Author: Ratko V Tomic
Date: 23:59:53 10/20/00
Go up one level in this thread
>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.
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