Author: Bruce Moreland
Date: 05:40:19 08/18/98
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On August 18, 1998 at 03:34:05, fca wrote: >Now for any individual game the odds favour Ferret (a few super-GMs or n-tuple >cpu craftys excepted), as the odds favour a casino though I concede for >different reasons (Ferret's 'cos it plays so well, the casino because of the >rules). Say the mathematical point expectation for Ferret per game against this >opponent is 0.51. > >So, how much advantage does the punter have from the ability to "walk away" as >soon as he is "ahead" (whatever "ahead" means - let us forget grading as then >the question is too complex for me)? Is this an advantage at all? Please >ignore all psychological considerations, this is a "straight" ( ;-) ) math-chess >question. If I really was scoring 51% against the pool in individual games, but the members of the pool want to win matches, not games, and I will accept any request for a game, and never make my own requests, then I will lose most of the matches. Assuming no draws (bad assumption, but this just changes the numbers, but not what they mean), and that everyone will stick around for exactly three games, or until they are ahead, or until they can't win, I get the following breakdown, W being a win for them and L being a loss for them: 49% W (win) 26% LL (loss) 13% LWL (loss) 12% LWW (win) So in this case I lose about 61% of the matches even though I win 51% of the games. It can only get worse if they are willing to play more games. If they will play five games, they can pick up another 6% I think. So they are up to 67% So I think that if it is your goal to win a match, it is a major advantage to be the one who decides when the match ends. Which is one reason I don't want to play a non-specific number of games against Morovic, I might add. Another thing, is that if these opponents are really that close together, a won match should result in an increase in rating. So most of the time you'll win not only the match, but rating points, even though you are the weaker player by a small fraction. If you play enough matches this will balance out, since ratings are based on individual games, and nothing about this experiment changed the fact that you still lost 51% of the games. bruce
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