AUCTION GO - followups.
Bill Taylor
Hello all; go-lovers and mudslingers alike! ;-)
I've collected up the last batch of Auction-Go comments that seem to need
responses. If I've overlooked something, apologies, and please ask again.
__________
|im |yler writes...
>If you were watching a game of auction go between two players using fractional
>bids who are both out to win and they make fractional bids, then the
>additional quantity of information you obtain from looking at their fractions
>as opposed to whatever integer value this increases their score to is
>precicely zero.
A rather big claim, made in your usual style, but it contains a valid point.
If there *were* some informational advantage to be gained from watching
auction go with fractional bids allowed, it should be possible to come
up with a fairly simple example. Maybe? Bill S - howbout it?
>OTOH, I don't think fractional bids detract particularly, either.
I think they're rather messy. And also suffer from the charge of
"building the results into the theory". They also have the disadvantage of
either infinitesimal-drawishness, or an articifial cutoff.
> > (Or half-integers in our case, to avoid ties.)
>You guys always seem to have really got it in for ties.
It *does* look that way! Actually, I'm for *increasing* the number of
ties at regular go, as my posts on "thick komi" pursue. However, for
an essentially academic game such as this, it's probably better to
cut them out as much as possible.
>I can't see /why/ you would give one side an advantage in the way
>in which you seem to be proposing ;-)
You make it sound like we're giving some *particular* side an advantage;
like black in standard go, or white in standard go with a 30-point komi.
No. Quite the reverse. We're after player-symmetry as a main goal.
As we keep observing, PERFECT play will give no advantage - both will
pass at the very start. But in practise, someone's bound to bid at
least one point, (bound to be a bargian!), and as no-one has much of
a clue as to the optimum price at the start, there's no practical
disadvantage. You seem to be flogging a dead horse on this one!
____
Thanks for your comments anyway |im.
--------
From: bills...@aol.com (BillSpight)
> I got the impression that indeed you intended to apply numerical values
>to board positions in Auction Go.
Yes, that would be nice. So far, it's been possible; but there is no
guarantee that that will continue. And saddest of all, there's no real
hope that they can be added together, CBG style. But then, even much
simpler hot games can't really be either - only number-value games
can be perfectly added. (i.e. very cold games)
>I agree that doing so is problematical.
Good, that's one area of agreement then! ;-)
>On the 3x3, for instance, this position
. X .
O X X
. O .
>does not seem to me to have an obvious sensible numerical value, at this point.
I *will* get around to it, eventually! Both a mean value and an auction value.
> In fact, I got the impression that one of the reasons for Auction Go was
> to have a game which demonstrated the validity of such values... ...Was I
> mistaken about your intentions?
Well, motives are usually mixed. To begin with, I was simply under the
enchantment of John Tromp's simple idea of always bidding. And yes, it
seemed to offer the prospect of an extra handle on numerical values; it
still does, but it's clearly not as simple as we may have hoped. And then
finally, after doing quite a bit of investigation, I was struck by, AMAZED by,
how much NEATER one variant was, over the rest which had very messy results.
The neat variant was published - half-point accounts, richer player bids 1st.
>Auction Go does not appear to be a combinatorial game.
I think you went back and forth on this, over several posts.
Is the above still your view? It is mine, at the mo.
Now to specifics. There is at least ONE major blunder I made in passing,
without having given it enough thought. It is certainly true, as you
observed and exemplified, that the "richer names the move price" version
is NOT the same as the true auction versions.
Indeed, one can give *extremely* simple examples...
*
/ \ the rest of the board is finished, and is even.
/ \
b4 b1 White has 2.5 in the bank.
In the auction version, white bids 1; and wins whether black
accepts, or bids 2. First-bid is a BIG advantage indeed!
In the set-price version, white loses; whether he sets the
price at either 1 or 2. Interesting. Where does justice lie?! ;-)
I have a followup question though:-
Is it true that the English-auction version and the Dutch-auction version
have (theoretically) identical optimal outcomes for every position?
My guess is YES; but I've been bitten too often, to insist on it yet!
--------
> I am also interested in hearing what satguru BT has to say about them.
"Satguru"? What's a satguru? Anyway, Barry's positions...
From: Barry Phease <bar...@es.co.nz>
>I find this idea of Auction go very interesting,
Good!
> but hard to follow.
In what way? Do you mean, hard to follow the rules, or hard to see
what determines the optimal outcomes and values? Or yet other?
Top-left of boards shown; Barry's positions:-
. O O
X X O value = 0, temp = 1. Correct bid = 1, Auction go result = 0
. X O
Yes; this is unswervingly zero at auction go. A true dame!
O O O
. X O
. X O value = 1, temp = 1. Correct bid = 1.5, Auction go result = 0.5
X X O
. X O
X X O
Well, one can't make a fractional bid, (this isn't the starting position!)
But the value is correct as a mean value:
If O gets to bid first, he should bid 1, and the result is 0.
If X gets to bid first, he should bid 1, and the result is 1 (to X).
We might say: correct bid =1; value = 0.5 +/- 0.5 (bank account decides).
O O O
. X O
. X O
. X O
X X O
. X O
X X O
>value = 1.5, temperature = 1.5. Correct bid = 1.75, Auction go result = 1.25
This one is quite tricky!
I make it:- correct bid = 1; auction-value = 1.5 +/- 0.5
Bank account determines, but in a two-step way! Specifically:-
If X is ahead on accounts, he bids 1, and wins 2 more points.
If O is ahead enough to win two 1st-bids, he bids 1, black should
overbid 2, and black gains 1 point from the position.
If O is ahead by only 0.5, he bids 1, winning this move (for "quits"),
but loses the 2nd auction, thus losing one more point anyway.
With that done, I'll leave the last one as an exercise for the reader. ;-)
See y'all later,
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
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Darren Cook
Thanks for collecting together the recent comments on this thread.
I've not been following it closely so I'm probably about to say
something very stupid...
>Indeed, one can give *extremely* simple examples...
> *
> / \ the rest of the board is finished, and is even.
> / \
> b4 b1 White has 2.5 in the bank.
>In the auction version, white bids 1; and wins whether black
>accepts, or bids 2. First-bid is a BIG advantage indeed!
Why not let black bid 1 as well? If both players bid the same value,
then toss a coin to see who gets the points and who gets the move.
As an observer (wanting to learn a pro's opinion of the value of a
move):
If both players want to bid the same value then that value is
correct.
If one player bids 2 and the other bids 1, then it tells me the
correct value is 1 or 2, which is less useful.
'correct' assumes the pro's never make mistakes of course.
Re: first move. If I bid 20 for the privelege and my opponent bids 21,
then one of us is wrong, but I'm happier (I get 21 pts while in my
opinion the opponent has just played a 20pt move). Of course if he
thought the move was worth 23pts, he is happier, but sealed bids would
stop this kind of bluffing.
If we both bid 20 pts for the first move then we toss a coin to see
who plays and who gets the points. Both players get something they
perceive as being of equal value.
What do you think?
BillSpight
Dear Bill,
(and Tim and Barry, et al.):
>If there *were* some informational advantage to be gained from watching
>auction go with fractional bids allowed, it should be possible to come
>up with a fairly simple example. Maybe? Bill S - howbout it?
Well, I am not sure what Tim means by an informational advantage. That is
why I suggested that the player who can bid fractions has a play advantage over
a player who cannot. A play advantage is easy to understasnd. <s>
>And [fractional bids] also suffer from the charge of
>"building the results into the theory".
Do you mean that someone might claim that just because a final result was
a fraction that the original position must have had a fractional value, and
that such a claim is unjustified? What about a different claim, that,
supposing that one player sets the price of a move, that it will never be wrong
to set the price at a certain fraction for a given board position? Is that
"building the results into the theory?" Or what about my claim, that allowing
a player to bid fractions gives him an advantage versus not being allowed to do
so?
