Is there an estimate for Perfect Play ELO?

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Topic Rybka Support & Discussion / Rybka Discussion / Is there an estimate for Perfect Play ELO?

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By Uly

Date 2010-09-22 08:36

I guess Labyrinth meant "reasonable time", if Rybka would find the move in 2000 years it's as if she never found it.

And anyway, positions have been posted where Rybka "depths out" at ply 59, just stops searching, and doesn't find the move.

By Athinira (**)

Date 2010-09-18 20:44

In my opinion, you can't define "Perfect Play" in ELO.

Perfect play is the equivalent of being able to evaluate any chess position or chess move with the scores "Win, Draw or Loss" and never be wrong about it. But even in a scenario where that is possible, some moves might be more physiologically intimidating, in case the perfect engine is playing against an imperfect opponent. Two moves might both be evaluated "Draw", but one move might increase the chance that your opponent makes a mistake.

Putting this another way: ELO doesn't represent playing strength in itself (at least in the world of computer chess). Rather, it represents the ability to improve your position (even if the position is still a forced draw). True chess evaluation is not about evaluating whether a position is won, lost or drawn (which is a criteria for playing perfect chess), but rather it's about evaluating how you can best increase your chances of winning.

By ThudanBlunder (**)

Date 2010-09-18 21:49 Edited 2010-09-18 21:53

> True chess evaluation is not about evaluating whether a position is won, lost or drawn (which is a criteria for playing perfect chess), but rather it's about evaluating how you can best increase your chances of winning.

True, but any subjective factors are hard to quantify reliably and may even backfire.

So, sticking with an objective model for the moment, according to von Neumann and Morgenstern every zero-sum game of perfect information (such as chess) has an optimal strategy. In chess this optimal strategy would be a series of 'best moves'. But how does one define a 'best move'. Consider White's first move. We can divide all possible games of chess into 20 categories, corresponding to the 20 possible first moves for White. For each first move we can add up the aggregate number of points that the move would score from all possible games beginning with that first move. So the move would score one point for every win and half a point for every draw. If using this system the best first move turns out to be (say) 1. e4 then we can do the same for Black from the position after 1. e4, and so on. I think this would result in one version of Perfect Play. However, as chess is almost certainly a draw with best play, against imperfect opposition it is probably better to choose the move which maximizes the number of wins in any given position.
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By Athinira (**)

Date 2010-09-18 23:12

> But how does one define a 'best move'

One doesn't, because it is impossible against imperfect opponents. Different moves work differently against different human opponents.

Your approach of scoring moves based on how many winning/losing/drawing positions is one way to try generalizing it, but it's sadly not a good way, because it artificially scores moves highly if those moves lead to a position where your opponent can make alot of bad moves/mistakes. In the position below, for example, your system would rate any white move with the e2 knight highly because black can do alot of wrong moves that results in mate with 2. Re8. That, and it also scores moves that prolong the game higher.

rn4k1/p1br1pp1/q6p/2pp2n1/P7/N1P5/1PBPN1PP/R1Q1R2K w - -

And if your opponent isn't human/is perfect... well, why are you playing in the first place then, when you can't win anyway? :)

Topic Rybka Support & Discussion / Rybka Discussion / Is there an estimate for Perfect Play ELO?

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