Is there any proof ensuring there can be no dominant strategy for chess? By dominant strategy, I mean a way of playing that always works regardless what the opponent do.

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    Quite the opposite... there IS a dominant strategy, and it can be proven that there is one. – GendoIkari Mar 19 '18 at 17:35

One of the following is true:

  • There is a dominant strategy for White.
  • There is a dominant strategy for Black.
  • There are strategies for both players that guarantee they don't lose, i.e. perfect play results in a draw (e.g. as in Tic-Tac-Toe).

No one knows which is true. Most experts guess that perfect play leads to a draw, and a few believe White can always win. It is unlikely Black has a dominant strategy, but no one has been able to rule it out either. Theoretically, a computer working for long enough could just try everything and tell us the answer, but with today's best technology and algorithms that would take prohibitively long.

Here are some important features of chess that together guarantee that one of the 3 cases above is true:

  • Chess is a game of complete information, i.e. both players always know everything that is going on.
  • Players take turns (as opposed to playing simultaneously, e.g. as in Rock Paper Scissors)
  • The game always ends eventually (at least under tournament rules as of 2014, after enough moves are made that aren't irreversibly advancing the game, it's a draw).
  • There is no randomness.
  • There are only 2 players.

Intuitively, these facts let you completely reason out the consequences of everything that could possibly happen (if I do A, my opponent could do B or C, in which case I could do D or E...). For a more formal explanation of why this implies there are either dominant or drawing strategies, see Zermelo's Theorem.

[Parts of this answer are synthesized from earlier answers/comments.]

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    Very nicely broken down. (Am I correct in assuming you have some CGT background?) I've researched this issue a little, and recall that White seems to win by a narrow statistical margin, but, as you note, the game remains unsolved. I found a wiki on first move advantage the questioner may find useful: en.wikipedia.org/wiki/First-move_advantage_in_chess – DukeZhou Aug 11 '17 at 19:07

essentially, it seems that in a more complex game, it is more likely that there will be a draw. Connect-Four is the most complex game we have solved so far, and although the first player wins, that is due to the mathematical nature of the game (i.e., it is impossible to go back to a previous position like for one side of chess). There is no proof that either side wins in a perfect game of chess, however, a draw is very likely since most expert games are beginning to end that way. We don't have to explore every single chess game possible--just the strongest moves. (NH3 is stupid, guys. It doesn't help us at all)

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  • If you've never opened Ammonia as White, you've never truly lived. +1 – user45266 Dec 18 '18 at 3:49

The term "dominant strategy" is generally used for games with incomplete information (or simultaneous moves, which can be analyzed as a game with incomplete information). In a deterministic game where players take turns and there is no secret information, the term "perfect play" is generally used, rather than "dominant strategy". The term "dominant strategy" refers to a strategy that is better than every other strategy, regardless of what the other player does. However, in chess, you always know what your opponent did on their last turn, so the "regardless of what your opponent does" part is a bit redundant. The term "strategy" is often used to refer to the entire decision tree, including what you would have done if your opponent had done something different, but even there, the "regardless of what your opponent does" part doesn't add much; two strategies can't possibly have different results unless they differ with regard to moves actually taken.

And technically speaking, there is a weakly dominant strategy in chess (that is, a strategy that does as well as or better than every other strategy), but there isn't a strictly dominant strategy in chess (that is, a strategy that does better than every other strategy).

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Since chess is open-information deterministic game, it is bound to have some kind of optimal strategy for both players, which would result in same outcome every time, provided both players play perfectly. IMO this outcome would probably be a draw, but could be victory for either side.

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  • So, what about today's best computer players? I mean, did we find the best strategy for chess? – Ahmet Bilal Jul 14 '16 at 14:56
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    No, we didn't. Chess is too complex to fully compute, even for today's computational powers. Computers just exceeded the ability of top players to find better options. – Deo Jul 14 '16 at 15:31
  • This seems basically correct, though it's proven true, so I would remove the "bound to". Calling it an "optimal strategy" in the general case is a little misleading though. If the outcome is "white wins", then if white plays perfectly, any strategy for black results a loss, so it doesn't make sense to call one "optimal". – murgatroid99 Jul 14 '16 at 15:39
  • Thanks, those are valid points, should I edit? Although I'm not sure about changing "optimal". If expected outcome of perfect play is a draw, both players indeed have to play optimally to achieve it. I don't see better wording to cover all the cases, without going into too much details. – Deo Jul 14 '16 at 16:24
  • If it was my answer, I would reorder it. The crux is that if one player can force a win, only that player has an optimal strategy, and if neither player can force a win, both need an optimal strategy to force a draw (assuming win/loss/tie are the only outcomes we care about). So, you could talk about the possible outcomes, and then about who needs an optimal strategy to achieve those outcomes. Also, the theorem I linked requires that the game has alternating turns, so I would suggest mentioning that characteristic of chess too. – murgatroid99 Jul 14 '16 at 16:34

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