>And saddest of all, there's no real
>hope that they can be added together, CBG style.
Not in any simple way such that if you add the board value to the bank
value you can predict the outcome of the game. That does not take into account
the bidder's advantage.
>>Auction Go does not appear to be a combinatorial game.
>
>I think you went back and forth on this, over several posts.
>Is the above still your view? It is mine, at the mo.
No, I changed my mind only once, when I realized that you could define
moves so that they alternate. Auction go is a combinatorial game. But since
who has the move depends on the bank balance, most positions are integers.
>Is it true that the English-auction version and the Dutch-auction version
>have (theoretically) identical optimal outcomes for every position?
>My guess is YES
Where I would look for a difference would be in potential draws. <s>
>"Satguru"? What's a satguru?
Teacher of truth, true teacher.
>> I got the impression that indeed you intended to apply numerical values
>>to board positions in Auction Go.
>
>Yes, that would be nice. So far, it's been possible; but there is no
>guarantee that that will continue.
Well, surely it is possible to bracket board positions between the winning
and losing bank accounts. And I do not see how you can get any more precise
values.
>And saddest of all, there's no real
>hope that they can be added together, CBG style. But then, even much
>simpler hot games can't really be either - only number-value games
>can be perfectly added. (i.e. very cold games)
But I expect that most, if not all positions (once we figure out how to
evaluate them) will add in the go theory sense. Such that, taking the
advantage of the bid into account, we can predict the outcome of the game with
perfect play.
I expect that if the value of the bid is 0, then, if the sum of the board
position and the bank balance favors one player, that player will not lose with
best play; at worst the game will be a draw. The only way I know to eliminate
the value of the bid is to use fractional bids.
Best,
Bill
BillSpight
Dear Darren,
> If both players want to bid the same value then that value is
>correct.
1) Both players may be wrong. <g> I suppose that you were assuming
correct bidding.
2) The bid may be correct, in the sense of being the best possible choice
of bids. But the value of the play may not be among the choices. Then the bid
cannot equal that value.
I submit that that is the case in Auction Go without fractional bids.
Best,
Bill
BillSpight
Dear Tim and Bill T.,
>>If you were watching a game of auction go between two players using
>fractional
>>bids who are both out to win and they make fractional bids, then the
>>additional quantity of information you obtain from looking at their
>fractions
>>as opposed to whatever integer value this increases their score to is
>>precicely zero.
>
Since Bill believes that you have a point, Tim, what is it? If I start
with 1 3/4 and end up with 2, then I have gained 1/4. Knowing the result gives
the same information as knowing the amount gained. I took it that that was all
you meant. Did you mean something more?
Best,
Bill
BillSpight
Dear Bill,
>In the auction version, white bids 1; and wins whether black
>accepts, or bids 2. First-bid is a BIG advantage indeed!
>
>In the set-price version, white loses; whether he sets the
>price at either 1 or 2. Interesting. Where does justice lie?! ;-)
Justice lies in fractional bids. <g>
Bill
Barry Phease
Bill Taylor wrote:
> O O O
> . X O
> . X O value = 1, temp = 1. Correct bid = 1.5, Auction go result = 0.5
> X X O
> . X O
> X X O
>
> Well, one can't make a fractional bid, (this isn't the starting position!)
> But the value is correct as a mean value:
>
> If O gets to bid first, he should bid 1, and the result is 0.
> If X gets to bid first, he should bid 1, and the result is 1 (to X).
If the correct mean value is not biddable then the bidding process is
all-important. This is disturbing to me. If the possibility of
infinitely long bidding is the problem then a tender process or cut and
choose makes people choose their best estimate in the first place.
--
Barry Phease
Bill Taylor
dar...@factcomm.NOSPAM.co.jp (Darren Cook) writes:
|> Thanks for collecting together the recent comments on this thread.
My pleasure!
|> >In the auction version, white bids 1; and wins whether black
|> >accepts, or bids 2. First-bid is a BIG advantage indeed!
|>
|> Why not let black bid 1 as well? If both players bid the same value,
|> then toss a coin to see who gets the points and who gets the move.
OUCH! Of course this could be done. But it would turn the game into
one with an element of chance, which is against all we go players, (indeed
abstract board players), stand for. ;-) Qua go players, that is.
An element of chance is even one step more than playing with incomplete
information, (hi Bill!) These elements take us over the line from
go-like games, (CBG style), and into poker-like games.
And it would be much nastier analyzing them as well. Ouch.
|> Re: first move. If I bid 20 for the privelege and my opponent bids 21,
|> then one of us is wrong, but I'm happier (I get 21 pts while in my
|> opinion the opponent has just played a 20pt move). Of course if he
|> thought the move was worth 23pts, he is happier, but sealed bids would
|> stop this kind of bluffing.
But just introduce another kind! Guesswork as to your opponent's
intentions is irremovable in any situation that could remotely be called
a game. It's almost part of the definition of the word! But there's no
need to build it into the systerm even further, with incomplete information,
(such as sealed bids).
Reasonable questions. You may disagree with the answers of course, but
that just means you want to play one of a different family of games.
No harm in that, but we should keep the distinctions clear.
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
God does not play dice with the universe, he plays Go.
God does not play dice with the universe - god *is* the dice.
-------------------------------------------------------------------------------
_______
/\ o o\
/o \ o o\_______
< >------> o /|
\ o/ o /_____/o|
\/______/ |oo|
| o |o/
|_______|/
Bill Taylor
Barry Phease <bar...@es.co.nz> writes:
|> > If O gets to bid first, he should bid 1, and the result is 0.
|> > If X gets to bid first, he should bid 1, and the result is 1 (to X).
|>
|> If the correct mean value is not biddable then the bidding process is
|> all-important. This is disturbing to me.
Yes, I understand your concern, which is a very legitimate one. It may
be that this auction mechanic gives some (variable) player too much of
an advantage, in the quest to avoid ties. But as a practical matter,
I strongly doubt it would be an essential problem till near the end of
the endgame; and as a theoretical matter, integer values for positions
are usually obtained anyway, by sandwidging, rather than spotting-on.
|> If the possibility of
|> infinitely long bidding is the problem then a tender process or cut and
|> choose makes people choose their best estimate in the first place.
Yes; cut-and-choose would be the "fairest", in the sense of local natural
justice. Making the richer do the cut would also "look fair", as I mentioned
before. It leaves the starting protocol a bit up in the air, but that can be
simply remedied no doubt. Indeed, it looks like a very viable alternative.
When I get some time I may go back and check out how the results of
this mechanic compare with the other. I didn't do this in my preliminary
investigation, not having thought of it till I mentioned it absent-mindedly
in passing just a day or two ago. It may be good. Who knows? It may
even be a *better* mechanic than E or D auctions.
Good points Barry.
-----------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-----------------------------------------------------
*-----------------*
| |
|ALWAYS THINK AHEA|
|D |
| |
*-----------------*
Bill Taylor
I meant to get back to this enquiry of Bill Spight's...
. X X 3x2 board.
O O . what is its status at auction go?
It turns out that this is worth zero, (of course!), BUT with ANY
advantage in banked points being enough for a win.
e.g. X with half a point in the bank, can bid zero, and wins; because...
. X X
O O O is worth 2 to X. (O with 2.5 wins, with 1.5 loses)
This last result is itself far from obvious, of course! To evaluate
these, you have to be ready to go around a cycle of positions several
times till you converge on an answer. Even then you may have to look
at other cycles as well!
The original position is an odd one; it is a rare case of a VERY COLD
position - neither player wants to move first! Whoever moves, loses points
from it. So whoever has the excess points (even just 1/2) merely bids zero,
and the opponent has to move (or better - just passes and loses by 1/2).
-----------------
Oh yes - there was another one I mentioned - actually I'd already done it.
X X . this turns out to be worth 4 to X.
