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There are a number of chess programs that will calculate win % based on any board arrangement. Is there a specific opening (first move) for white or black that is best from a probabilistic standpoint?

I'm guessing there is for white, and the optimal black opening will depend on what move has been made prior. I'm trying to make no presumption on the skill level of players from which these probabilities have been calculated.

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    I think you might get better answers at chess S.E: chess.stackexchange.com
    – Cohensius
    Feb 4 at 9:38
  • I'm pretty sure the answer here is "yes, but we don't know what it is. Chess is too complicated", although as this is a game theory question you will need to define much more precisely what you mean by "a probabilistic standpoint". Feb 4 at 15:04
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    If there is an optimal move it is likely going to depend on the skill level of both players.
    – Joe W
    Feb 5 at 14:28
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    @JoeW If the optimality of a move depends on how your opponent responds to it, it is by definition not optimal. I agree that in general "how good" a move is can depend on the strength of your opponent (and how well you can handle the subsequent board state), but an optimal move cannot in some cases be sub-optimal. A move whose strength relies upon your opponent making a mistake isn't optimal, optimal moves must assume optimal responses. Feb 5 at 14:59
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    @NuclearHoagie If chess was a solved game you might have a point but as it isn't and there are many different philosophy's in how you play and open that means what is an optimal move in one game isn't in another.
    – Joe W
    Feb 5 at 20:21

3 Answers 3

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From a game-theory standpoint, from each opening, either:

  1. White can win for sure,
  2. Black can win for sure,
  3. Both players can force a draw.

This is known as Zermelo's theorem and it is true to any finite, 2p game, with perfect information, where players move alternately and no chance involved.

Therefore, if Chess will be solved and a White win will be found, then we could say that optimal openings are the ones that white can win for sure. If it will be found that black can force a draw from any opening, then any opening that both players can force a draw will be optimal.

From probabilistic standpoint, we can look at the win/lose/draw statistic of games that started from each opening. However the skill of the players is crucial. I am no Chess expert but I know that some openings are easier then others. What I am saying is that the win/lose/draw statistic of a certain opening can hugely differ when looking at games between amateurs or games between masters.

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    I don't think this addresses the actual question. It explores some of the theory behind what could lead to an answer, and it looks like this is leaning towards a "no" opinion but doesn't actually come out and say it.
    – Andrew
    Feb 5 at 14:33
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    Actually Its more like a "yes". After Chess will be solved there will be a list of moves that lead to a sure White win (this list might be empty). More practically, we can look at games statistic of a certain Skill level, and find the first move that leads to highest win rate of White in that skill level.
    – Cohensius
    Feb 5 at 14:39
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    Then in that case I think the answer needs a pretty major rewrite, because it didn't read that way to me. It also relies pretty heavily on the question of "If chess can be solved" with the assumption that it can
    – Andrew
    Feb 5 at 14:40
  • @Cohensius, I'd presume the best a computer can do is calculate a subgame-optimal strategy, and even this will depend on the skill level of the player and opponent. Truly, was hoping for someone who has read so many chess manuscripts that this question has been addressed. Feb 6 at 2:24
  • @Andrew, The "From probabilistic standpoint" part does not relies on solving chess, just data of games in a certain skill level. I am not sure what you mean by a major rewrite, if you think you can improve the answer then please edit it.
    – Cohensius
    Feb 6 at 20:46
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This question is vague, so the answer itself is unclear. At the risk of giving you more than you wanted, here're some answers anyway.

If you take "best from a probabilistic standpoint" to mean that the game-theoretic result is the best one possible, and all winning positions are equivalent (and all drawn positions are equivalent), then the answer is "no". That's because chess is almost surely a draw, so unless your opening move is so bad you lose immediately afterwards,* your first move is just a choice between different options that are equally good. In that sense 1. e4, 1. d4, 1. c4, and 1. b4 are all equivalent.

If on the other hand you take "best from a probabilistic standpoint" as the opening evaluation of the strongest chess engines today, then the best moves are likely 1. e4 and 1. d4. These are the two moves that engines are most likely to choose, if left to their own devices, on move 1. The exact "best move" depends on several factors however, such as 1) hardware used 2) time you let the engine think for and 3) which version of the engine is used (different versions of the same engine prefer different moves).

On yet another hand, if you take the "best from a probabilistic standpoint" as the move that wins the most in chess databases, then the best move depends on the database you use, how much importance you ascribe to statistical significance, and whether you impose any cutoffs like "master games only". Doing neither of the latter two means 1. Na3 is best according to these two databases. You write in the OP that "I'm trying to make no presumption on the skill level of players" - but if you take this literally, then worstfish** is a legitimate player, and you can easily skew your results by getting worstfish to play against random_move.

So what does "best from a probabilistic standpoint" mean to you? The answer will differ for different definitions.


*There is some circumstantial evidence that 1. g4 is the only first move that is losing for White.

**This is Stockfish configured to play the worst move available.

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  • Excellent input, and yes the question is somewhat theoretical in that no computer can "calculate" chess and no database has calibrated win probabilities from every match at every skill level. Thanks for meshing well with some of the other answers. Feb 7 at 3:14
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The current consensus is that chess will not be solved, at least not any time soon. Because the game isn't be solved, that means there is no single optimal opening move for white, and even more so for black.

Chess is one of the games where you play your opponent as much as you play the game, different styles, strategies change how good each possible opening move is because of how players will go through the rest of the game. The Scholars Mate for example is a great opening move against very new players because it leads to the fastest possible win, but against someone who is experienced it's overextending valuable pieces without significant defenses.

White is making their opening move on a single possible board state, black on the other hand has 20 possible board states (8 white pawns can each move up one or two makes 16, 2 knights can either move left or right for the other four), and each of those board states would have moves that are better or are worse based on what white has access to and exposed with their first move.

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  • All true, and remember this thread should you read something scientific! Feb 6 at 2:26

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