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# FIBS formula question/comment

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### Murat Kalinyaprak

Oct 20, 1998, 3:00:00â€¯AM10/20/98
to
Here is a detailed explanation of variables and
calculations I found at a web site about FIBS
rating calculations:

----------------------------------------------------------------------
What do the variables mean?

n = the length of the match.
P1 = the rating of Player 1.
P2 = the rating of Player 2.
E1 = the experience of Player 1 right before finishing the match.
E2 = the experience of Player 2 right before finishing the match.
PE1 = experience factor for Player 1 (calculated).
PE2 = experience factor for Player 2 (calculated).
D = the difference between the two ratings (calculated).
F = the probability of the favorite winning the match (calculated).
U = the probability of the underdog winning the match (calculated).

How are the Variables calculated?

D = absolute value of P1-P2
U = 1/(10^(D*SQRT(n)/2000)+1)
F = 1-U
PE1 = maximum(1, 5-((E1+n)/100))
PE2 = maximum(1, 5-((E2+n)/100))

How is the rating change calculated?

If Player 1 is higher rated and wins, P1's rating increases by
4*PE1*SQRT(n)*U
If Player 1 is higher rated and loses, P1's rating decreases by
4*PE1*SQRT(n)*F
If Player 1 is lower rated and wins, P1's rating increases by
4*PE1*SQRT(n)*F
If Player 1 is lower rated and loses, P1's rating decreases by
4*PE1*SQRT(n)*U
If Player 2 is higher rated and wins, P2's rating increases by
4*PE2*SQRT(n)*U
If Player 2 is higher rated and loses, P2's rating decreases by
4*PE2*SQRT(n)*F
If Player 2 is lower rated and wins, P2's rating increases by
4*PE2*SQRT(n)*F
If Player 2 is lower rated and loses, P2's rating decreases by
4*PE2*SQRT(n)*U
----------------------------------------------------------------------

Before I make comments, let me make sure of one
thing. Is this the same/currently used formula
that many people describe as "simple", "beautiful",
"stable", "proven to work", "accurate", etc...?

The variable "U" that seems to be the heart of this
formula goes completely above my head. What is that
"2000"...? Why square-root and not cube-root (pun
intended!) of "n"...?

While at it, let me try explaining the formula I had
previously suggested, following the above format:

----------------------------------------------------------------------
What do the variables mean?

M = the length of the match.
P1 = the rating of Player 1.
P2 = the rating of Player 2.
D = the difference between the two ratings (calculated).
W = half of "players rating window" (constant).

How are the Variables calculated?

D = absolute value of P1-P2
W = arbitrarily set by me to 50, as an example.

How is the rating change calculated?

Player 1's rating changes to: P1 & (M+M*((W-D)/abs(W-D)))/2
Player 2's rating changes to: P2 & (M+M*((W-D)/abs(W-D)))/2

& = "+" for the winning player, "-" for the loosing player.
----------------------------------------------------------------------

As is, my above formula will produce a "divide by 0"
error when P1=P2, but I'll let rgb's math majors put
the final touch on it since I'm a little rusty/slow
with devising elegant formulas. In actual programming
it would of course be simpler to use "if" clauses...

In an imaginary range of ratings from 0 to 2000, the
value 50 for W would mean an average 5% inaccuracy;
increasing going down, and decreasing going up the
ratings range. I think this may be an unintentional
but welcome effect of this system. Any comments on
this...?

I also would like to revise my initial suggestion
about starting new players at an arbitrary rating
like 1000 (or 1500). I think a better approach would
be to start them at the "most common rating" for the
entire system, which can be computed daily or weekly
and rounded to increments of 50, for example. This
approach would speed up the process of finding one's
place better than the existing adjustments based on
experience or suggested modifications similar to the
chess rating systems. After starting at wherever the
biggest bulge may occur in the ratings distribution,
the majority will get to where they belong faster
than from any other arbitrary point and/or using any
other means of expediting the process. Also, if the
rating range shifts up or down as a whole (because
more beginner or expert players flowing in, or even
because all players getting better in time, etc.)
that entry point would also shift along dynamicly.

I hope not everybody lost interest in this subject
and I'm not talking to myself... :)

MK

### Hank Youngerman

Oct 20, 1998, 3:00:00â€¯AM10/20/98
to
Despite the complexity, the formula is fairly simple in that....

1) A certain number of points are at stake in each match - that number
is 4 times the square root of the length of the match

2) There is a calculation as to the relative likelihood of the two
players winning. The odds of the favorite winning increase as the
length of the match increases.

3. The point split is based on the odds of winning. If you play a
4-point match (I know no one does, but it makes the numbers come out
more even) there are 8 points at state. If you are a 62.5% favorite
to win, you will either win 3 points or lose 5.

4. For the first 400 games you play, your rating moves more quickly.

I would like to see some emprical analysis of the relative likelihood
of winning and losing - but other than that - the formula seems pretty
sensible to me.

### Gary Wong

Oct 20, 1998, 3:00:00â€¯AM10/20/98
to
hankyou...@home.com (Hank Youngerman) writes:
> I would like to see some emprical analysis of the relative likelihood
> of winning and losing - but other than that - the formula seems pretty
> sensible to me.

Careful what you wish for, you just might get it :-)

I performed an experiment testing these three hypotheses:

* That the basic Elo system could accurately describe the distribution
of backgammon game results, if matches were all of the same length.

* That the FIBS implementation of the Elo system accurately describes
the distribution of backgammon game results, for matches of all
lengths.

* That the FIBS implementation of the Elo system systematically
overestimates the underdog's chances in shorter than average matches,
and overestimates the favourite's chances in longer than average
matches.

The details are written up at:

but the bottom line is that my data (several thousand one-pointers that
Abbott played against opponents ranging from 1280-1880) showed no evidence
refuting _any_ of the three hypotheses above. I was going to go into
more detail (graphs of observed winning probabilities vs. FIBS-predicted
winning probabilities vs. best-fit Elo predicted winning probabilities
specifically fitted to the match length, etc.) but once I got as far as
what's on that web page, I'd pretty much satisfied my own curiosity so I
think it's pointless going any further.

(The one thing I would be interested in is performing the same kind of
analysis on longer length matches, if anybody has data available.
Unfortunately the chi-squared test I used needs LOTS of data; preferably
over 1000 matches of identical length. If they all involve the same
player, that's even better; if that player is a bot and so we know their
ability didn't change while the data were being collected, that's better
still.)

My current opinion is that the Elo system can be a very good predictor
of backgammon game distributions; that the FIBS implementation (with
the ratings difference scaled by the square root of the match length)
is flawed but adequate; and that FIBS systematically overestimates
the underdog's chances in short matches and overestimates the favourite's
chances in long matches. As I said, I've satisfied my own curiosity and
am now going to shut my mouth on this topic (bet you thought you'd never
hear me say that :-)

Cheers,
Gary.
--
Gary Wong, Department of Computer Science, University of Arizona
ga...@cs.arizona.edu http://www.cs.arizona.edu/~gary/

### Murat Kalinyaprak

Oct 21, 1998, 3:00:00â€¯AM10/21/98
to

>I performed an experiment testing these three hypotheses:

> * That the basic Elo system could accurately describe the distribution
> of backgammon game results, if matches were all of the same length.

> * That the FIBS implementation of the Elo system accurately describes
> the distribution of backgammon game results, for matches of all
> lengths.

> * That the FIBS implementation of the Elo system systematically
> overestimates the underdog's chances in shorter than average matches,
> and overestimates the favourite's chances in longer than average
> matches.