. . X (O with 4.5 wins, with 3.5 loses)
This means it is equal in value (at auction go) to...
. X .
. . X ...which was the one I mentioned earlier.
This shows that the auction-go mechanic doesn't pick up the very *subtlest*
differences:-
The two positions are equivalent if X moves next; or if
O moves next & then X; and pseudo-equivalent if O moves twice then X;
but if O gets to move THREE TIMES, then the former postion is better
for X than the latter, (which has become 6 to O).
Interesting. I wonder if the mean values show up this remote difference.
They must do. I'll get out my old stuff again.
I wonder if this is one where fractional bids may make a genuine difference?
Hmmmmmm...
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
Every problem has at least one solution which is elegant, neat - and wrong.
-------------------------------------------------------------------------------
Darren Cook
>|> Why not let black bid 1 as well? If both players bid the same value,
>|> then toss a coin to see who gets the points and who gets the move.
>OUCH! Of course this could be done. But it would turn the game into
>one with an element of chance, which is against all we go players, (indeed
Okay, how about: if both players bid the same then black gets the move
and white gets the points. Next time it happens, white gets the move
and black gets the points.
The point is that both players get something of equal value (in their
opinion) so it makes no difference at all who gets the move and who
gets the points.
If two gods sat down to play Auction Go, they would be bidding exactly
the same as each other on every move because they'd know exactly how
much each move is worth. So the moves would alternate. At the end it
would be a draw.
While I'm pretending I know what I'm talking about I'll also say that
the gods would only need to bid integer values. The score on the board
at the end can only be an integer value.
>|> thought the move was worth 23pts, he is happier, but sealed bids would
>|> stop this kind of bluffing.
>... incomplete information, (such as sealed bids).
I don't see how sealed bids is incomplete information (even though
you've already answered this question before in this thread). All the
information you need to decide the value of the next move is on the
board.
>Reasonable questions. You may disagree with the answers of course, but
>that just means you want to play one of a different family of games.
I thought the point of Auction Go was a version of Token Go that would
be useful if the temperature was hotter in the middle game than in the
opening (Token Go just degenerates into normal go until the endgame if
this is the case).
So the key is how much useful information we can extract from the game
about move values. If the second player is not allowed to bid what he
thinks is the value of a move because the first player has already bid
it, then the rules are forcing him to give us inaccurate information.
Now I'm thinking about this, it would be good to require each player
to write down not just their bid but the move they will play if they
win. Even more information, as we learn the biggest move for both
black and white each time.
The players must already have decided their move to be able to decide
their bid so it is no hardship for them. That the other player sees
what his opponent is thinking can only be good - less chance to be
surprised, so less chance of bad moves muddying the information we
get.
All the above is thinking as a computer go programmer - a vulture
circling the board looking for training data. But would anyone play
Auction Go for pleasure? I'd rather play normal go :-).
Bill Taylor
bills...@aol.com (BillSpight) writes:
|> >> I got the impression that indeed you intended to apply numerical values
|> >>to board positions in Auction Go.
|> >
|> >Yes, that would be nice. So far, it's been possible; but there is no
|> >guarantee that that will continue.
|>
|> Well, surely it is possible to bracket board positions between the winning
|> and losing bank accounts. And I do not see how you can get any more precise
|> values.
The situation so far, is that almost all positions can be bracketted as
you say. That is:
account A lets X win; \ so in this case we might call
account A-1 lets O win. / the position's value (A-1/2), (an integer).
But not quite all positions are such. There are things that could go wrong.
One is, it could be like this...
account A lets X win; \
account A-1 is a draw (by cycling); } presumably we call this (A-1) to O;
account A-2 lets O win. / (a half-integer value).
Positions like this have cropped up in micro-board games.
Then the middle line above could be expanded to more than one line,
e.g.
account A lets X win;
account A-1 is a draw (by cycling);
account A-2 is a draw (by cycling);
account A-3 lets O win;
though (presumably) we would not call these other than an integer value
or a half-integer value, depending on the parity.
However, still finer values could conceivably crop up if in such a case as
the last, it was available to one player to force the position to EITHER
of the draw cycles when starting from either one, and for the other player
to have no such powers. Probably these can't occur, and they aren't terribly
significant even if they can, but they would adds a little (not much) to
the nuances of value.
Not much of a help, I'm afraid.
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
I don't know as much as God, but I know as much as he did at my age.
-------------------------------------------------------------------------------
Bill Taylor
Just a quick follow-up to my earlier followup to the Followup article...
I suggested that mean-values should surely distinguish
. X . X X . so that the latter could be seen
. . X and . . X to be better for black.
It is so. Once you get the hang of calculating these, it's not too hard.
------------
X X .
. . X mean value = a; where a = (6 + b)/2.
X X .
. O X mean value = b; where b = (6 + c)/2.
X X O
. O . mean value = c; where c = (b - a)/2.
This gives a = 30/7 , b = 18/7 , c = - 6/7.
------------
. X .
. . X mean value = d; where d = (6 + e).
. X .
. O X mean value = e; where e = (6 - e).
Thus e = 3 , d = 4.
------------
So X X . is indeed better than . X . by 2/7 of a point!
. . X . . X
And as in auction go, X X . is still a position where it HURTS to move,
. O O by almost 2 points! (61/35, in fact).
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
What is the colour of unexposed photographic film?
-------------------------------------------------------------------------------
Bill Taylor
dar...@factcomm.NOSPAM.co.jp (Darren Cook) writes:
|> >OUCH! Of course this could be done. But it would turn the game into
|> >one with an element of chance,
|>
|> Okay, how about: if both players bid the same then black gets the move
|> and white gets the points. Next time it happens, white gets the move
|> and black gets the points.
Could do. But then this partly brings back the asymmetry of having
an alternating series of moves; and its concommittant destruction
of the nice situation=position effect, i.e. having the board position
contain ALL the info about game status. This makes analysis much simpler.
|> >... incomplete information, (such as sealed bids).
|>
|> I don't see how sealed bids is incomplete information (even though
|> you've already answered this question before in this thread).
It still baffles me how this simple concept can cause so much trouble!
Even to expert game theorists like Bill Spight. I guess it's down to
unfamiliarity with the basics of traditional vonNeumann style game theory.
|> Now I'm thinking about this, it would be good to require each player
|> to write down not just their bid but the move they will play if they
|> win. Even more information, as we learn the biggest move for both
|> black and white each time.
An interesting idea! It would have no effect on the analysis of optimum
plays, etc, but would have HUGE psychological implications! And would
(as you say) be more interesting for the audience. MUCH more!
A very fruity thought.
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
An eye for an eye, a group for a group.
-------------------------------------------------------------------------------
Darren Cook
>|> Okay, how about: if both players bid the same then black gets the move
>|> and white gets the points. Next time it happens, white gets the move
>|> and black gets the points.
>Could do. But then this partly brings back the asymmetry of having
>an alternating series of moves; and its concommittant destruction
>of the nice situation=position effect, i.e. having the board position
>contain ALL the info about game status. This makes analysis much simpler.
I can see how that would be nice. But don't you currently need to know
the points each player has to decide who will bid first? So everything
is not on the board.
Tim Tyler
BillSpight (bills...@aol.com) wrote:
: Dear Tim and Bill T.,
: >>If you were watching a game of auction go between two players using
: >fractional
: >>bids who are both out to win and they make fractional bids, then the
: >>additional quantity of information you obtain from looking at their
: >fractions
: >>as opposed to whatever integer value this increases their score to is
: >>precicely zero.
: Since Bill believes that you have a point, Tim, what is it?
First of all, I'm sorry that I failed to reply to your initial query
about a game in which one player is permitted to play fractional move
values and the other is constrained to play integers.
