Author: Ratko V Tomic
Date: 08:55:16 10/16/99
Go up one level in this thread
> Even after seeing your equations, I'm still not sure how you can > determine the pondering percentage by the winning percentage. If you know the rating difference you can compute total/effective thinking time difference or time ratio (using D=C*(R-1), using value C=100 rating points gain for doubling the thinking time). Once you have full thinking times ratio, and you know the time controls each _nominally_ got, you will notice that the effective thinking time ratio (as obtained from rating difference) is greater than the nominal time controls ratio, e.g. in the 1st match both had equal nominal times, but the time ratio from performance difference was 1.78, i.e. the pondering Rebel had more actual/effective time. Hence you can compute how much extra time the pondering version got to reach the times ratio expected from the performance ratings difference. That extra time can only come from the pondering time gain, and that's how you get G, the gain hit rate. (Obviously, in a fairly small sample as this you have a significant statistical error marging, so take the numbers 80% with a grain of salt.) >If pondering Rebel had win 100% of the games, would you say it pondered >with 100% accuracy? No. That could be only due to a statistical fluctuation in a 100 (or any finite number) game match. For example, if instead of different time controls you used depth D and D+1 versions, the D+1 will guess correctly the move of D version in every single move, 100% guess rate. Yet it will lose 20-30 percent of games. Guessing what the opponent will play doesn't mean it will find a correct answer to that move. >(And were you not the one saying that a shallower >search can produce ultimately better moves in >many cases? In these cases, a correct pondering would _worsen_ the result. :) > It's not something I made up. There are papers with D vs D+1 types of results. So it is a well known fact, not an opinion. A shallower search can in some "good percentage" of positions produce better move than the deeper search. Obviously the exact meaning of "good percentage" depends on positions, on depths used for the two versions and the kind of search algorithms and evaluations used. In any case, it is not anywhere near zero or negligible. The cause of this seemingly paradoxical phenomenon are the inaccuracies in the evaluation functions and the tree traversal approximations used in minimaxing (which cut down the branching factor below sqrt(Width) which is the rigourous minimaxing optimum i.e. from 6 down to 3 or 4 in a typical middle game; e.g. some kind of forward pruning or other heuristic shortcuts). So when program evaluates some root move, and comes back with value V, that means only a kind of median or average value of a distribution of values, as if you said that some nation has $9500 per capita on the bank accounts. Some people will have more, some less, that's only the average. So when program comes back with Value(Move)=1.5 pawns, that's a hypothetical average (its estimate) over unknown distribution of values (which can be sampled over many games). In each individual position the actual value (as a perfect player would give) will be almost always completely different, just as your savings account will be almost always different from the national per capita savings average. Therefore, the phenomenon of a shallower search finding a better move than a deeper search, is as "strange" as someone from US having a larger saving account than someone from Japan, even though per capita savings for Japanese may be larger than for Americans. >Again, I thank Ed for running this experiment, and hope that he or others can >continue to make similar experiments to determine The Truth. :) Yes, the Ed's experiment was a nice result to have.
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