>but the bottom line is that my data (several thousand one-pointers
>that Abbott played against opponents ranging from 1280-1880) showed
>no evidence refuting _any_ of the three hypotheses above.

>.....My current opinion is that the Elo system can be a very good

>predictor of backgammon game distributions; that the FIBS

>implementation (with the ratings difference scaled by the square

>root of the match length) is flawed but adequate

where you have the log of the last 1000 games played
by Abbott. As you did in your above analysis, I did
eliminate players with less than 400 experience and
ended up with 815 matches of which Abbot had won 435
and lost 380. The average rating of its opponents was
1615.79 and its winning rate was 53.37%.

Then I logged on to FIBS to see what rating difference
would give me 53.37% chance of winning and found out
that it's about 120 points (my rating at this time was
1668). Looking at the table in your web page mentioned
above, (given that you mentioned R=1505 for Abbott), I
could see that it would have that same winning chance
against opponents rated at around 1400, which gives
approximately the same ratings difference also.

Abbott's current rating on FIBS is 1552. I believe at
the time we were talking about those last 1000 matches
so) it was well below 1500 but let's just stick with
the higher number here and say 1550. If I understand
all this rating stuff correctly, for Abbott to have a
53.37% winning chance against opponents rated at 1615,
its own rating would have to be around 1735... That's
a whopping discrepency of almost 200 points.

Let's stress that even the higher number above (1550)
that I picked would be its end rating not its average
rating. Considering it won 435 out of the 815 games I
included in my analysis, its starting rating and/or
average rating must have been lower than that. I think
while talking about loosing streaks its rating was
around 1460's(?) and at that time its average rating
during those 1000 logged matches may have been around
1450's. So, we may be talking here about a discrepency
that's possibly as high as 250 points or even higher.

Unless I'm misunderstanding/misinterpreting things
and way off in my above numbers, I would conclude
that FIBS current rating system may not be just
slightly flawed and still adequate; but actually
grossly inaccurate...

MK

BTW, looking at the "wwllwll..." sequences that you
looking at the log of those 1000 matches by just
scrolling it up and down for a few minutes, I had
come to the conclusion (which I posted in response
games to much higher rated opponents and that it had
done better than expected overall. It looks like a
more careful examination of that log confirms what

### Murat Kalinyaprak

Oct 21, 1998, 3:00:00â€¯AM10/21/98
to
In <362c044d.5390690@news> hankyou...@home.com wrote:

>Despite the complexity, the formula is fairly simple in that....

Complex=simple...? :)

>1) A certain number of points are at stake in each match - that
>number is 4 times the square root of the length of the match

What is this based on? Why 4 times? Why square root?
Please don't take my questions personally and/or feel
obligated to answer, but I'm really making an effort
to understand all this.

>4. For the first 400 games you play, your rating moves more quickly.

This is a minor issue, but where did 400 came from?

>I would like to see some emprical analysis of the relative
>likelihood of winning and losing - but other than that - the
>formula seems pretty sensible to me.

I would like to see such data also but preferably from
different sources than the ones using the said formula
to begin with. Otherwise, I'm not sure if any analysis
done on the data based on ratings produced by a formula
in order to see if that same formula works could be
considered valid...

MK

### Jim Williams

Oct 21, 1998, 3:00:00â€¯AM10/21/98
to
Gary Wong wrote:
>
> I performed an experiment testing these three hypotheses:
>
> * That the basic Elo system could accurately describe the distribution
> of backgammon game results, if matches were all of the same length.
>
> * That the FIBS implementation of the Elo system accurately describes
> the distribution of backgammon game results, for matches of all
> lengths.
>
> * That the FIBS implementation of the Elo system systematically
> overestimates the underdog's chances in shorter than average matches,
> and overestimates the favourite's chances in longer than average
> matches.
>
> The details are written up at:
>
> http://www.cs.arizona.edu/~gary/backgammon/elo.html
>
> but the bottom line is that my data (several thousand one-pointers that
> Abbott played against opponents ranging from 1280-1880) showed no evidence
> refuting _any_ of the three hypotheses above. I was going to go into
> more detail (graphs of observed winning probabilities vs. FIBS-predicted
> winning probabilities vs. best-fit Elo predicted winning probabilities
> specifically fitted to the match length, etc.) but once I got as far as
> what's on that web page, I'd pretty much satisfied my own curiosity so I
> think it's pointless going any further.
>
> (The one thing I would be interested in is performing the same kind of
> analysis on longer length matches, if anybody has data available.
> Unfortunately the chi-squared test I used needs LOTS of data; preferably
> over 1000 matches of identical length. If they all involve the same
> player, that's even better; if that player is a bot and so we know their
> ability didn't change while the data were being collected, that's better
> still.)

This touches on a question I have been evaluating. I am suspicious of
the fibs rating forumla in the way it accounts for match length. I have
collected a lot of match results and checked empirically whether the
winning probability as predicted by the FIBS rating formula actually
matches the observed winning probability for a given match between
players
of known ratings. I sampled the players ratings before recording any
matches so that the random errors in the ratings would be uncorrelated
with with the outcome of the observed games. Only matches where both
players had at least 1000 experience points were included. Currently
the number of recorded results is as follows:

1 point matches 19926
3 point matches 12036
5 point matches 8621

1, 3, and 5 account for 90% of all matches.

I then took the fibs ratings formula for win probability:

P = 1/(1 + 10^(D*sqrt(N)/2000))

Rather than using the match length for N, I used an effective
match length where the effective match length was chosen so
that the formula gave the best fit with the observed data.

The results were what I expected only more extreme. The effective
match lengths which gave the best fit were as follows:

match length effective match length
---------------------------------------------------------
1 1.6
3 1.6
5 2.1

Due to the limited number of matches recorded, the standard error
on these effective match lengths is about 0.25 . If anyone notices
zbest lurking on fibs, he is collecting more data to try to get
a more accurate fix on these numbers.

These numbers suggest that a 3 point match has exactly the same
skill component as a 1 point match, and a 5 point match only
slightly more.

I am at a loss to explain these numbers, but the implication is
that if you want to increase you rating, play 1 point matches
agains the weakest opponents you can find, and play long matches
against the strongest opponents you can find. It also suggests
that if we want to make backgammon more a game of skill and less
a game of luck, we should eliminate the doubling cube.

### Gary Wong

Oct 21, 1998, 3:00:00â€¯AM10/21/98
to
mu...@cyberport.net (Murat Kalinyaprak) writes:
> >.....My current opinion is that the Elo system can be a very good
> >predictor of backgammon game distributions; that the FIBS
> >implementation (with the ratings difference scaled by the square
> >root of the match length) is flawed but adequate...

>
> where you have the log of the last 1000 games played
> by Abbott. As you did in your above analysis, I did
> eliminate players with less than 400 experience and
> ended up with 815 matches of which Abbot had won 435
> and lost 380. The average rating of its opponents was
> 1615.79 and its winning rate was 53.37%.

I took a look just now and got exactly the opposite results (ie. Abbott
lost 435 and won 380). Note that a "w" in the 3rd column means _Abbott_
won, and an "l" means _Abbott_ lost. 53.37% is the _loss_ rate; the
observed win rate is 46.6%. In a sample of this size, the standard error
works out to 1.7%.

> Then I logged on to FIBS to see what rating difference
> would give me 53.37% chance of winning and found out
> that it's about 120 points (my rating at this time was
> 1668).