I've been away and my news server has expired this article :-/
Initially I thought that the asymmetrical game would be unfair, but as
I thought about it it appeared to me that is was, in fact, an excellent idea
to help in clarifying the values of moves in auction go.
My analysis of it is not one which I'm terribly confident of, but here
it is anyway:
If the first move is constrained to be a integer value + 1/2, then you
were correct (IMO) in pointing out that the player who was able to bid
the fractional values would have an advantage and would win the game.
If, however, all his moves are constrained to be integer values, including
the initial one then then it is my opinion that the player who is able to
make fractional bids will have no advantage whatsoever over him, and the
expected result of the game will be a draw.
[there is one additional point that needs to be made at this juncture -
if /infinitessimal/ bids are allowed for the 'fractional' player, then
he still has an advantage and can win by an infinitessimal ammount.
I'm sure that you will be happy with just rational bids, or indeed
probably with just multiples of (1/2)^1000]
To my way of thinking the initial result where the fractional player has
an advantage is explained by the following:
Say the initial position is worth some (integer) value, say 10, points.
If the integer player bids 10 points then the result will be a draw.
Any higher fraction bid would result in a loss.
However, if the integer player is only allowed to bid half-integers then
the highest he can bid is 9.5 points. The fractional player can then
bid 9.9 points.
A bid of 10.5 points would lose by 1/2 a point.
However, not bidding and allowing the 9.9 point bid to pass would lose by
0.1 points - the integer player will lose either way.
In other words, the integer player loses because he is not permitted to
bid the 'exact' value of the move initially.
: If I start with 1 3/4 and end up with 2, then I have gained 1/4.
: Knowing the result gives the same information as knowing the amount gained.
: I took it that that was all you meant. Did you mean something more?
Alas, I'm not sure what you mean here. I'll just restate my position with
a related example in the vague hope that that will help clarify things.
Assuming that things start off with the integer player not being forced to
play anything other than integers initially (see above):
If 'fractional' makes a fractional bid then either:
A) He has overbid and probably made a mistake and possibly lost or
B) Integer can legitimately bid the next highest integer.
It therefore seems to me that the only way in which 'fractional'
makes any moves is if they're either overbids, or integers. In neither
case does this give him any advantage over the 'integer' player.
--
__________
|im |yler The Mandala Centre http://www.mandala.co.uk t...@cryogen.com
Tim Tyler
Darren Cook (dar...@factcomm.NOSPAM.co.jp) wrote:
: I thought the point of Auction Go was a version of Token Go that would
: be useful if the temperature was hotter in the middle game than in the
: opening (Token Go just degenerates into normal go until the endgame if
: this is the case).
: So the key is how much useful information we can extract from the game
: about move values. If the second player is not allowed to bid what he
: thinks is the value of a move because the first player has already bid
: it, then the rules are forcing him to give us inaccurate information.
Well, that's not quite right - he's hardly giving innacurate information
by *not* bidding ;-)
: Now I'm thinking about this, it would be good to require each player
: to write down not just their bid but the move they will play if they
: win. Even more information, as we learn the biggest move for both
: black and white each time.
: The players must already have decided their move to be able to decide
: their bid so it is no hardship for them. That the other player sees
: what his opponent is thinking can only be good - less chance to be
: surprised, so less chance of bad moves muddying the information we
: get.
This /might/ be construed as extremely bad, though. A variant /could/ be
concocted where each player wrote down their move and only the player
who bid higher revealed their move at the time. This would make the
game more similar to go as it is currently played without forefitting
any information wvailable to those wishing to subsequently analyse
the game - you're right in that the /quality/ of this information might
not be quite as good, though.
: All the above is thinking as a computer go programmer - a vulture
: circling the board looking for training data.
;-) The currently proposed game has some interesting aspects from this
perspective - /if/ bids start low and work up, then you know one players
value of the move exactly, and know that the other player thinks the move
is worth at least the value of the current bid.
If an initial bid is ever accepted, then you know that one player thinks
the move is worth at least that much, and the other player either agrees
with their estimate, or thinks it is worth less - this is usually
significantly less information that is obtained in the first case.
: But would anyone play Auction Go for pleasure?
/Your/ version of auction go, maybe not. It may indeed be that some
compromise is best reached between extracting the largest possible quantity
of information from the players, and allowing the players to play unmolested.
Sometimes I think that /just/ taking a token once in a while will complicate
things from the players point of view more than enough...
: I'd rather play normal go :-)
Well yes, that's an easier game :-)
BillSpight
Dear Bill,
>|> >... incomplete information, (such as sealed bids).
>|>
>|> I don't see how sealed bids is incomplete information (even though
>|> you've already answered this question before in this thread).
>
>It still baffles me how this simple concept can cause so much trouble!
>Even to expert game theorists like Bill Spight. I guess it's down to
>unfamiliarity with the basics of traditional vonNeumann style game theory.
>
Well, there is the problem of the definition. McKinsey gave a definition
using the word "previous". By his definition of "game" "previous" is
ambiguous. In the case of one-time simultaneous (sealed) bids by two players,
there are two games in McKinsey's sense that fit that situation. In one, one
player's bid is previous, in the other, the other player's bid is. Did
McKinsey mean to imply that the first player to seal his bid had perfect
information but the second one did not? I doubt it.
There is a theorem that games of perfect information have saddle points
with pure strategies; i. e., there is always an optimal move for each player.
That is not the case for all games with simultaneous moves.
However, I strongly suspect that Auction Go cum sealed bids does have a
saddle point with pure strategies. And I think that that was the thrust of
Darren's statement. He continued: "All the information you need to decide the
value of the next move is on the board." If the next move has a single value
and one seals a different bid, there is a chance that the opponent can take
advantage. So each player's minimax bid is the value of the play, and that is
a pure strategy.
Best,
Bill
BillSpight
Dear Tim,
A minor point, which is beside the main discussion:
>: So the key is how much useful information we can extract from the game
>: about move values. If the second player is not allowed to bid what he
>: thinks is the value of a move because the first player has already bid
>: it, then the rules are forcing him to give us inaccurate information.
>
>Well, that's not quite right - he's hardly giving innacurate information
>by *not* bidding ;-)
The second player has to bid or not. His choice does give information,
even if it is not to bid. The question of accuracy comes in if it is also
correct not to bid, even if the first player has not bid the value of the play.
That is obviously the case if the first player has overbid. <s>
Best,
Bill
BillSpight
Dear Tim,
>: If I start with 1 3/4 and end up with 2, then I have gained 1/4.
>: Knowing the result gives the same information as knowing the amount gained.
>: I took it that that was all you meant. Did you mean something more?
>
>Alas, I'm not sure what you mean here. I'll just restate my position with
>a related example in the vague hope that that will help clarify things.
How easy it is to misunderstand! <s>
I always wonder why people seem so sure that they do understand. <hmm>
Your example helps a lot. Many thanks. I'll get back to you soon.
Best,
Bill
Tim Tyler
Bill Taylor (mat...@math.canterbury.ac.nz) wrote:
: dar...@factcomm.NOSPAM.co.jp (Darren Cook) writes:
: |> >OUCH! Of course this could be done. But it would turn the game into
: |> >one with an element of chance,
: |>
: |> Okay, how about: if both players bid the same then black gets the move
: |> and white gets the points. Next time it happens, white gets the move
: |> and black gets the points.
: Could do. But then this partly brings back the asymmetry of having
: an alternating series of moves; and its concommittant destruction
: of the nice situation=position effect, i.e. having the board position
: contain ALL the info about game status.
Unless I'm mistaken the requirement that the first bid be negative and
the insistence that the initial bid be an integer and a half, the game isn't
symmetrical /anyway/ - the second player makes the winning bid and the person
who made the first bid resigns...
: |> >... incomplete information, (such as sealed bids).
: |>
: |> I don't see how sealed bids is incomplete information (even though
: |> you've already answered this question before in this thread).
: It still baffles me how this simple concept can cause so much trouble!
