=228
-------------------------------------------------------------

Harry Sigerson

unread,
Apr 6, 2007, 10:26:58 AM4/6/07
to
On Fri, 06 Apr 2007 00:35:05 GMT, jazze...@hotmail.com (-) wrote:


> It is "fair" to keep the discussion about "fairness" alive.
>

Yes, and to...


> Rather often it is the -appearance- of "fairness" that persuades the
> players that conditions are "fair."
>

Inconsistencies in Results at the top, that is among the best of the bunch
is you like, if not too blatant will tend to be 'acceptable'; though this is
tendency has to owe something to the contenders having an appreciation of the
difficulties of pairings. By the same token any feedback from the contenders wrt
to even not-so-blatant inconsistencies can only be assessed/addressed by those
who wrote and are re-writing the applications.

> ...one guiding precept in computer science has been "there ain't


> no such thing as the fastest code" (TANSTATFC). Too often we have
> encountered some improvement over prior constructions, however slight.
>

That'll be the Gilding the Lily step.

> ...Tournament Directors can do a bunch


> of little cosmetic things that key upon "fairness perceptions" though
> accomplish not much or nothing at all, in terms of entropy^2 reduction.
> How things are done or said seems to preoccupy "the way of the world"
> rather than what's actually transpiring for factual background.
>

There's a word for that, which escapes me... starts with 'Po'. It's
either Politics or Politesse perhaps both.

> We are
> encountering a great shake-out where large numbers of highly qualified
> individuals decline to continue their participation. As a consequence
> those tournament winners will not necessarily be the best players. :-(
>

Perhaps its the time delay involved in assessment and collating of real
tournament results that's the dampener.

Harry.

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