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.
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.
- 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)
- Has such model been used before to study chess or any other game?
- Could it be interesting to investigate chess or chess engines in this way?