: Even to expert game theorists like Bill Spight. I guess it's down to
: unfamiliarity with the basics of traditional vonNeumann style game theory.
Definitely in my case. IIRC, you stated that the reason why simultaneous
bids were considered to be incomlete information was that the analysis
decomposed them in to a temporal order, so at the time that one bid was
made, the information about the other (simultaneous) earlier move was
hidden.
Perhaps this isn't the place to discuss this, but what on earth is the point
of such an analysis, apart from to get rid of a 'problem' with simultaneous
moves? If there is no other point, what /is/ this 'problem' with
simultaneous moves? Does imagining the moves being played in a universe
with discrete time steps help with this 'problem'?
You may be right in that this is how it is 'defined' in game theory, but
to me the definition looks like an arbitrary piece of unnecessary dogma
- I would view defining things like this rather than in the way in which
many correspondents here seem to think of it is like presribing which
side of the road everyone should drive on - i.e. there's no reason to define
it one way rather than another - in short, yuck.
I'm opposed to go being turned into a game of incomplete information in
general, but I have absolutely no problem whatsoever with sealed simultaneous
bids. The game would still remain utterly determininstic - what exactly is
the difficulty with the idea, if any?
[snip a very fruity thought]
BillSpight
Dear Tim,
<<
First of all, I'm sorry that I failed to reply to your initial query about a
game in which one player is permitted to play fractional move values and the
other is constrained to play integers.
I've been away and my news server has expired this article :-/
Initially I thought that the asymmetrical game would be unfair,
>>
Excellent intuition! <s>
<<
but as I thought about it it appeared to me that is was, in fact, an excellent
idea to help in clarifying the values of moves in auction go.
My analysis of it is not one which I'm terribly confident of, but here it is
anyway:
If the first move is constrained to be a integer value + 1/2, then you were
correct (IMO) in pointing out that the player who was able to bid the
fractional values would have an advantage and would win the game.
If, however, all his moves are constrained to be integer values, including the
initial one then then it is my opinion that the player who is able to make
fractional bids will have no advantage whatsoever over him, and the
expected result of the game will be a draw.
>>
Given the assumption that fractional values are no more than fictions,
estimations, heuristics, or the like, yours is a reasonable position.
<<
[there is one additional point that needs to be made at
this juncture -
if /infinitessimal/ bids are allowed for the fractional'
player, then he still has an advantage and can win by an infinitessimal
ammount.
I'm sure that you will be happy with just rational bids,
or indeed probably with just multiples of (1/2)^1000]
>>
I require much less to make my point.
<<
To my way of thinking the initial result where the
fractional player has an advantage is explained by the
following:
Say the initial position is worth some (integer) value,
say 10, points.
>>
You mean the value of a move, not the count of the position, right? And
that the count is 0. <s>
<<
If the integer player bids 10 points then the result will
be a draw.
Any higher fraction bid would result in a loss.
However, if the integer player is only allowed to bid
half-integers then the highest he can bid is 9.5 points.
The fractional player can then bid 9.9 points.
A bid of 10.5 points would lose by 1/2 a point.
However, not bidding and allowing the 9.9 point bid to
pass would lose by 0.1 points - the integer player will
lose either way.
In other words, the integer player loses because he is
not permitted to bid the 'exact' value of the move
initially.
>>
A clear example, and a good point, given your assumptions.
<<
: If I start with 1 3/4 and end up with 2, then I have
: gained 1/4. Knowing the result gives the same
: information as knowing the amount gained.
: I took it that that was all you meant. Did you mean
: something more?
Alas, I'm not sure what you mean here. I'll just restate
my position with a related example in the vague hope that
that will help clarify things.
>>
My previous reply may have been ambiguous. I meant that it is easy for
people to misunderstand each other, not that it is easy to misunderstand
Auction Go and such. Although that is true, too, I expect. <g>
<<
Assuming that things start off with the integer player
not being forced to play anything other than integers
initially (see above):
If 'fractional' makes a fractional bid then either:
A) He has overbid and probably made a mistake and
possibly lost or
B) Integer can legitimately bid the next highest integer.
>>
Excellent point!
<<
It therefore seems to me that the only way in which
'fractional' makes any moves is if they're either
overbids, or integers. In neither case does this give
him any advantage over the 'integer' player.
>>
Well put. Now to show the fractional advantage:
7x7 board:
O O . O . O .
O O * O O . O
* * * . O O .
. * * * * O .
* * . O . O .
* * * * * O .
. * . O . O .
First let's assess it as regular go. The action is in the top left. The
rest of the board is miai. If Black plays first we may have:
O O 1 O . O .
O O * O O . O
* * * 5 O O .
. * * * * O .
* * 4 O 2 O .
* * * * * O .
. * . O 3 O .
Black gets 27 points, White 22, for a net score of +5.
If White plays first:
O O 1 O . O .
O O * O O . O
* * * 4 O O .
. * * * * O .
* * 5 O 3 O .
* * * * * O .
. * . O 2 O .
Black gets 22 points, White 27, for a net score of -5.
The original position has a count of 0 and a miai value of 5.
Auction go: Let the bank balance be 0.
I. Both players bid integers. Let Black bid first.
Variation 1.
1. Black bids 5. (A mistake.)
2. White accepts.
3. Black takes the 4 White stones.
. . * O . O . Bank balance: -5
. . * O O . O
* * * . O O .
. * * * * O .
* * . O . O .
* * * * * O .
. * . O . O .
3. White bids 2.
4. Black accepts.
5. White plays and bids 2.
. . * O . O . Bank balance: -3
. . * O O . O
* * * . O O .
. * * * * O .
* * . O O O .
* * * * * O .
. * . O . O .
6. Black accepts.
7. White plays and bids 0.
. . * O . O . Bank balance: -1
. . * O O . O
* * * . O O .
. * * * * O .
* * . O O O .
* * * * * O .
. * . O O O .
8. Black bids 1.
9. White accepts.
10. Black plays.
. . * O . O . Bank balance: -2
. . * O O . O
* * * * O O .
. * * * * O .
* * . O O O .
* * * * * O .
. * . O O O .
11. White bids 0.
(We know where this is headed. Let's cut to the end.)
. . * O . O . Bank balance: -4
. . * O O . O
* * * * O O .
. * * * * O .
* * * O O O .
* * * * * O .
. * * O O O .
Black has 26 points on the board; White has 23 and a bank balance of 4.
White wins by 1 point. You may verify that no one has erred after B 1.
Variation 2.
1. Black bids 4.
2. White bids 5. (A mistake. If he accepts he can tie.)
3. Black accepts.
4. White connects his stones.
O O O O . O . Bank balance: 5
O O * O O . O
* * * . O O .
. * * * * O .
* * . O . O .
* * * * * O .
. * . O . O .
5. Black bids 2.
6. White accepts.
7. Black plays and bids 2.
O O O O . O . Bank balance: 3
O O * O O . O
* * * . O O .
. * * * * O .
* * . O * O .
* * * * * O .
. * . O . O .
8. White accepts.
9. Black plays and bids 0.
O O O O . O . Bank balance: 1
O O * O O . O
* * * . O O .
. * * * * O .
* * . O * O .
* * * * * O .
. * . O * O .
10. White bids 1.
11. Black accepts.
12. White plays.
O O O O . O . Bank balance: 2
O O * O O . O
* * * O O O .
. * * * * O .
* * . O * O .
* * * * * O .
. * . O * O .
Now Black will make "0" bids and eventually take off the 2 White stones.
Black gets 24 points on the board plus 2 points in the bank; White gets 25
points on the board. Black wins by 1.
The Auction Go temperature is 4, and the optimal result is a tie.
II. Black bids integers and bids first if the bank balance is 0. White is
allowed to bid in halves.
