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I asked this question at chess.stackexchange, but perhaps it is more suited here. This question might be equally applicable to other games which are not solved games and which have three outcomes: win/loss/draw. I am most familiar with chess, so here it goes.

Some preliminaries regarding chess, chess engines, etc.

If you know everything about chess and chess engines you can skip this section.

Chess engines/computers evaluate the position in a game based on some algorithm (details of which are not important here) and give a numerical score, where positive numbers mean advantage for white, and conversely negative numbers advantage for black. These numbers always fluctuate from move to move (basically due to the algorithm).

Empirical evidence has shown that starting from a position with an evaluation approximately within the interval [-1,1] still end in draw with perfect play (as much as we know what perfect play is). Exact numbers for the interval boundaries are not important for the question.

If the evaluation of a position is outside of this interval white/black will win with perfect play if the evaluation >1 or <-1 respectively. In order to win typically the player with an advantage would increase their advantage, so the evaluation would subsequently increase with the number of moves made, e.g. from +2, to +3, +4, ... +10.

In order to get from a draw position (evaluation in [-1,1]) to a won position, one of the players has to make a mistake.

An example for what this looks like is here, where at the bottom of the page ("Computer analysis") there is a graph of evaluation vs. move number. White made a mistake at move 15 resulting in an evaluation of -2.4 and black subsequently increased its advantage to -5.

Proposed model

The situation described reminds me of the escape from a local potential minimum. As follows:escape.

Starting a game of chess the evaluation (blue circle) will be at 0 (or small positive reflecting the fact that white moves first). If players keep on playing perfect moves the evaluation will fluctuate a bit but stay around 0 (blue arrow).

In chess typically a player can chose between many moves that keep equality, so there is some "resistance to a decisive result" which is depicted by the "potential hill/barrier"

If one player, e.g. black makes a big mistake/blunder (red arrow) the evaluation can escape the hill and the "particle/evaluation" will roll down the hill to even larger values as the game goes on, which means that one player will win.

Questions

  1. Is there anything intrinsically wrong with modelling chess games like this? (I understand that in many games you have blunders from both sides and the evaluation can go back and forth)
  2. Has such model been used before to study chess or any other game?
  3. Could it be interesting to investigate chess or chess engines in this way?
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closed as off-topic by Jon Custer, Michael Seifert, sammy gerbil, Yashas, John Rennie Mar 22 '17 at 6:44

  • This question does not appear to be about physics within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I'm voting to close this question as off-topic because it is not a question about physics, but using a vaguely physics-like concept to analyze chess. $\endgroup$ – Jon Custer Mar 21 '17 at 14:26
  • $\begingroup$ It is not necessarily off-topic; for example the concept of entropy that was originally introduced in physics has successfully propagated into information theory. $\endgroup$ – Maxim Umansky Mar 21 '17 at 14:59
  • $\begingroup$ Zermelo's theorem in game theory looks relevant here $\endgroup$ – Maxim Umansky Mar 21 '17 at 15:03
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This question belongs probably to some other site, since simulation of non-physical processes is out of the scope here.

There is nothing intrinsically wrong with your proposed model, in the sense that it reflects the behavior you want to simulate.

That being said, I am skeptical that it has been used since it does not improve the capacities of current models.

The main problem of simulating chess is evaluating correctly the position, because then the game can be reduced to a search for the optimal value. This is, finding a function that takes the relevant inputs and that computes fast and correctly a value to assign to the current situation in the game, such that it reflects the chances of winning.

While your picture helps understanding the ideas you spoke about, it is of little use for modeling, just as knowing that in order to win you need to bring the value closer to a winning range. Knowing what the optimal evaluation is, does not help deciding which plays are more convenient, or which should be avoided. Instead, the useful information comes from the evaluation process or function, which says what moves are optimal and which are blunders.

Unless you propose a different process for evaluating the situation, its advantage will not become apparent.

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  • $\begingroup$ I did not mean to use this to improve on engine algorithms. Rather it might be useful for insight into human play. $\endgroup$ – user1583209 Mar 21 '17 at 14:18
  • $\begingroup$ In that sense, I am of the opinion that human way of playing chess has more to do with the human mind than with the mathematics of the game. It is unclear whether the human mind does any optimization computation at all, its representations are probably far from logical, at least in the mathematical sense, and hence a harder to model. $\endgroup$ – rmhleo Mar 21 '17 at 14:28
  • $\begingroup$ I agree with this. I think it's neat to model it as a local minimum potential, while showing blunders as a potential increase which may allow access to even lower states. That said, I also see no application for it. It was derived from the chess algorithms, this is nothing the algorithms don't really tell you with experience. $\endgroup$ – JMac Mar 21 '17 at 16:12

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