David Richerby <davidr@[EMAIL PROTECTED]
> writes:
> By the way, just to inject some actual data on the magnitude of the
> draw problem in chess...
>
> http://www.chessgames.com
has a large database of games, mostly
> between strong players. Their `opening explorer'[1] gives win/loss/
> draw statistics for the most commonly played openings. Of these, the
> moves 1.e4, 1.d4, 1.Nf3 and 1.c4 account for 98.3% of the 460,000
> games in the database. Restricting to those four opening moves, we
> see that:
>
> 36.8% of games (167,000) are won by White
> 36.6% of games (166,000) are drawn
> 26.6% of games (120,000) are won by Black
>
> We already have 63.4% of games ending in a win by one player or the
> other. Is it really necessary to `solve' this `draw problem'?
>
> Another issue is this: it is clearly seen that White has an advantage.
> White scores, on average, 0.551 points per game, compared to Black's
> 0.449 points per game. Any system that reduces the score for draws
> will make Black's position slightly worse, since he gets more of his
> points from draws. The option of giving a third of a point for draws
> would give White 0.490 points per game and give Black 0.388: White
> goes from scoring 55.1% of the available points to scoring 55.8% of
> the points. This effect is smaller than I would have expected.
Just for comparison, BAP scoring assigns a value of
(2*.368+1*.366+0*.266) = 1.102 for white
(0*.368+1*.366+3*.266) = 1.164 for black
or 48.6% to white
I don't know if it's ever been proposed, but
3/2/4 rather than BAP's 2/1/3 would assign values of
(3*.368+2*.366+0*.266) = 1.836 for white
(0*.368+2*.366+4*.266) = 1.796 for black
or 50.6% to white.
Similarly, having a draw worth 2/3 to black, 1/3 to white yields
(1*.368+1/3*.366+0*.266) = .490
(0*.368+2/3*.366+1*.266) = 0.510
Of course, I have no idea how representative of modern
tournament results the above pro****tions are.
Phil
--
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