1. Black bids 4.
2. White bids 4 1/2. (An overbid if fractions don't matter.)
3. Black accepts. (We know that she loses if she bids 5.)
4. White connects his stones.
O O O O . O . Bank balance: 4 1/2
O O * O O . O
* * * . O O .
. * * * * O .
* * . O . O .
* * * * * O .
. * . O . O .
5. Black bids 2.
6. White bids 2 1/2. (Another overbid?!)
7. Black accepts.
8. White plays.
O O O O . O . Bank balance: 7
O O * O O . O
* * * . O O .
. * * * * O .
* * . O O O .
* * * * * O .
. * . O . O .
9. Black bids 2.
10. White bids 2 1/2. (Is there no stopping this fool?)
11. Black accepts.
12. White plays.
O O O O . O . Bank balance: 9 1/2
O O * O O . O
* * * . O O .
. * * * * O .
* * . O O O .
* * * * * O .
. * . O O O .
13. Black bids 0.
14. White bids 1.
15. Black accepts.
(Etc. Etc.)
O O O O . O . Bank balance: 12 1/2
O O * O O . O
* * * O O O .
. * * * * O .
* * O O O O .
* * * * * O .
. * O O O O .
Black gets 18 points on the board plus 12 1/2 in the bank, for 30 1/2
points; White gets 31 points on the board to win by 1/2.
You may verify that Black can do no better. The fractional advantage
wins. QED.
Best,
Bill
Robert Jasiek
> You may verify that Black can do no better. The fractional advantage
> wins. QED.
Need it be a fraction? Or does a tiny bid of "I bid an infinitesimal Up"
suffice? Why not bid arbitrary games? (Note: Up = {{0|{0|0}}.)
--
robert jasiek
http://www.snafu.de/~jasiek/
Tim Tyler
BillSpight (bills...@aol.com) wrote:
: Dear Tim,
: A minor point, which is beside the main discussion:
: >: So the key is how much useful information we can extract from the game
: >: about move values. If the second player is not allowed to bid what he
: >: thinks is the value of a move because the first player has already bid
: >: it, then the rules are forcing him to give us inaccurate information.
: >
: >Well, that's not quite right - he's hardly giving innacurate information
: >by *not* bidding ;-)
: The second player has to bid or not. His choice does give information,
: even if it is not to bid.
Yes, I agree.
: The question of accuracy comes in if it is also correct not to bid, even
: if the first player has not bid the value of the play.
: That is obviously the case if the first player has overbid. <s>
As you say, if the first player has overbid then it is correct not to bid.
I think that in this case not bidding would provide the information that
the second player thought that the first players bid was either correct,
or an overbid.
I don't see that this is a case of 'the rules forcing him to give us
innacurate information'...?
I didn't mean to imply that not bidding always provided no (or accurate)
information. If the first players bid is too low, the second player /may/
provide inaccurate information by not bidding - but he is not forced to do
this by the rules.
BillSpight
Dear Robert,
>> You may verify that Black can do no better. The fractional advantage
>> wins. QED.
>
>Need it be a fraction? Or does a tiny bid of "I bid an infinitesimal Up"
>suffice? Why not bid arbitrary games? (Note: Up = {{0|{0|0}}.)
>
>
Interesting!
Up is positive, and so could be the winning margin, if allowed. <g>
A practical problem with allowing infinitesimals and arbitrary games is
that they are not strictly ordered. If you bid 5, can I bid {6|3*} next? If
they are simultaneous bids, who wins the auction? And then what do we do with
the games, play them?
Best,
Bill
Robert Jasiek
Dear Bill,
> A practical problem with allowing infinitesimals and arbitrary games is
> that they are not strictly ordered.
Such bidding should be restricted to theory.
> If you bid 5, can I bid {6|3*} next?
As you like. Define what you want. Only consider games that are numbers
for next bid restrictions. Or use some mean values. Or bid only once.
> If
> they are simultaneous bids, who wins the auction?
As above.
> And then what do we do with the games, play them?
Do what you want. It is for theory, anyway. Ignore all not-number
games. Or add their mean values. Or...
Best,
Bill Taylor
dar...@factcomm.NOSPAM.co.jp (Darren Cook) writes:
|> >Could do. But then this partly brings back the asymmetry of having
|> >an alternating series of moves; and its concommittant destruction
|> >of the nice situation=position effect, i.e. having the board position
|> >contain ALL the info about game status. This makes analysis much simpler.
|>
|> I can see how that would be nice. But don't you currently need to know
|> the points each player has to decide who will bid first? So everything
|> is not on the board.
Ah - yes - that is so. Silly me. The game staus DOES depend on that,
as you say, that was a boo-boo. What I should have said was that the
FULL ANALYSIS of the game did not depend on other matters such as whose
turn is it. By full analysis, I mean the discovery of the SET of point
balances that lead to a black win; to a white win; and to a draw.
Sorry for being so misleading.
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
Watch out for my definitive series of books on Prime Numbers.
Just coming into print now... volume I: "The Even Primes"
-------------------------------------------------------------------------------
Tim Tyler
[snip Bill's helpful example]
: You may verify that Black can do no better. The fractional advantage
: wins. QED.
I see no flaw in this analysis.
To review my views of related matters on this thread:
In a game where one side is allowed to bid integers, and the other may
use fractional values, I now agree that the second player has the advantage.
I was initially less certain of this point than my initial one about
non-integer values not containing any additional information over bids
of plain integers.
Now, (though I'm not /sure/ of this either) Bill S.'s example would appear to
indicate that this was mistaken as well.
Lastly to address the point which makes the discussion relevant to this
thread: would it be better to allow bids in auction go to be fractional?
Before reading Bill's post I was fairly ambivalent on this issue - I thought
that non-integer bids were not particularly harmful, but not exactly
necessary, either.
If it were put to the vote now, I'd probably vote for it, in my uncertainty
- to be on the safe side, so to speak.
However, a point occurrs (I think Bill S. mentioned it originally):
He has demonstrated that if 'the gods' are allowed to use non-integer bids
then they /will/ take advantage of them and /not/ bid integers.
If it were also demonstrated that a game which allowed non integer bids
(by both parties) could come to a different conclusion (in terms of
win/loss/draw) than one which allowed only integer bids, then I would
vote /for/ allowing non-integer bids in the rules.
If it could be proved that allowing such bids could make no difference
to the outcome of the game, then I would probably vote that they not
be allowed in the rules, (/despite/ the fact that they appear to have
useful and interesting properties - in the example already given).
I would do this on roughly the same grounds that I would also vote against
having both sides write down what move they would make and yield this
information publicly to their opponent after each move. These grounds are
essentially pragmatic ones - e.g. can you conveniently represent your bid
by presenting a handful of stones to your opponent.
The first case would require a single example and the latter one a proof.
Lastly, thanks for Bill for taking the time to give his example. I find
his result contrary to my intuition and thus very interesting.
The rest of the thread isn't so bad either IMO - keep up the good work ;-)
BillSpight
Dear Tim,
>Lastly, thanks for Bill for taking the time to give his example. I find
>his result contrary to my intuition and thus very interesting.
>
Glad you liked it.
>The rest of the thread isn't so bad either IMO - keep up the good work ;-)
I concur. Everybody has added something interesting to the discussion.
<s> Many thanks to Bill Taylor for devising Auction Go.
>If it were also demonstrated that a game which allowed non integer bids
>(by both parties) could come to a different conclusion (in terms of
>win/loss/draw) than one which allowed only integer bids, then I would
>vote /for/ allowing non-integer bids in the rules.
>
>
7x7 board:
O O . O . O . Bank balance: 0
. O * O O . O
* * * . O O .
. * * * * O .
* * . O . O .
* * * * * O .
. * . O . O .
Pardon me if I do not write out the analysis. But I claim
1) if both sides are allowed to bid in halves, Black wins;
2) if both sides must bid integers, the first bidder wins.