Yes, FIBS predicts this win rate at a difference of 117 points (the
loss rate naturally means a difference of -117). Since there's some
sampling error in the 53.37% figure, we should really be more
conservative and give this figure with the standard deviation, which
is unfortunately a whopping 60 points.

> Abbott's current rating on FIBS is 1552. I believe at
> the time we were talking about those last 1000 matches
> so) it was well below 1500 but let's just stick with
> the higher number here and say 1550.

Yes, 1550 is certainly too high. The best estimates I have of Abbott's
true ability are 1503 or 1478, in that those ratings most closely predict
the observed win rate distributions (1503 using the best-fit Elo parameters
to observed 1-point matches; 1478 using the FIBS "d sqrt(n) / 2000" method
which I believe overestimates the underdog's chances for 1 point matches).
Unfortunately these are MLEs (maximum likelihood estimators; ie. they are
obtained numerically by observing that higher or lower values than 1503 or
1478 respectively predict the observed data less accurately) and I do not
know how to measure the uncertainty in this value. In any case, if you
want a figure to use with the FIBS variant of the Elo system, the best
estimate I can give you is 1478.

> If I understand
> all this rating stuff correctly, for Abbott to have a
> 53.37% winning chance against opponents rated at 1615,
> its own rating would have to be around 1735... That's
> a whopping discrepency of almost 200 points.

Since it really _lost_ 53.37% of games, our estimation is in fact 1615
_minus_ 117, or 1498. This estimate is again subject to a standard error
of 60 points.

> Unless I'm misunderstanding/misinterpreting things
> and way off in my above numbers, I would conclude
> that FIBS current rating system may not be just
> slightly flawed and still adequate; but actually
> grossly inaccurate...

I don't think there's any discrepancy at all. From the 1000 game sample
we derive an estimated rating of 1498; from the MLE calculations shown on
the web page we get 1478. This disagreement is well within the margin
of error. (If there is anybody out there who observes Abbott's long term
rating, I believe they would trust that these are reasonably accurate
estimates of its true performance as well. It tends to fluctuate anywhere
from the low 1400s to mid 1500s.)

> BTW, looking at the "wwllwll..." sequences that you
> looking at the log of those 1000 matches by just
> scrolling it up and down for a few minutes, I had
> come to the conclusion (which I posted in response
> to your article) that Abbott had lost a lot of its
> games to much higher rated opponents and that it had
> done better than expected overall. It looks like a
> more careful examination of that log confirms what
> I had quickly observed then.

I don't understand what you mean here. Losing games to much higher rated
opponents is surely nothing more than we would expect? And I see no
evidence that it has done better than expected overall, either in the
1000 game sample here or the larger sample categorised by opponent strength
on the web page.

### David Montgomery

Oct 21, 1998, 3:00:00â€¯AM10/21/98
to
In article <362E02...@giga-net.com> Jim Williams <ji...@giga-net.com> writes:
>Rather than using the match length for N, I used an effective
>match length where the effective match length was chosen so
>that the formula gave the best fit with the observed data.
>
>The effective match lengths which gave the best fit were as follows:
>
> match length effective match length
>---------------------------------------------------------
> 1 1.6
> 3 1.6
> 5 2.1
>
>Due to the limited number of matches recorded, the standard error
>on these effective match lengths is about 0.25 .

Wow. Great work Jim (and Gary). This is cool stuff.

I'm only a little surprised by the results for 1 and 3 pointers,
since I've long thought that 1 point matches were underrated and
3 point matches overrated.

However, theoretically it seems entirely implausible that 1 and 3
should be equivalent. A 3 point match will always have a game
played to conclusion (like a 1 pointer), and will have many other
decisions in earlier games. So I'm certain that there is more
skill in a 3 pointer than in a 1 pointer.

Besides the uncertainty due to the amount of data, it could well
be that people play 3 pointers so bad that this fact is obscured.
I think most people play 3 pointers really badly, especially at
-2:-3.

I'm very surprised by the results for 5 pointers.

Could you make your data publicly available? I would like to
try some alternative analyses.

David Montgomery
mo...@cs.umd.edu
monty on FIBS

### Gary Wong

Oct 21, 1998, 3:00:00â€¯AM10/21/98
to
Jim Williams <ji...@giga-net.com> writes:

> Gary Wong wrote:
> > (The one thing I would be interested in is performing the same kind of
> > analysis on longer length matches, if anybody has data available.
> > Unfortunately the chi-squared test I used needs LOTS of data; preferably
> > over 1000 matches of identical length. If they all involve the same
> > player, that's even better; if that player is a bot and so we know their
> > ability didn't change while the data were being collected, that's better
> > still.)
>
> [snip]

> Currently the number of recorded results is as follows:
>
> 1 point matches 19926
> 3 point matches 12036
> 5 point matches 8621

Wow, that's exactly the data I would have liked in the first place! :-)

> The results were what I expected only more extreme. The effective

> match lengths which gave the best fit were as follows:
>
> match length effective match length
> ---------------------------------------------------------
> 1 1.6
> 3 1.6
> 5 2.1
>
> Due to the limited number of matches recorded, the standard error
> on these effective match lengths is about 0.25.

This is very encouraging! My result of d/1634 for the MLE exponent for
1-point matches (instead of the d sqrt(n)/2000 = d/2000 that FIBS
predicts) works out to an effective match length of 1.5, which is well
within the margin of error for agreement with your value of 1.6.

(I'd like to know how you measured the standard error on those quantities.
The 1634 figure I got was a chi-squared minimum parameter, but tacking a
variance onto that takes way more estimation theory than I understand.)

> I am at a loss to explain these numbers,

I don't think we need much more explanation than we already have, do
we? We expect that gammons and the cube lead to significant
dependence between points in a multi-point match; with a bit of
hand-waving (see previous articles) we see that these effects mean
that "effective match length" increases LESS than linearly with "real
match length". (Loosely speaking, these two will be equal at the
"average match length", which seems to be between 1 and 3.)

This is more or less the suspicion I think we've had all along (the
earliest reference I can find is an article by David Montgomery in
1995, at http://www.bkgm.com/rgb/rgb.cgi?view+44).

The fact that 1 and 3 point matches seem to yield the same effective
match length is probably meaningless considering the margin of error.
(Assuming the standard error decreases with the square root of the
number of samples, then the effective match length for 1-pointers
from the total of our data is 1.56 with standard error 0.21.)
Also, Peter Fankhauser found in an analysis of the Big Brother
database (http://www.bkgm.com/rgb/rgb.cgi?view+139) that the favourite
expected to gain a tiny fraction of a point (0.011) in 3 point matches,
suggesting that the effective match length in that case was just _over_
3. However, that was from a sample of only 185 games and only
measured highly ranked players, so may be subject to considerable
sampling error (especially when applied to the entire FIBS population).

> but the implication is
> that if you want to increase you rating, play 1 point matches
> agains the weakest opponents you can find, and play long matches
> against the strongest opponents you can find.

Yup. And drop when you're losing, and use Jellyfish to select your
moves, and use more than one account, and...

> It also suggests
> that if we want to make backgammon more a game of skill and less
> a game of luck, we should eliminate the doubling cube.

