Author: Jay Scott
Date: 04:55:18 07/31/98
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On July 31, 1998 at 01:51:57, blass uri wrote: >The programs I know give me evaluation in pawns and I prefer to see >in the evaluation function the predicted result of the game(number between 0 >and 1) and not an evaluation in pawns. For my part, I'd prefer a probability distribution giving the chances of a win, loss or draw. But the chess programmers don't seem to have any plans for it. What you are asking for can be called the equity of the position. It's (probability of win) + 0.5 * (probability of draw), if you assume that a draw is worth 0.5. (In a tournament or match, the value of a draw may be more or less than 0.5, depending on the tournament or match situation.) You can use Komputer Korner's table (from his posting in this thread) to get a rough idea of how to convert a score from pawns to equity. However, it may be that every program is different. If so, you'll have to calibrate each program you're interested in separately. One way to estimate a program's score->equity conversion is by having the program play a lot of games against itself (it should be against an equal opponent, and what opponent is more equal than itself?). Divide the range of scores into intervals, maybe 0-0.2, 0.201-0.3, etc. For each interval, count up the number of times that a score in that interval occurred in won, lost, and drawn games. Then you know what a score in that interval means. You need a lot of games to make the statistics valid. It would be nice to automate the process. For example, to do it with crafty you'd like to write a program that reads crafty's log and adds up all the numbers. I'd like to recommend this exercise to chess programmers as a way to test the meaning and validity of their evaluation functions. You can also use it to examine individual evaluation factors. For example, if you're wondering about your two-bishops bonus, you can run the numbers only for positions where one side has the advantage of two bishops. If the bonus is too big, you should expect to see a flatter curve, or a shifted curve, as the score goes up more than the chance of winning. You're less likely to see an effect if the bonus is too small, because the side with two bishops will be willing to give them up without taking full advantage of them. Summary: You get more information from the detailed behavior of the evaluation function in test games than you get from only the results of the games. Jay
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