Chess as random process Not sure whether this is more of a physics or a chess question.

Looking at the evaluation graph (computer evaluation vs. move number) of a game of chess, I realized that there are some similarities to the physics model of escape from a local potential minimum. Let me explain:

While none of the players make a mistake the evaluation will stay at values around zero corresponding to a draw. This I would associate with the motion of a particle in a local minimum, whose coordinate (=evaluation) might fluctuate a bit around the minimum value.

If a player makes a mistake, the evaluation will increase to let's say +2, corresponding to a won position. Normally (i.e. with a very high probability) white should win this game. Until mate, the evaluation will further increase to +3, +4, +5....

This process is similar to the escape from a local minimum. A blunder can "activate" the particle so that it can leave the local minimum and it will subsequently accelerate to larger coordinates (evaluation increases).



Have there been any studies on chess using such model?

Does it make sense at all?
I'd argue the process you're talking about can be represented by Markov Chain. It solves the continuous problem raised by @Brian.

I don't know where to find a proper state diagram for your question.The following diagram is for a simple board game. Imagine we model the transition probability from win to lose (or win to draw) as the blunder probability, this is similar to what you are asking.



We can represent "local minimum" described in your question as an absorbing state.

More generally, if you want to assume some latent factors for making a blunder (e.g. bad opening, personal issues), you could generalize to hidden markov model. It's possible to use the EM algorithm to fit a model from engine PV evaluations.

Given a fitted model, you can query the probability of a blunder given a chess game.


  Have there been any studies on chess using such model?


No studies that I am aware of.