Oh dear, them's fighting words ;-) My OPINION (I won't attempt to
substantiate this) is that the cube can add a significant amount of
skill to the game by creating the opportunity for costly cube errors
(which will naturally tend to be made more often by less skilled
players). In matches of constant _length_, a match played with no
cube and no gammons be will more of a game of skill purely because more
matches will be played and the variance in the result will be lower;
however, in matches of constant _time_, I suspect (hope? :-) that
cubeful games will be more skillful. In the time that it takes to
play a 15-point match, you might only be able to fit in (say) a
5-point cubeless, gammonless match. My guess is that the cubeful
match is a better test of skill. Whether it is or not, I also
believe it's the most interesting.

topic ;-)

### Murat Kalinyaprak

Oct 22, 1998, 3:00:00â€¯AM10/22/98
to
In <362E02...@giga-net.com> Jim Williams wrote:

>These numbers suggest that a 3 point match has exactly the same
>skill component as a 1 point match, and a 5 point match only
>slightly more.

>I am at a loss to explain these numbers...... It also suggests

>that if we want to make backgammon more a game of skill and less
>a game of luck, we should eliminate the doubling cube.

Without quoting the entire article, what you presented
was indeed very interesting, and I must say that your
last sentence is music to my ears... :)

MK

### Murat Kalinyaprak

Oct 22, 1998, 3:00:00â€¯AM10/22/98
to
In <wtaf2pa...@brigantine.CS.Arizona.EDU> Gary Wong wrote:

>mu...@cyberport.net (Murat Kalinyaprak) writes:

>I took a look just now and got exactly the opposite results
>(ie. Abbott lost 435 and won 380). Note that a "w" in the
>3rd column means _Abbott_ won, and an "l" means _Abbott_ lost.
>53.37% is the _loss_ rate; the observed win rate is 46.6%.

Oops, I got it backwards... The numbers I ended up
with sure had looked like they could be way off to
the point that I had felt a need to say something
about such a possibility in my last paragraph...

>> Then I logged on to FIBS to see what rating difference
>> would give me 53.37% chance of winning and found out
>> that it's about 120 points

>Yes, FIBS predicts this win rate at a difference of 117

>points (the loss rate naturally means a difference of -117).

>> Abbott's current rating on FIBS is 1552. I believe at

>> the time we were talking about those last 1000 matches
>> so) it was well below 1500

>In any case, if you want a figure to use with the FIBS variant

>of the Elo system, the best estimate I can give you is 1478.

Sounds reasonable to me. Around the days I was looking
at those 1000 matches, I think it was fluctuating
between 1540's and 1560's...

>> If I understand
>> all this rating stuff correctly, for Abbott to have a
>> 53.37% winning chance against opponents rated at 1615,
>> its own rating would have to be around 1735... That's
>> a whopping discrepency of almost 200 points.

>Since it really _lost_ 53.37% of games, our estimation is in
>fact 1615 _minus_ 117, or 1498. This estimate is again subject
>to a standard error of 60 points.

Thanks for correcting my "whopping mistake"...

>> Unless I'm misunderstanding/misinterpreting things
>> and way off in my above numbers, I would conclude
>> that FIBS current rating system may not be just
>> slightly flawed and still adequate; but actually
>> grossly inaccurate...

>I don't think there's any discrepancy at all. From the 1000
>game sample we derive an estimated rating of 1498; from the
>MLE calculations shown on the web page we get 1478. This

>disagreement is well within the margin of error.

More than close enough for me and nothing next to
the "discrepency" that had emerged from my wrong
figures. As my numbers were coming out drasticly
different than even what I would expect, I had
started to wonder if the analysys I was trying to
do made any sense at all. I was trying to derive
a rating for Abbott based on its opponents ratings
but we don't know how those players had attained
their ratings (i.e. were they mostly multi-point
match players who happen to play occasional 1-pt
matches against others including Abbott, or were
they 1-pointers especially seeking to play against
players like Abbott)? Am I wrong to think that this
process may get highly circular and produce skewed
results beyond satandard/acceptable...?

>> BTW, looking at the "wwllwll..." sequences that you
>> looking at the log of those 1000 matches by just
>> scrolling it up and down for a few minutes, I had
>> come to the conclusion (which I posted in response
>> to your article) that Abbott had lost a lot of its
>> games to much higher rated opponents and that it had
>> done better than expected overall. It looks like a
>> more careful examination of that log confirms what
>> I had quickly observed then.

>I don't understand what you mean here. Losing games to much
>higher rated opponents is surely nothing more than we would
>expect? And I see no evidence that it has done better than
>expected overall, either in the 1000 game sample here or the
>larger sample categorised by opponent strength on the web page.

My mistaking 53% vs 46% win rates led me to attempt
such a link; but even without this error it would be
a meaningless thing to say anyway because the context
was different. As oppesed to this time, at that time
I was focusing on Abbott's losses and your "wwllwll..."
sequence was in front of me then, and I had the "w"s
and "l"s straight. The point then was that Abbott had
won almost just as much against stronger players than
it lost to weaker players, and that there was no signs
of constantly huge/long series of losses that could be
called "loosing streaks" (and/or related to opponents'
streghts at the same time). Ignoring players with less
than 400 experience this time is another thing that
makes such a link/comparison meaningless also. Doing
the same might have well led to different clustering
of "l"s and "w"s at that time also. In short, never
mind that last paragraph...

MK

### Murat Kalinyaprak

Oct 22, 1998, 3:00:00â€¯AM10/22/98
to
In <wt90i9a...@brigantine.CS.Arizona.EDU> Gary Wong wrote:

>Jim Williams <ji...@giga-net.com> writes:

>> that if we want to make backgammon more a game of skill and less
>> a game of luck, we should eliminate the doubling cube.

>Oh dear, them's fighting words ;-) My OPINION (I won't attempt to
>substantiate this) is that the cube can add a significant amount of
>skill to the game by creating the opportunity for costly cube errors
>(which will naturally tend to be made more often by less skilled
>players).

Am I the only one actually trying to substantiate my
view on the cube, at the expense of compromizing my
potentially higher/precious :) FIBS rating...? Where
are all the other Turks/Greeks/Armenians/Iranians/etc.
who would assumendly have stronger checker player and
weaker cube skills, to tell us about their experiences
and opinions on this subject...?

What I'm doing on this is different than my saying
that I beat JF in my living room, at which you would
have to take or not take my word for it. This time
it's all happening on the FIBS and in the open. Since
I'm making the effort there, let me also tell a little

1- My current experience is reaching 1300 and after
the first 100 or so games, I have been playing 5 point
cubeful matches almost exclusively.

2- Although I don't feel good about rejecting invitations
from lower rated players, for at least the last 700-800
games I have almost exclusively played against higher
rated players, just to avoid arguments about my picking
on lesser players. Despite my rating not going up and
getting any closer to theirs, it seems like it's getting
easier and easier for me to get matches with higher rated
players (maybe because they remember/recognise my name
more).

3- I refuse to read up on using the cube and learn to
compute probabilities, etc. Occasionally I ask feedback
from my opponents (after the fact of course:) on how I
did with my doubling or taking the cube. But all I want
to hear back is whether I did right or wrong. Although I
appreciate if they try to get detailed with numbers, etc.
I either don't understand or not even try to understand
those details. The intent in this is to validate that I
can indeed do quite well with the cube if I try hard
enough (even if based on my own criteria) and that when
I do a bad take I'm most likely doing it knowingly.

4- When I try to use the cube "right", it's based on
mostly nothing more than what I would base my checker
play on (i.e. a much simpler/casual observation on how
the board "looks" at what stage in the game, etc.) Its
only the magnitude of the consequences are different
(i.e. taking a chance with leaving blots is much less
risky than losing more points after a bad take). When
I use the cube "knowingly wrong" it's based on the same
criteria also (i.e. based on probably sound criteria but
for the wrong reason of stubbornly going against it)...

