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Chess is usually considered a mostly "fair game" between White and Black because the opening position of pieces has mirror symmetry (between players). In practice it also appears to be a fair game because it is combinatorially complex, so if White has a first-move-advantage, it is hard to detect in actual play.

What are some examples of changes in the rules of chess where the game can be made exactly mathematically fair, including eliminating any possibility of White's possible first-move-advantage, and without adding any chance events (such as a coin toss as to who moves first)?

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    $\begingroup$ What does any of this have to do with computer science? $\endgroup$ – Kyle Jones Oct 16 '17 at 18:18
  • $\begingroup$ Chess is often studied using computer algorithms, including simulating grandmaster-style play, and measuring win and draw rates. $\endgroup$ – tomoka kazuki Oct 16 '17 at 18:57
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    $\begingroup$ We don't know if chess is not absolutely fair: it's unsolved game. $\endgroup$ – rus9384 Oct 17 '17 at 6:36
  • $\begingroup$ Agreed - chess may be a draw, and it is possible (although unlikely) that chess even has an equal number of imperfectly played games that lose for White as lose for Black. But we do know that the game-graph is non-symmetrical in terms of move options between White and Black. As early as the second move, White can control some squares on the 5th rank, which is a tempo before Black can do the same. From here Black's choice of moves can already be described as reacting to White, rather than creating a board position of his own choosing. $\endgroup$ – tomoka kazuki Oct 17 '17 at 13:43
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We can run a pair of games, sequentially, where player one first plays white, then black.

Let's write W for win, L for lose and D for draw, from the point of view of player one. In the cases WW,WD,DW, player one wins the match. In the cases LL,LD,DL, player one loses the match. In the cases WL,LW,DD, the match is a draw. (If a draw match is undesired, play another match.)

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  • $\begingroup$ That's not a bad idea. Tournaments can be fair, whereas a single instance of the game is not. Very close to an ideal answer. $\endgroup$ – tomoka kazuki Oct 16 '17 at 19:04
  • $\begingroup$ I like this idea, however, I'm not convinced. This seems like an inherently different game than chess. Maybe call it "two-game chess". Is there a way to modify this such that one game of chess is fair? $\endgroup$ – ryan Oct 17 '17 at 1:11
  • $\begingroup$ This solution while logical works less and less the closer you get to the two competitors playing perfectly. If both played the game perfectly, you would draw infinitely or the white player (or black player if that side later on is seen as having an advantage) always wins, forming a never ending cycle of WL WL WL $\endgroup$ – Hatefiend Oct 17 '17 at 7:21
  • $\begingroup$ @ryan I actually have the same opinion. The above one is a generic technique that can be applied to any game, and is not specific to chess. Making a single game of chess fair is intuitively much harder to do, and might need to twist the rules of the game so much that the game is hardly chess anymore. Still, I'd also be interested to see if something like that exists. $\endgroup$ – chi Oct 17 '17 at 7:27
  • $\begingroup$ @Hatefiend I agree. Yet, suppose we modify chess so that white and black are perfectly balanced. When two competitors approach perfection, they would probably draw most of the time, and need to play a large number of tie-breaking games to determine a winner. The only way to avoid this, as far as I can see, would be to remove "draw" as an outcome of a single game. This would mean that one side has an advantage, though it might be very hard to play perfectly. One could argue that this new game is no longer chess. I'd like to see "fair chess" proposals in this direction. $\endgroup$ – chi Oct 17 '17 at 7:33
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Chess has not been solved: that is, there is no runnable algorithm which can look at a board and see if there is a move that will guarantee a win for one player. Minimax does this in principle, but when starting from a fresh chess board, would take far too much time to complete. So, we don't know who would win if we had two perfect, omniscient players.

This is in contrast to Checkers, which has been solved. It turns out that if both players play perfectly, it will always be a draw.

So the answer to your question could be that chess is already mathematically balanced between both sides. Or it could be that one side can always win if playing optimally. But we don't know, and may never know.

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Simple. Throw a coin to decide who moves first.

In a single game, white has a distinctive advantage. Usually you play tournaments where each side plays white and black equally often.

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    $\begingroup$ The question asked without adding chance. $\endgroup$ – tomoka kazuki Oct 16 '17 at 19:03

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