lucasart wrote:mwyoung wrote:
Here is my result of a small 1 year sample of Magnus Carlsen games. Games from chessgames.com. Run with Fritz elo calculator.
2012 rating as white 2820
2012 rating as black 2766
First move advantage seems very important at the top levels.
The sample may be small to conclude, in theory. But in practice, your conclusion is correct, as well as the order of magnitude of the white elo advantage.
I've collected lots of statistics, by letting my engine play itself 10,000 games at different skill levels, and what appeared was that the equivalent "white elo advantage" was
* very small at weak levels, barely 10 ELO. this is simply because weak players often lose because of stupid blunders, whose occurence can be considered as an orthogonal source of random noise.
* gradually increasing with the skill level, reaching about 35 ELO at 2500 ELO.
I conjecture that it continues to grow, and eventually starts to decrease and go to zero as ELO goes to infinity. The point is that, after some insane ELO values are reached, the chess level becomes so near perfect that almost all games are drawn, so the white's advantage gets forcefully diluted by all the draws:
* when ELO goes to infinity, it is possible that P(White wins)/P(Black wins) remains significant, but it doesn't matter, because P(Black wins) <= P(White wins) << P(draw).
* Even in the worst case scenario, where P(white wins)/P(black wins) --> + infinity, the fact that P(draw) --> 1- ensures that white's ELO advantage goes to zero anyway.
Lucas, an interesting point indeed.
You will excuse me, I am no good at formulae, but logical thinking and common sense tell me that the elo gain is going to increase continuously up to the very last moment when opponents start playing perfect chess.
If we assume the first move advantage in terms of evaluation is some 15 centipawns (or whatever other value not very different from that), than there will be a number of variations leading to a draw with perfect play. There are no reasons however for the eval with perfect play to draw closer to zero, unless we continue the game right to the point of leaving only both kings on the board.
By 15 centipawns' advantage, and assuming no perfect play, a reasonable conclusion by today's top humans and engines, the number of variations that would increase the score for the stronger side would be larger than the number of variations that would decrease the score, favouring the weaker side. At lower elo levels, players have more difficulty assessing which variations lead to increase or decrease of the score, and therefore chance events have a bigger role, meaning that some variations that should lead to an increase of the score actually lead to its decrease. Obviously, the elo gain will be small.
Again, assuming no perfect play, and gradually rising strength of the opponents, the elo gain will be bigger, as those players will recognize much better which variations lead to an increase and which to a decrease of score, eliminating chance events. Those players will be making a better use of the availability of a relatively larger portion of variations increasing the score.
I guess this will go on like that until perfect plai is reached. i suppose that at 3200 elo the elo gain is much bigger than at 2800 (Carlsen level). Maybe Ingo or Stefan could provide some stats for percentage of white/black wins from their databases, although the short time control might support chance events.
I looked at the 2 recent matches, run by Clemens Keck, of Komodo against Houdini and Stockfish, and the data is as follows:
31 games in Komodo-Stockfish, 5 white wins, 2 black wins and 24 draws
19 games in Houdini-Komodo, 7 white wins, 1 black win and 11 draws
Overall 50 games, 12 white wins, 3 black wins and 35 draws
Maybe someone could do the maths, by I think white performance is significantly better than at top human level. But we could also take as a reference the match of the probably best 2 currently, it is 7 to 1, that should probably ring a bell:)
We should also bear in mind, that once the 15 centipawns' advantage starts increasing, the number of variations favouring the stronger side will also increase in relation to the number of variations, decreasing the score, and drastically so with the drastic increase in score. By 30-35 centipawns (of course, assuming an accurate evaluation) there might still be a sufficient number of variations available, not increasing the score, but I doubt very much that once you reach the 40 centipawns-half a pawn threshold, the side lagging behind in score will be able to hold on to a draw.
Just my....
Best, Lyudmil