5- I may be considering the match score much more than
what other players would perhaps do, but not necessarily
claiming that I do it right, and only in certain cases.
For example, if one doubles when I'm 3-0 or 3-1 ahead,
I'll most likely take unless things look really bad. My
reasoning is that, if he looks like he's kind of winning
anyway, giving an extra free point doesn't worry me next
to the possibility that with things turning around by a
little bit I may win the match. I may do the same at 3-2
although more conservatively but still surely way too
often to be considered right.

6- Occasionally I get comments back that indicate a little
wrong cube decisions and ended up winning anyway. I also
wonder if I'm getting repeat matches beacause the other
players want to prove back to me that their way is indeed
right and that in the long run I'll be the loser with my
current attitude/approach.

7- My rating is still staying around 1670's or so and
not taking a dive as of yet...

What I'm doing must certainly be visible to at least some
players who played against me and the result is visible
also. There must be something little that one can deduct
from all this, isn't there...?

>however, in matches of constant _time_, I suspect (hope? :-) that
>cubeful games will be more skillful. In the time that it takes to
>play a 15-point match, you might only be able to fit in (say) a
>5-point cubeless, gammonless match. My guess is that the cubeful
>match is a better test of skill. Whether it is or not, I also
>believe it's the most interesting.

Can I argue the exact opposite?:) Remember our recent
match where we kept doubling as the game turned around
time and again incredibly, to finally end with 1 pip
difference? The cube was just sitting next to the board,
while the dice and checkers were doing all the trick,
which we both had found interesting. If we were playing
for money, at a much earlier stage either one of us would
have had too many butterflies in the stomach in proportion
to dollar bills in the pocket and would have dropped.
Then we would have never seen the rest of the interesting
going on because it wasn't even a rated match which would
cost FIBS rating points).

The most boring part of any game is the beginning where
opening moves are made almost roboticly, etc. Often it
only gets interesting much later in the game. Too many
games never get past that boring early stages because
of the cube... So, talking about constant time vs match
length, with the cube one would end up playing 15 short,
less interesting games vs. 5 long more interesting ones.
I see it as a matter of quantity vs. quality. I think
cube adds much less to the game or even takes away from
it when played as a pass-time than when played for points
or money. Also, based on my own experiments, I'm coming
to believe more and more that the effect of the cube can
be dampened/neutralized to a much greater extent that
one may expect (although certainly not completely)...

MK

### EdmondT

Oct 22, 1998, 3:00:00â€¯AM10/22/98
to
>>Jim Williams <ji...@giga-net.com> writes:
>
>>> that if we want to make backgammon more a game of skill and less
>>> a game of luck, we should eliminate the doubling cube.
>

I've said before that I am Armenian, have been playing since I was 9, and my
father, who is 86 is just a terrific BG player. He and his friends play
without the cube, and generally play 5 game matches for a buck a game. Gammons
count, backgammons are meaningless. The winner of the original dice throw
picks up the dice and throws them again for the opening roll.

He and the folks he plays with don't consider the cube part of the game. As a
result, having "skill" in the cube is not something they think is part of BG
skill.

It seems to me that this is the point. There is no question that cube
decisions involve skill -- but if you are a player who is used to playing
without the cube, that skill doesn't seem like its a skill associated with the
game, but rather an outside skill that affects the game.

### Murat Kalinyaprak

Oct 23, 1998, 3:00:00â€¯AM10/23/98
to
In <19981022073836...@ng143.aol.com> EdmondT wrote:

>>>Jim Williams <ji...@giga-net.com> writes:

>>>> that if we want to make backgammon more a game of skill and
>>>> less a game of luck, we should eliminate the doubling cube.

>It seems to me that this is the point. There is no question

>that cube decisions involve skill -- but if you are a player
>who is used to playing without the cube, that skill doesn't
>seem like its a skill associated with the game, but rather
>an outside skill that affects the game.

This is well said and may need a slight clarification
that the effect it has on the game doesn't really alter
how the game is played but rather how the score is kept.

I hope nobody will say that given a certain board and
a dice roll, they would play differently based on the
current value of the cube, etc. We know that the much
worshipped robots don't do that...

In a world where people gamble on whose frog will jump
farther, it's no wonder that bg is used as a gambling
tool and the cube is not much more than the primitive
stake-jacking practice of "double or nothing", which
may predate the invention of the wheel. The cube could
be and is indeed used in many other games. If a couple
of scientists could concoct some formulas to calculate
the odds, equity, etc. in it, we could even talk about
how much skill it would take to use a cube in multi-hop
frog jumping contests...

The argument that cube skill has nothing to do with
what is/should be called "backgammon" could be shown
by the fact that people can use the cube in relation
to bg without even having the least bit of knowledge
about playing bg. Joe and I could sit in a room and
"play cube" based on a match being played by two bg
players playing in another room. All we would need is
for someone to calculate and report to us after each
move the numbers used in double/take/drop decisions.
Even with as little knowledge about the cube as having
a little cheat-sheet in our hand, (telling us what's
the appropriate action at which values), using those
numbers we could "skill the cube out of each other"
without knowing the "b" about "backgammon"...

During some past discussions, people had argued that
players with higher checker-play skills would reach
the cube point sooner and/or more often, etc. And I
had in return offered that I would be willing to play
(for FIBS points) any player higher rated than me who
would be willing to double invariably after "N" moves
during each game. The "N" here would be determined by
"predicting" how soon the more skilled player would
reach the cube point based on the difference in our
ratings. If no scientist can concoct a formula to make
such a prediction, I wouldn't care if they pulled some
number out of the air. So far nobody argued against me
on this nor has anybody taken me up on my offer.

I reserve the right to double back, but had kind of
hoped that someone would propose to limit me to always
take and never redouble (as this was part of a point I
wanted to drive home the point that in that case it
wouldn't matter if the doubling took place before the
first move, "N'th" move or the very last move... The
end result would have been nothing more than playing
cubeless and counting each point two instead of one...

Certainly there must be lots of players on FIBS with
stronger checker-player skills than mine. Since the
argument had included the claim that they would reach
the cube point "more often" (i.e. >50% of the time),
they should have nothing to lose but much to gain. So,
I was a little disappointed that nobody volunteered to
participate in this potentially fun experiment...

Way back when, some people had even claimed that if
they had ran into me on a train and didn't know my
name (and/or my face), they would feel confident that
they could beat me. Where are they to miss out on such
a chance to rake up FIBS points two by two, (and dunk
my rating)...? I'm still willing to pay the price in
precious FIBS points, if anybody is willing to try to
show me that backgammon (checker-play) skill and cube
skill are in any way linked at all...

MK

### Mel Rappaport

Oct 23, 1998, 3:00:00â€¯AM10/23/98
to
Murat Kalinyaprak wrote:

> I hope nobody will say that given a certain board and
> a dice roll, they would play differently based on the
> current value of the cube, etc. We know that the much
> worshipped robots don't do that...

I do that ALL THE TIME. I play matches with the cube in play.
Whether ahead or behind or even VASTLY affects my style.
I may be wrong, but I play very risky when a lot behind,
and very conservatively when a lot ahead, with lots of
gradations in between. In bridge, this is called swinging,
or anto-swinging , as the case may be. -12,-6 with the
cube at 1 is vastly different with the cube at 4 and even
different than the cube at 8 and that different when the
cube is at 16.