Best,
Bill
Bill Taylor
t...@BITS.bris.ac.uk (Tim Tyler) writes:
|> Unless I'm mistaken the requirement that the first bid be negative and
|> the insistence that the initial bid be an integer and a half, the game isn't
|> symmetrical /anyway/ - the second player makes
Ah - but it's still symmetrical between the players before the first move
has taken place; that's the key. There's no equaivalent of "black" and
"white" as in most board games. Of course every game *must* be (able to
become) asymmetric *after* moves begin - otherwise it could scarely
be called a "game"!
|> ... the second player makes the winning bid and the person
|> who made the first bid resigns...
You ARE prone to confuse perfect play with practical play, aren't you!
By this reasoning; regular go (with some komi) will either go
1. resign or 1. <move> 2. resign. Please desist from this trivia.
|> : |> >... incomplete information, (such as sealed bids).
Sigh. This is irrelevant to all other threads here. Please - wherever I say
"with complete information" just read "with no simultaneous bids or moves". If
you really want to argue the toss, take it to rec.games.abstract or sci.math.
and we (and others) can debate there.
|> I'm opposed to go being turned into a game of incomplete information in
|> general,
Good.
|> but I have absolutely no problem whatsoever with sealed simultaneous bids.
Clearly! I don't either, all that amount; but it's just that it crosses
that narrow but deep chasm, between chess-like games and poker-like games.
|> The game would still remain utterly determininstic
It has no (built-in) element of chance, if that's what you mean; i.e. no
randomizing element beyond the actions of the players. Yes; true.
If you don't like my epithet "poker-like", try "GOPS-like".
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
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There is only the one universal go game, played on a cosmic board.
And whenever we play, we are just resolving one small region of it.
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Tim Tyler
BillSpight (bills...@aol.com) wrote:
: Many thanks to Bill Taylor for devising Auction Go.
: >If it were also demonstrated that a game which allowed non integer bids
: >(by both parties) could come to a different conclusion (in terms of
: >win/loss/draw) than one which allowed only integer bids, then I would
: >vote /for/ allowing non-integer bids in the rules.
[snip example]
OK, I didn't expect to be doing this but here you go:
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| Bill X |
| / \ |
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While playing through this example I felt that I came to a better
understanding of what had previously been referred to on this thread as
the advantage of having first bid.
With integer bids, it would appear to be the case that there are many
circumstances in which it is advantageous to have the first bid.
This effect should cause players to try to bid the lowest value which they
think will cause their opponent to accept their offer. Compared to having
bids which alternate up gradually from a small figure, this offers /less/
information about what the two players think.
Generalising wildly from the example I've looked at I guess that this happens
less frequently if bids are permitted to be fractional. If this is correct
then there it would seem to matter less who has first bid. This is good,
at least from the perspective that you no longer have a strong need of
rules to govern who has the first bid.
If correct, it also would also mean that bids should start low and creep
upwards slowly - the reason being that if you increase your bids by small
values you are less likely to overshoot the value at which your opponent
would have passed. This means that the possibility of having an infinite
number of bids in games with fractional bidding isn't just a theoretical
problem. Players are motivated to start bidding low and increas in small
values.
Lastly some thoughts about clocks.
I believe (if an 'english' auction is to be used) then allowing a specific
quantity of time for the bids is a viable alternative to quantising the bids
by either only permitting multiples of some given number as valid bids, or
demanding that each bid exceed the previous wone by some small number.
However, unless care is exercised, fractional auction go may degenerate into
a game of manual and verbal dexterity on the bidding front - English
auctions and fractional bidding don't seem to mix terribly well :-/
If a system of simultaneous sealed bids were to be used then most of the go
clocks I have seen would not be suitable, as they don't allow both sides
to be active simultaneously ;-)
Tim Tyler
Bill Taylor (mat...@math.canterbury.ac.nz) wrote:
: t...@BITS.bris.ac.uk (Tim Tyler) writes:
: |> Unless I'm mistaken the requirement that the first bid be negative and
: |> the insistence that the initial bid be an integer and a half, the game isn't
: |> symmetrical /anyway/ - the second player makes
: Ah - but it's still symmetrical between the players before the first move
: has taken place; that's the key. There's no equaivalent of "black" and
: "white" as in most board games. Of course every game *must* be (able to
: become) asymmetric *after* moves begin - otherwise it could scarely
: be called a "game"!
It's true that it's symmetrical before the game starts. That sort of symmetry
was not what I was referring to, though.
: |> ... the second player makes the winning bid and the person
: |> who made the first bid resigns...
: You ARE prone to confuse perfect play with practical play, aren't you!
Needless to say, I was exaggerating ;-)
: By this reasoning; regular go (with some komi) will either go
: 1. resign or 1. <move> 2. resign. Please desist from this trivia.
My point was not *intended* to be trivial. I would regard a game where the
first player is /not/ forced to bid an extra half point as symmetrical.
Regular go with some integer komi would be the same.
If you have the half point in there then, strictly speaking, you need to
play an even number of games, with the 1/2 point advantage alternating
in order to even things up.
The point is an aesthetic one, and I don't expect anyone to agree, but I
don't think that jigo is sufficiently frequent on commonly used boards to
go to these lengths in order to avoid it.
: |> : |> >... incomplete information, (such as sealed bids).
: Sigh. This is irrelevant to all other threads here. Please - wherever I say
: "with complete information" just read "with no simultaneous bids or moves". If
: you really want to argue the toss, take it to rec.games.abstract or sci.math.
: and we (and others) can debate there.
I already know that you use these terms synonymously. I'm concerned that they
have very different connotations in my mind and in the minds of others.
"Lacking complete information" is like an emotionally-loaded term in some ways.
: |> I'm opposed to go being turned into a game of incomplete information in
: |> general,
: Good.
: |> but I have absolutely no problem whatsoever with sealed simultaneous bids.
: Clearly! I don't either, all that amount; but it's just that it crosses
: that narrow but deep chasm, between chess-like games and poker-like games.
It depends on where you put that chasm. Clearly(?) the situation is right
on the edge of one side or the other of the chasm. I wouldn't want
simultaneous bids to be thrown out on the grounds of a definition that, to
my mind, could have placed simultaneous bids equally well on either side.
I don't like the differences to play that sealed moves introduces either -
as you have pointed out, the character of a sealed move game is completely
different - but I don't think the whole idea has some sort of metaphysical
problem with it and shouldn't be considered as a result.
BillSpight
Dear Bill,
>|> but I have absolutely no problem whatsoever with sealed simultaneous bids.
>
>Clearly! I don't either, all that amount; but it's just that it crosses
>that narrow but deep chasm, between chess-like games and poker-like games.
>
"Narrow but deep chasm." Gee, Bill, is your thinking fuzzy enough? <g>
Poker requires mixed strategies (e. g., bluffing) to play correctly. I
doubt if the same is true of Auction Go with sealed bids.
Best,
Bill
BillSpight
Dear Tim,
>With integer bids, it would appear to be the case that there are many
>circumstances in which it is advantageous to have the first bid.
>
>This effect should cause players to try to bid the lowest value which they
>think will cause their opponent to accept their offer.
Well, let's take our original simple example, where 3 is an overbid, but 2
is not. By bidding 2 the bidder guarantees an advantage. If he bids less, the
opponent can bid 2 and gain an advantage. The bidder may gain a bigger
advantage by bidding less than 2, but risks loss if the opponnent bids 2. In a
sense, bidding 2 is correct play, even if one could gain more by bidding less
with a particular opponent.
The same holds true with fractional bids if there are some fractions which
are not allowed. Typically there will be two allowed bids, one of which is an
overbid and one which is the next lower allowed bid. Correct play is to bid
the latter.
