The probabilistic game of chess

as the title says. any thoughts? no trash. no gutter. nobody below 21. or let's say 30 years old. that should reduce server load for this thread, hopefully. or i will bask in the calm of silence, and make it part of my hitch-hiking blog.

I would say that with best play by both sides, chess is deterministic. However, in the real world, a less-than perfect engine or human player can make moves that are accidentally bad or accidentally good, and that introduces an element of chance into the game.

no trash. no gutter. nobody below 21
Perfect! Let's start with removing this thread.

Chess has been played with dice.
See: https://en.wikipedia.org/wiki/Dice_chess#History

what about plans that have objectives beyond human combinatorial horizon. mine is 3 whole move max. yet i do think about how the game could evolve beyond that, i make choices about the likelihood of a position to yield better combos further than ability to make pure deterministic calculation. probability does not mean uniform probability. Are theories to date, predictive enough to make 100% predictions beyond that human horizon? within that horizon, one can often have no material gain differences between seen candidates, then has to rely on some instinct, or explicit rules from "theory" or "analysis", but are those deterministic? if not, are they quantifiable in terms of probabilities? somehow? again not uniform. you know that it may turn out that a probability density, be concentrated on a point. could be one move. all bets on that move says the probability.

PS: the agist restriction was a joke. because hormone tends to be at higher levels and chess combined with that age, might lead to knee jerk reactions to the topic title. lack of experience with life, may narrow the gamut of angles that the title may be looked at. but everybody is welcome to try some interpretation of the title. without panicking.

@dboing #5. "i make choices about the likelihood of a position to yield better combos ... "
Are you saying this is how you personally play, which is how it reads, or that this is a hypothetical?
If you play that way, then I'd say you are playing in a style that emphasizes attack. That style can win many games. At the higher levels of chess, OTB especially, other considerations are considered.

Material gain is only one factor used by both humans and computers. It is interesting to read the eval function of Stockfish to get an idea of what the programmers considered important besides material gain. Being a programmer, you will have no trouble reading it. See: https://github.com/official-stockfish/Stockfish/blob/master/src/evaluate.cpp

@dboing There is a commercial chess variant called "No Stress Chess". It uses cards to inject probability into chess.
It is touted as a way to help people learn chess, but start will all the pieces. There are levels of rules so that not all the rules are thrown at the novice at once. A typical card is for one piece and has the basic piece movements on it as a picture and text description.

https://www.amazon.com/Winning-Moves-Games-Stress-Chess/dp/B0007Q1IO4

@dboing I just thought of something else you might find interesting. Humans do not always play the best move even if they know what it is! That's because "best" is a relative concept.

Here is a specific example. The game is Rosanes, Jakob - Anderssen, Adolf, 1862. The game is featured as game 1 in "Masters of the Chessboard", by Richard Reti. I have it in a study here:

Black's move 16... Red8 is actually a blunder! It is in the sense that it drops the score by 6 points. Yes, Black is still winning and the move was, per Reti, "A quiet waiting move quite in the Anderssen manner and preparing a brilliant combination..."

Well, objectively, you should not assume that your opponent is going to make a mistake, but instead that they will play the best move possible. Of course in practice there are some masters who purposely don't make the best move. Like Anderssen here, who figures that Rosanes will not see the mate in 5 after 17.Nf3?? . I'm here assuming that Anderseen saw 16...Qa5, which with best play by both sides ends up with White losing the Queen to prevent mate. If Anderseen saw that, then his choice of the other move was guided by some other definition of "best". Thanks to his choice, the pretty mate is recorded history.

@jomega very interesting posts, food for thought. I don't really know how I play, I was more describing the most likely situation that may arise, where the question arises of choosing among variations that have no difference in material gain within horizon.

I do seek to improve my understanding of the kind of theories that can help make such choice within my fluctuating horizon (in the wide sense used in chess literature, or in my narrow minded sense from the wheel of science in physical sciences).

Currently i have been playing mostly correspondence, for various reasons, but what emerges from that experience, is that:
even if I have an algebraic notation digital notepad*, at my disposition, my horizon limit stills shows in how wide and or deep i can explore without feeling lost (saturating my short term memory or something like that). so it makes it clear to me, that I need to be smarter than pure combinatorial deterministic logic, and train some other skills I discussed above. So what I described is more what I would like to do, so that my inner probabilistic model of what happens beyond my combinatorial horizon, gets better at judging fast how wide to start my combo candidates, and for a given max depth, how to judge fast, which line is going downhill, from looking at the position. I hope this answers your question. My wording may have been too concise, to make my point clearer. I am trying concise over precise, and I am doomed to fail. anyway.

I wonder how many players accept that they have a finite combinatorial horizon. and what they do, when their lines candidates on notepad or in their mind, does not show material gain. do they stop playing the game?

• = (lichess move explorer through the in-game analysis button, which BTW looks like a horse-shoe, but depending on the angle one looks at it)

It will take time for me to digest your posts, and the links suggested. This thread can survive a month without new posts....

@dboing No matter what level of chess strength people are at, they know they can only look ahead so far; which is what I assume you mean by "combinatorial horizon". The look-ahead process creates a tree; either in the mind or written somehow. It is best if the terminal nodes of that tree are what is called "quiescent" - meaning that at that node you can evaluate it without further look ahead. This process is described well in the book "Think Like a Grandmaster" by Kotov.

Now you said "... the question arises of choosing among variations that have no difference in material gain....". So this would mean that the terminal nodes you have not eliminated by using just material as a consideration now need to be evaluated by some other means. Most people refer to this a "positional evaluation" - meaning evaluation without considering material.

There is a long history in chess of what to look at in that case. In my courses here on Lichess I cover this in many ways. The first is to consider what is called features determined by pawn structure. The main study for that is here:

The references I used for that study included [PCC] "Point Count Chess" by I. A. Horowitz, Geoffrey Mott-Smith, 1960. See chapter 3 in the link above for the categories. Don't bother about the point system they used; that was a silly idea. The idea is to learn the categories and what they mean. The more modern reference I used was [RYC] "How to Reassess Your Chess" by Jeremy Silman, 1993. That book is on the Silman Imbalance Theory of chess. Silman's theory has fewer categories.

It takes a long time to learn all of that, and then to get it internalized, but it certainly is not the end of the learning process. The next thing after those, would be to learn the pawn structures themselves. These have been categorized as well. There are two main references I know of for this. The first is the Soltis classification and the second is the one by Kotov. The Soltis classification is the one used on Wikipedia. Also in my studies. The Kotov one is much simpler and is in his book "Think Like a Grandmaster."

My top level study on the Soltis pawn structure classification:

This is admittedly a very academic way of looking at how to learn positional considerations. For a beginner it is much better to start with some good books that are talking about positional considerations as well as tactics. I'd recommend the books "Logical Chess Move by Move", by Chernev and then "Masters of the Chessboard" by Reti. Book these books are light on variations and more on ideas. They have mistakes in analysis, but that is not very important.