> The argument that cube skill has nothing to do with
> what is/should be called "backgammon" could be shown
> by the fact that people can use the cube in relation
> to bg without even having the least bit of knowledge
> about playing bg. Joe and I could sit in a room and
> "play cube" based on a match being played by two bg
> players playing in another room. All we would need is
> for someone to calculate and report to us after each
> move the numbers used in double/take/drop decisions.

Using that strategy, we can all make billions every week.
All we need is someone else to calculate and report the
true value of a a stock versus it's market price and we
will manage how much to invest.

Pardon the satire. The correct assessment of the
outcome of a position is a very difficult skill. The
selection of a choice of moves from all legal moves
is a DIFFERENT very difficult skill. What you propose is
two people can read multiplication tables, or log
tables, ... and can play at calculating. What you imply
is that doing elementary calculations is the same as
combining the net outcome of trillions (or sometimes 36)
outcomes for a given position.

> And I
> had in return offered that I would be willing to play
> (for FIBS points) any player higher rated than me who
> would be willing to double invariably after "N" moves
> during each game. The "N" here would be determined by
> "predicting" how soon the more skilled player would
> reach the cube point based on the difference in our
> ratings. If no scientist can concoct a formula to make
> such a prediction, I wouldn't care if they pulled some
> number out of the air.

As I am wont to say when I pontificate on mathematics,
you are mixing apples with grey.

My algorithm goes:
BEGIN
At every turn that I may cube,
before I roll,
Assess the "Net value" of all possible outcomes of
the current position, if I don't double.
Assess the "Net value" of all possible outcomes of
the current position, if I do. double.
Choose the higher "Net Value:

Comment: No mention of move number appears.

Subroutine Assess(Returns Net Value)
<Body>
END

The same position can occur 6 or 12 or 2000000
rolls after the game starts. Why is it better or worse.
You invented a metric (always good) of length from opening.
You argued (this time questionable) that net value monotonically
increases with increase in your metric. You attached a
decision test to that metric
to prove or disprove your argument (always double at
move N even if you are way behind and will drop the
redouble the next roll). The marketplace implicitly voted
on your argument, 2750 to 0, that you are wrong. Now
is the time to either re-market your invention, or replace it.

Good luck!

### EdmondT

Oct 23, 1998, 3:00:00â€¯AM10/23/98
to
>Murat Kalinyaprak wrote:
>
>> I hope nobody will say that given a certain board and
>> a dice roll, they would play differently based on the
>> current value of the cube, etc.

I doubt there are many people who play the same way regardless of the score.

Oct 23, 1998, 3:00:00â€¯AM10/23/98
to

Murat Kalinyaprak <mu...@cyberport.net> wrote:
>I hope nobody will say that given a certain board and
>a dice roll, they would play differently based on the
>current value of the cube, etc. We know that the much
>worshipped robots don't do that...

In money play I don't play differently based on the value of the cube,
except perhaps doubled/undoubled for Jacoby considerations. But I do
play a lot differently based on *ownership* of the cube. That's a
perfectly normal part of backgammon.

In match play, the value of the cube and the match score factor into
my plays.

-Patti
--
pat...@netcom.com/pat...@gammon.com |
http://www.gammon.com/ | "I trust you. It's just
or just yell, "Hey, Patti!" | that I'm scared of you."

### Murat Kalinyaprak

Oct 24, 1998, 3:00:00â€¯AM10/24/98
to
In <19981023142220...@ng38.aol.com> EdmondT wrote:

>>Murat Kalinyaprak wrote:

>>> I hope nobody will say that given a certain board and
>>> a dice roll, they would play differently based on the
>>> current value of the cube, etc. We know that the much
>>> worshipped robots don't do that...

> I doubt there are many people who play the same way
> regardless of the score.

I agree but I wasn't equating cube value with score.
In a cubeless 5 point match, if I'm ahead 4-0, I may
play much more relaxed than if I'm behind by 0-4. In
a 5 point cubeful match if the cube has already gone
up to 4 in the second game with me being 0-1 behind,
I would feel the same pressure but I would still see
this as a matter of score, because I can find myself
in that position with or without the cube (i.e. it's
not exclusively a consequence of using the cube)...

BTW: those robots are said to play differently based
on score (match length) also; there would be nothing
to contrast between them and humans on that...

MK

### Murat Kalinyaprak

Oct 24, 1998, 3:00:00â€¯AM10/24/98
to

>>I hope nobody will say that given a certain board and
>>a dice roll, they would play differently based on the
>>current value of the cube, etc. We know that the much
>>worshipped robots don't do that...

>In money play I don't play differently based on the

>value of the cube, except perhaps doubled/undoubled
>for Jacoby considerations.

Jacoby who...? :) This goes above my head, so I'll
skip...

>But I do play a lot differently based on *ownership* of
>the cube. That's a perfectly normal part of backgammon.

There may be something for me to learn here. Would
you or anybody else care to illustrate this with a
couple of examples...?

>In match play, the value of the cube and the match
>score factor into my plays.

As I myself do it, I have no doubt that others play
differently based on the score. However, within this
context the value of the cube is not an independent
factor. One can look at the cube value as already
lost points plus 1. For example, if the cube is at
4 in a 9 point match and you are 3-5 behind (or 5-3
ahead), you could look at it as though the cube was
at 1 and you were 3-8 behind (or 8-3 ahead)...

I chose these numbers so that ownership of the cube
doesn't get mixed in the same argument. If the score
in my example was 1-3 (or 3-1), then by your above
statement ownership of the cube may be an additional
factor effecting one's play(??) [hopefully I'll get
to see some examples on this]

MK

### Murat Kalinyaprak

Oct 24, 1998, 3:00:00â€¯AM10/24/98
to
In <3630B1...@mail.beehive.com> m...@bernstein.com wrote:

>Murat Kalinyaprak wrote:

>> I hope nobody will say that given a certain board and
>> a dice roll, they would play differently based on the
>> current value of the cube, etc. We know that the much
>> worshipped robots don't do that...

>I do that ALL THE TIME. I play matches with the cube in play.
>Whether ahead or behind or even VASTLY affects my style....

Sorry for all the confusion my saying "current
value of the cube" may have caused. What I'm
after, is a factor that exists only because of
the cube. My difficulty is in trying to name
something which I don't even know if it exists.
The effect of score (i.e. being ahead, behind,
even, etc.) is there whether using the cube or
not. One reader mentioned "ownership of cube"
as something causing her to play differently.
That's the sort of things I'm looking for...

>> had in return offered that I would be willing to play
>> (for FIBS points) any player higher rated than me who
>> would be willing to double invariably after "N" moves
>> during each game. The "N" here would be determined by
>> "predicting" how soon the more skilled player would
>> reach the cube point based on the difference in our
>> ratings. If no scientist can concoct a formula to make
>> such a prediction, I wouldn't care if they pulled some
>> number out of the air.

>As I am wont to say when I pontificate on mathematics,
>you are mixing apples with grey.

Just for you and anyone else who may be missing
the point, let me try one more time:

I previously argued that the cube amplifies the
luck factor. Others argued back that it doesn't
because the more skilled player would get to the
cube point with or without luck (i.e. by skill),
and that he would get there sooner and more often
than the less skilled played. I hope this is all
clear to everybody so far...?

"More often" simply means "at least more than 50%
of the time". There should be no problem with it
as it must be easy enough for anyone to understand.
"Sooner" however, lead to questions like "when",
"how soon", etc. Now let's work this through your
algorithm...

>My algorithm goes:
>BEGIN
>At every turn that I may cube,
>before I roll,

>Assess the "Net value" of all possible.......