One may get an infinte auction when all fractions are allowed and it is
*not* possible to make the bid just below the first overbid. Then there is no
bidder's advantage, but there may be an advantage if one's opponent can be
induced to accept an underbid or make an overbid. One risks nothing by such
tactics.
Best,
Bill
Bill Taylor
bills...@aol.com (BillSpight) writes:
|> "Narrow but deep chasm." Gee, Bill, is your thinking fuzzy enough? <g>
Eh?
|> Poker requires mixed strategies (e. g., bluffing) to play correctly.
|> I doubt if the same is true of Auction Go with sealed bids.
Well that is a good question! I'd been wondering myself. I believe it's
precise anough to be capable of a definite answer, so I'll have a look into
it. Why don't you try to beat me to it?
An example; or proof of nonexistence thereof; is the goal.
Cheers,
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Bill Taylor W.Ta...@math.canterbury.ac.nz
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The answer may be right but it's not the answer I want.
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Bill Taylor
t...@BITS.bris.ac.uk (Tim Tyler) writes:
|> The point is an aesthetic one, and I don't expect anyone to agree,
Excellent.
|> : "with complete information" just read "with no simultaneous bids or moves".
|> I already know that you use these terms synonymously. I'm concerned that they
|> have very different connotations in my mind and in the minds of others.
That's why I tried to clarify.
|> "Lacking complete information" is like an emotionally-loaded term in some ways.
Hmmmmm... you seem to see emotionally laiden phrases as easily as some other
people see, ah, see, hmm, prejudicial cultural derision.
|> I don't like the differences to play that sealed moves introduces either -
|> as you have pointed out, the character of a sealed move game is completely
|> different -
You mean we agree?!
|> but I don't think the whole idea has some sort of metaphysical
|> problem with it and shouldn't be considered as a result.
I agree with that too - I've no objection to them being discussed; I was
answering a query as to why I wasn't (yet) ready to discuss them.
Cheers,
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Bill Taylor W.Ta...@math.canterbury.ac.nz
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I think, therefore I am confused.
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Nick Wedd
In article <6hh24r$134$2...@cantuc.canterbury.ac.nz>, Bill Taylor
<mat...@math.canterbury.ac.nz> writes
>|> Poker requires mixed strategies (e. g., bluffing) to play correctly.
>|> I doubt if the same is true of Auction Go with sealed bids.
>
>Well that is a good question! I'd been wondering myself. I believe it's
>precise anough to be capable of a definite answer, so I'll have a look into
>it. Why don't you try to beat me to it?
>
>An example; or proof of nonexistence thereof; is the goal.
I am convinced of the nonexistence thereof. Outline of proof follows.
Let's map the allowable bids onto even integers for W, odd ones for B
(there must be some tie-break rule, preventing equality).
There must exist some odd P such that if B knew W's bid, and it were
less than P, B would outbid W by 1; and if it were greater than P, B
would bid any smaller number.
There must exist some even Q such that if W knew B's bid, and it were
less than Q, W would outbid B by 1; and if it were greater than Q, W
would bid any smaller number.
If Q>P, {Q,Q-1} is a stable strategy.
If Q<P, {P-1,P} is a stable strategy.
Nick
--
Nick Wedd ni...@maproom.demon.co.uk
Tim Tyler
Bill Taylor (mat...@math.canterbury.ac.nz) wrote:
: t...@BITS.bris.ac.uk (Tim Tyler) writes:
: |> The point is an aesthetic one, and I don't expect anyone to agree,
: Excellent.
: |> : "with complete information" just read "with no simultaneous bids or moves".
: |> I already know that you use these terms synonymously. I'm concerned that they
: |> have very different connotations in my mind and in the minds of others.
: That's why I tried to clarify.
: |> "Lacking complete information" is like an emotionally-loaded term in some ways.
: Hmmmmm... you seem to see emotionally laiden phrases as easily as some other
: people see, ah, see, hmm, prejudicial cultural derision.
Typically I view using emotionally loaded terms as an unpleasant tactic in
arguments. I /try/ to avoid doing it and I try to point out when other people
do it. Note that I wasn't actually saying you were doing it here.
'Lacking complete information' is a fairly cold and clinical really. It does
have negative connotations for me in this context which 'simultaneous sealed
bids' does not.
: |> I don't like the differences to play that sealed moves introduces either -
: |> as you have pointed out, the character of a sealed move game is completely
: |> different -
: You mean we agree?!
Our conclusion is the same, but /perhaps/ the underlying reasoning is not
identical.
I would much prefer an English auction to sealed bids under most circumstances.
There are two reasons why I'm considering sealed bids at all.
1) They usually[1] provide better, easier to analyse information about what
both players think a move is worth.
2) There appear to be problems (discussed elsewhere) when english auctions
are used in conjunction with fractional bids. Fractional bids have
their own advantages and disadvantages - this point is clearly only
relevant when they are used.
[snip metaphysical problems]
--
__________
|im |yler The Mandala Centre http://www.mandala.co.uk t...@cryogen.com
[1] not always - sometimes the opposite is true - players /may/ be able
to gain information by looking at their opponent's last bid.
BillSpight
Dear Tim,
>There are two reasons why I'm considering sealed bids at all.
>
>1) They usually[1] provide better, easier to analyse information about what
> both players think a move is worth.
>
>2) There appear to be problems (discussed elsewhere) when english auctions
> are used in conjunction with fractional bids. Fractional bids have
> their own advantages and disadvantages - this point is clearly only
> relevant when they are used.
>
Having watched a similar game, I can add a third reason: timeliness. The
game used sealed bids, and was *very* slow. Any auction which took more time
would have been unbearably slow.
Bill
Bill Taylor
t...@BITS.bris.ac.uk (Tim Tyler) writes:
|> Our conclusion is the same, but /perhaps/ the underlying reasoning is not
|> identical.
Agreed.
|> There are two reasons why I'm considering sealed bids at all.
|>
|> 1) They usually[1] provide better, easier to analyse information about what
|> both players think a move is worth.
This is probably correct.
|> 2) There appear to be problems (discussed elsewhere) when english auctions
|> are used in conjunction with fractional bids.
Yes, if they are arbitrary fractions. I think my original idea of
half-integers on the first auction only, avoids these problems.
|> [snip metaphysical problems]
Well-snipped, sir!
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Bill Taylor W.Ta...@math.canterbury.ac.nz
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On with the sho(-dan)!
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Bill Taylor
Nick Wedd <Ni...@maproom.demon.co.uk> writes:
|> >|> Poker requires mixed strategies (e. g., bluffing) to play correctly.
|> >|> I doubt if the same is true of Auction Go with sealed bids.
|> >
|> >Well that is a good question! I'd been wondering myself. I believe it's
|> >precise anough to be capable of a definite answer, so I'll have a look into
|> >it. Why don't you try to beat me to it?
|> >
|> >An example; or proof of nonexistence thereof; is the goal.
|>
|> I am convinced of the nonexistence thereof. Outline of proof follows.
Yes, I'm sure that Nick's proof is good. It does seem as if sealed bids
would not (formally) induce a poker-style bluffing element.
Of course, from a practical, psychological, we-dumb-humans, point of view,
it would. If one player is usually happy to bid 5, 6, or 7 to open, (but
of course would rather get away with 5), and the other is happy to bid
6,7, or 8, and both of these facts are known to the other, then we have
a bluffing contest on our hands, with sealed bids. But, as I say, and as
everyone will realize anyway, that is "merely" a practical concern, not
a theoretical one. We already know that bluffing-like elements occur
in ordinary go - my favourite example being how far to crawl along
the 2nd/3rd lines, in a crawling race; or how far to go in a power-pushing
wall-building race out into the centre. Perhaps "playing chicken" would be
a better term than "bluffing" for these. But again, it's a practical
conceern, not a game-theoretical one.
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Bill Taylor W.Ta...@math.canterbury.ac.nz
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Some moves are merely KYUte, but others are truly DANgerous!
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