Author: Christophe Theron
Date: 19:19:01 10/21/00
Go up one level in this thread
On October 21, 2000 at 02:59:53, Ratko V Tomic wrote:
>>That was my point. If we both make errors at the same frequency, but yours
>>cost you 10 times as much as mine, you go broke first, assuming we start with
>>the same amount of money.
>>
>
>The problem with optimum bet size is a bit trickier. If gambler's odds of
>winning single game (e.g. a coin toss or dice roll) are P and if P>0.5, then the
>optimum bet he should place is C*(2P-1), where C is his current total capital,
>i.e. he should always bet 2P-1 fraction of his current net worth. If P<0.5 then
>player should bet 0 (i.e. if odds are against you, don't bet at all).
>
>Now suppose GT has specialized, very finely tuned king-attack tactics
>algorithms. It can compute in these situations faster, thus deeper and more
>accurately than a program without this specialized code. Since the truncated
>minimax will make errors, the more the shallower its search, the situation is
>similar to gambling. The deeper program will make errors, too, but its odds of
>error are smaller than of the shallower program.
>
>So, if in a double-edged king-side attack GT, due to its specialized king-side
>tactics code, has odds of 55% of outcomputing program X in each step, its
>optimum bet would be about 2*0.55-1=0.10, i.e. it should bet 1/10th of its
>current value. The total (approx) material value GT initially has is, say, (8*1
>+ 4*3 + 2*5 + 10)=40. If some exchanges took place, say 2 pieces and 4 pawns per
>side, the total material capital is around 30 per side. Now if GT can get at
>this point into the kind of position where its odds of outwitting X are 55%, it
>should start betting about 3 pawns, a full piece. The greater its odds of
>outcomputing X on each step, the more it should bet. For example if its odds are
>60% instead of 55%, it should bet 2*0.6-1=20%, i.e. with total capital 30, it
>should bet 6 pawns or 2 pieces worth.
>
>The trigger condition for a program to start gambling profitably is that its
>odds of outcomputing its opponent in a given type of position are better than
>even. In practice one doesn't know what are the odds of outcomputing opponent in
>a given position. So the way one would tune it in practice is to set the risk
>aversion to increase against the better tactician.
>
>Since in computer chess the rating is fairly well correlated with tactical
>abilities of the programs, in absence of any other information besides rating,
>GT should bet less against the higher rated programs. If more specific
>information is available on its next round opponent, it should bet less against
>programs which are good tacticians in king-attack positions. I suspect
>Christophe is already tuning GT's gambling affinity along these lines.
>
>For longer matches against the same opponent, GT could even automate this
>adjustment as a part of its regular learning, e.g. by increasing or decreasing
>the P after each game based on accumulated results so far. Unlike learning of
>the opening lines, where all lines learned are stored in a single data-base,
>this one (the value P or the optimum bet size) has to be opponent specific.
>
>A special case of the match here is GT playing against regular Tiger. Since both
>probably have the same specialized king-attack search code, the odds P are 0.5,
>hence GT should not gamble at all against Tiger, and if it does, it will not
>fare too well. Since it does appear (from reports here) that GT is weaker than
>Tiger in matches against it, it would follow that Christophe doesn't have the
>opponent specific learning (or even hand tuning) of GT's risk aversion (optimum
>bet size) for matches with a fixed opponent.
>
>Although the above dealt with king-side attack and risk taking, the relation of
>risk taking and existence of some kind of edge holds for any other type of edge.
>For example a program which has some special/unique endgame heuristics should
>take risks to steer the game into such endgames, and the greater the edge the
>greater bets it should place. Any other aspect of middlegame would work, too.
>For example some program may have special heuristics for blocked positions, the
>notoriously weak area of most programs. I think Junior has something of this
>sort, since it seems to like to get into blocked positions, more than other
>programs, so I suspect Amir has some special secret heuristics for these
>positions. Now, he only needs to up Junior's risk-taking drive to get into such
>positions (if playing against programs, not against humans). I haven't noticed
>in Junior any risk taking behavior, though.
Once again a smart and very much to the point message.
Thanks Ratko.
Christophe
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