At the beginning of a game you roll 53, then 22,
then 66, and hit two pieces of your opponent on
top of that. Your algorithm goes bananas: "Beep!
Beep! Double! Double!"....

If that happened, I'd say you got lucky and that
the cube allows you to capitalize on it. I may
also go further on to say that nobody can show
enough skill to reach cube point after only 3 or
6 or "N" moves unless he gets lucky. This isn't
the end of it either. I'll go on to say stronger
stuff further down...

>to prove or disprove your argument (always double at
>move N even if you are way behind and will drop the
>redouble the next roll).

A player rated at 2000 may reach cube point more
often and/sooner against a player rated at 1200,
but after a certain point (let's use my rating
of around 1670) just skill alone will not get
anybody to cube point more often and/or sooner
against his opponent, unless ge gets lucky, no
matter at what stage of a game...! Never...

>The marketplace implicitly voted on your argument,
>2750 to 0, that you are wrong. Now is the time to
>either re-market your invention, or replace it.

"Implicitly voted" meaning nobody argued back or
took me up on my offer...? Here is my conclusion:
the marketplace is made up of a mixture of people
of which some don't even have a clue as to what
I'm talking about, some agree with me and have no
reason to argue against me, some no longer argues
because they changed opinions and some who continue
to argue against me but can't put essence behind
their argument...

Here is my challenge to you all: Determine on your
own by whatever method or formula and come tell me
how many moves would it take for your skill to
start showing in a game at a sufficient degree to
overcome mine and reach the so called "cube point"
on the average. Then comit to playing "X" number
of matches against me, where you will consistently
double after that many moves in each game...

There is nothing special about me in this argument.
I believe that many other players could (and I wish
some joined in to do) make the same offer to anyone
within maybe 300(??) points of their ratings. As I
do, the ones with about 1700 rating should be able
to make a blanket offer to all players on FIBS since
the highest ratings go only to about 2000. I picked
300 (i.e. about 1950-my rating) because I played
such higher rated players (and observed) enough
times to feel fairly confident that most (if not
all) of them wouldn't take me up on this...

Of course, there is no guarantee that the reality
may turn out different than what I predict but I'm
not affraid to find out... Hey, what do we all have
to lose other than some FIBS points...? :)

MK

### Murat Kalinyaprak

Oct 26, 1998, 3:00:00â€¯AM10/26/98
to
Reposted due to recent spam problem...

In <19981023142220...@ng38.aol.com> EdmondT wrote:

>>Murat Kalinyaprak wrote:

>>> I hope nobody will say that given a certain board and
>>> a dice roll, they would play differently based on the
>>> current value of the cube, etc. We know that the much
>>> worshipped robots don't do that...

> I doubt there are many people who play the same way

### Murat Kalinyaprak

Oct 26, 1998, 3:00:00â€¯AM10/26/98
to
Reposted due recent spam problem...

>>I hope nobody will say that given a certain board and
>>a dice roll, they would play differently based on the
>>current value of the cube, etc. We know that the much
>>worshipped robots don't do that...

>In money play I don't play differently based on the

### Murat Kalinyaprak

Oct 26, 1998, 3:00:00â€¯AM10/26/98
to
Reposted due recent spam problem...

In <3630B1...@mail.beehive.com> m...@bernstein.com wrote:

>Murat Kalinyaprak wrote:

>> I hope nobody will say that given a certain board and
>> a dice roll, they would play differently based on the
>> current value of the cube, etc. We know that the much
>> worshipped robots don't do that...

>I do that ALL THE TIME. I play matches with the cube in play.

Oct 27, 1998, 3:00:00â€¯AM10/27/98
to

Murat Kalinyaprak <mu...@cyberport.net> wrote:
>Jacoby who...? :) This goes above my head, so I'll
>skip...

The Jacoby rule is nearly always used in money play. It says that
gammons and backgammons don't count unless the cube has been turned.

The reason is to speed the game up... it prevents someone from playing
out a position rather than cashing when he has a slight chance of
winning a gammon, and no chance whatsoever of losing.

-Patti
--
http://www.gammon.com/ | junkie software geek leatherbyke
or just yell, "Hey, Patti!" | nethead biker.

### Murat Kalinyaprak

Oct 29, 1998, 3:00:00â€¯AM10/29/98
to

> Murat Kalinyaprak wrote:

>>Jacoby who...? :) This goes above my head, so I'll skip...

> The Jacoby rule is nearly always used in money play. It
> says that gammons and backgammons don't count unless the
> cube has been turned. The reason is to speed the game up...
> it prevents someone from playing out a position rather
> than cashing when he has a slight chance of winning a
> gammon, and no chance whatsoever of losing.

Patti, thanks for explaining these. I was also
wishing for a couple of examples on how you play
"a lot differently" based on ownership of cube.
Oh well. Maybe it's your secret weapon that you
don't want your opponents to know...

Does anybody else play differently based on cube
ownership? If they do and don't consider it their
trade secret, I would appreciate a few examples
on how they play even "a little" if not "a lot"
differently based on cube ownership...

Let me also take this opportunity to offer a more
watered down challenge on cube usage.

I recognize that it may be difficult to concoct a
formula to predict how much sooner a more skilled
player will roll a joker (i.e. reach cube point:)
based on rating differences and this may be what
makes it difficult for anyone to take me up on my
offer...

So, I came up with an alternative challenge which
won't require such a formula (although it will be
much more disadvantageous for me). Here it is:

and I will play "X" number of "N" point matches.
You may double whenever you wish. But after you
double, I'll have these options.

- I may decide to take or drop at that point or
have the option to postpone my decision until
after the next roll. If I elect to postpone it
by one roll, consequences of my decision will
the same as in regular cubed play after that.
If I decide to make a decision right then, I'll
have the following choices:

a-If I decide to drop, nothing else is different.

b-If I take, you will take back your last move,
roll the dice again and we'll proceed normally
as in regular cube play from then on.

I believe this challenge is reasonable because
unless reaching cube point sooner means who'll
roll 66 first, it has to imply the more skilled
player will get to that point progressively...

Since the argument against me is that the cube
doesn't magnify the luck factor, once the more
skilled player reaches the stage one prior to
cube point, whether he rolls a 21, 43, 55 or 66
shouldn't really matter to the degree of making
or braking, should it...? Neither postponing my
decision by one turn should hurt since hopefully
a more skilled player will not run out of skill
in just one more turn...

If you guys think that I dream up stuff like
this in my sleep, you could be wrong. Although
I don't participate in them, I do quietly read
market, etc. which are full of better arguments
than mine to show that cube play is based on and
magnifies the luck factor. When the next day you
argue to the contrary, I basically take your own
arguments, throw them back at you in different
words and you don't know what to do with it...

So, we'll see if there will be any takers now...

MK

### Michael J Zehr

Oct 30, 1998, 3:00:00â€¯AM10/30/98
to
In article <363924...@cyberport.net>,

Murat Kalinyaprak <mu...@cyberport.net> wrote:
>So, I came up with an alternative challenge which
>won't require such a formula (although it will be
>much more disadvantageous for me). Here it is:
>
>and I will play "X" number of "N" point matches.
>You may double whenever you wish. But after you
>double, I'll have these options.
>
>- I may decide to take or drop at that point or
> have the option to postpone my decision until
> after the next roll. If I elect to postpone it
> by one roll, consequences of my decision will
> the same as in regular cubed play after that.
> If I decide to make a decision right then, I'll
> have the following choices:
>
>a-If I decide to drop, nothing else is different.
>
>b-If I take, you will take back your last move,
> roll the dice again and we'll proceed normally
> as in regular cube play from then on.
>

Can you explain this more clearly? I'm especially wondering about when
"right then" is and whether you really mean "one roll" or you mean a
turn by both players.

Here's the interpretation that makes the most sense to me:
I roll and move, you roll and move.
I double. You can drop and I win the value of the cube.
You can delay -- I roll and move, then you decide if you want to drop or
take.
Or you can take immediately and we both take back our last moves and
then I roll and play continues.

This looks like it's as much of an edge for you as your previous
challenge, which involved requiring the stronger player to spot you the
cube.

I can't double right after rolling a market losing sequence, since you
can take and make me take back the market losing sequence (essentially
force me to have doubled last turn when I had already decided not to).

I can't take hoping to roll a market losing sequence because you'll
delay and then if I roll the market loser you'll drop (essentially
forcing me to wait a turn to double).

I don't see how giving one player a big advantage with the cube proves
whether the cube magnifies skill or luck. If you really wanted to prove
it you'd take two players of unequal strength and have them play a long
series of games against each other, both with and without the cube, and
analyze the results. Here's one way of analyzing the results:

Play N games both with and without the cube. Don't use the Jacoby rule
for either set of games to minimize any variance caused by it. Count
the total number of points won or lost (total, not net, i.e. it must be
>= N for each set). Assuming the stronger player ended up with a net
positive for both sessions, divide the cubeful points by the cubeless
point to get the actual cube ratio. Divide the total points won or lost
with the cube with the total points on or lost without the cube to get
the theoretical cube ratio. If the actual is greater than the
theoretical, then the cube magnifies skill, otherwise it magnifies luck.

To get statistically valid answers, N might have to be very large, or
the experiement might have to be repeated many times. A statistican
could quantify this for you.

(Here's my theory for why the cube will magnify skill instead of luck:
the games that end with a drop of an initial double will on average have
fewer rolls in them than games in which the initial double is taken.
Since luck tends to average out over time, and skill tends to compound
over time, the longer games favor the more skillful player. So it's
more likely that luck evens out and skill decides the games that have a
higher cube value, and more likely the skill doesn't have many chances
to change the result and luck determines the games that are worth less.)

-Michael J. Zehr

### Murat Kalinyaprak

Oct 31, 1998, 3:00:00â€¯AM10/31/98
to
In <71bnf1\$m...@senator-bedfellow.MIT.EDU> Michael J Zehr wrote:

>In <363924...@cyberport.net> Murat Kalinyaprak wrote:

>Here's the interpretation that makes the most sense to me:
>I roll and move, you roll and move.
>I double. You can drop and I win the value of the cube.
>You can delay -- I roll and move, then you decide if you
>want to drop or take.
>Or you can take immediately and we both take back our
>last moves and then I roll and play continues.

Yes, despite the deficiency in my explaining it, you
interpreted it all correctly.

>This looks like it's as much of an edge for you as your
>previous challenge, which involved requiring the stronger
>player to spot you the cube.

You mean right after the first roll? If so, I would
agree with you. This is a loophole in my challenge,
which I would have to live with, if anybody went as
far to claim that he can show enough skill to reach
the cube point in a single roll/move... :)

In that case, I would suggest that we play 10+ point
matches, always take, never double back and thus turn
it effectively into a cubeless match where simply the
points are counted two by two. This would really work
against me but it would be the best thing I could do
lessen the damage...

Other than this possible situation, I'm not sure if
this modified challenge gives me as much of an edge
as where the stronger player would have to double at
a predetermined number of moves like 10, 15, 20, etc.
Whether I postpone my take/drop decision or make the
stronger player back up by one move, I think he would
still be in somewhat of a better position than having
to double in situations like having 3 men on the bar,
trying to get into a 5-point board, etc.

Actually, I was hoping that somebody would claim that
"N" could be calculated based on *probability* (using
a formula which would divide the rating difference by
the square root of match length and multiplying it by
pi, etc. :) Then, like Jacoby's, John's, Joe's rules,
I was going to propose a "Murat's rule" which would
say that (for the initial doubling) a player has to
wait until after "N" or has to double before "N" (or
loose his right to initial double during that game),
depending on whether we would want to give an edge to
the stronger or the weaker player... :)

>I can't double right after rolling a market losing sequence,
>since you can take and make me take back the market losing
>sequence (essentially force me to have doubled last turn when

I don't think you would want to double after losing
your market for the exact opposite reason, which is
that I wouldn't make you take your roll/move back
but let you live with it instead...

>I can't take hoping to roll a market losing sequence because
>you'll delay and then if I roll the market loser you'll drop
>(essentially forcing me to wait a turn to double).

I assume you mistyped when you said "I can't take"
because the rules don't effect you taking/dropping
decisions at all. But if I understant it corrently,
you're right. The option to "delay my decision" is
there to prevent you from constantly waiting one
additional turn to double. Otherwise, sometimes you
would lose your market and miss a doubling chance
but at least you wouldn't be forced to make a bad
(retroactively) double .

I realize the rules are harsh from a cube player's
point of view but they are necessary in an argument
about skill vs. one single lucky roll...

>I don't see how giving one player a big advantage with the
>cube proves whether the cube magnifies skill or luck.

Can you look at it as "not giving a big advantage"
to one player but as "taking away the big advantage
a single roll may give" to one player...?

If a player rated 300 points below me dared me to
play a number of 5-point matches without the cube,
where he would get one chance per game to make me

If taking away one lucky roll from the more skilled
player will ruin him, I would suspect his skill...

>Play N games both with and without the cube...... Divide

>the total points won or lost with the cube with the total
>points on or lost without the cube to get the theoretical
>cube ratio. If the actual is greater than the theoretical,
>then the cube magnifies skill, otherwise it magnifies luck.

I'll have to take time to digest this proposition
before I make any comments on it but it may very
well be one way of going about it.

>(Here's my theory for why the cube will magnify skill instead
>of luck: the games that end with a drop of an initial double
>will on average have fewer rolls in them than games in which
>the initial double is taken. Since luck tends to average out
>over time, and skill tends to compound over time, the longer
>games favor the more skillful player. So it's more likely
>that luck evens out and skill decides the games that have a
>higher cube value, and more likely the skill doesn't have many
>chances to change the result and luck determines the games
>that are worth less.)

I don't agree that higher cube value (past 2) means
necessarily longer game but I agree with your first
comment that if the initial cube is taken and the
game is played out, it should favor the stronger
player. Or the initial cube may come very late in
a long game. The key is that the game be long...

In fact, this is at the heart of my argument and I'm
experimenting with it while playing on FIBS. If you
have seen them, I have been writing about my taking
especially early cubes based on nothing more than
how much time left for checker play in a game. And
I'm doing this not against lower but higher rated
players than me. My rating hasn't reached theirs to
make a claim that I'm a better overall player (i.e.
checker+cube play) but I'm able to sustain a rating
at about 1700 so far. The fact that an overall lower
rated player can stand his ground against even higher
rated ones despite "bad takes" should be indication
of something, shouldn't it...?

cube taken lasting longer than dropped games, can be
ultimately taken to the argument that cubeless games
are the longest lasting ones yet... I had taken the
argument to that extent previously. Could it be that
without realising you are agreeing with me on cubeless
plays allowing one's skill to come out more, simply
because they last longer and skill wins over luck in
the long run...?

MK

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