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What would be a chess position, where a player (white or black) has a maximum possible number of different moves to make?

There are two options:
1. The position must be possible to obtain in a chess game.
2. Any position, involving any number of chess pieced are allowed. (Most probably it is optimal to fill the board with queens only, but what number of queens is optimal, they would get in a way of each other).

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  • $\begingroup$ I think ideally there would be no enemy chess pieces, but since the position must be possible to obtain in a chess game, there must be the king somewhere, which, if this problem weren't complicated enough, also entails that the king cannot be in check or checkmate (or otherwise presumably it could not be your turn again). OP, if I'm mistaken about this, please indicate as such. $\endgroup$ – Neil Jul 8 '14 at 10:39
  • $\begingroup$ @Neil, additional enemy pieces can help to cover enemy king from checks. But in case 2 there must be no enemies at all, if I do not miss any trick here. $\endgroup$ – klm123 Jul 8 '14 at 12:33
  • $\begingroup$ I don't think this will have an optimum answer without some serious computational power. You will be placing 17 pieces on the board (or more as they don't hurt if they don't block). The knights and queens question was hard enough and the hardest one had only 11 pieces of 2 types. It would be interesting to see what "max I could get" answers people could submit. $\endgroup$ – kaine Jul 8 '14 at 12:48
  • $\begingroup$ @kaine, I agree. $\endgroup$ – klm123 Jul 8 '14 at 13:33
  • $\begingroup$ I'm building a genetic algorithm in order to try to optimize a solution, though I won't be able to prove that it is the best solution of course $\endgroup$ – Neil Jul 8 '14 at 14:16
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For a legal position, this was (as of roughly 30 years ago, but I don't think it's been surpassed) the record for available moves for one side, 218 moves:

enter image description here

The book A Guide to Fairy Chess has a number more then-record positions, including confirming the queens-around-the-edge position from the other answers, as well as records for most moves available to both sides, most moves available without promoted pieces, most moves available using all 32 original men, etc. Let me know if you'd like any of the other records and I'll add them to this answer.

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    $\begingroup$ Do you have the list of move that produces this board position? $\endgroup$ – justhalf Jul 14 '14 at 5:07
  • $\begingroup$ @justhalf I don't, but it's not hard to construct - Black's last move was clearly h3-h2; before that White can e.g. uncapture a black piece with the Rg2, then at some point for instance unmove the Q from f4 and unmove the N from f1 back to d2 , letting out the black King, etc. White could even e.g. take back a move like c7xd8=Q to give Black more available moves. $\endgroup$ – Steven Stadnicki Jul 14 '14 at 5:32
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Your answer shows a chess board with a white queen at each edge and corner location - 28 queens in total - and you claim that there are 228 possible moves.

I make it 288 moves:

  • each queen in a corner has six possible moves available along the diagonal
    $4 \times 6 = 24$
  • each queen along an edge has 11 moves available, six straight and 5 diagonally
    $24 \times 11 = 264$

making not 228 but 288 possible moves in total.

enter image description here

Whether that is the maximum possible remains to be seen.

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  • $\begingroup$ You could also say that each of the 36 squares is threatened by eight queens - one in each direction - for an even simpler proof. $\endgroup$ – AxiomaticSystem Jul 4 at 15:09
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The best result I can get for option #2 is 288. enter image description here

I do not have a strict proof that this is a maximum, but I have something very close. Therefore I have feeling that this is it!

Here is the "proof":
Consider 1x8 board, you will easily see that the optimum value of 12 moves is achieved with 2 queens at the different ends.
From this you can naturally suppose that optimally you need to put 2 queens on any possible line. You can't put exactly 2 queens on all lines, but the position I show you have maximum number of lines with 2 queens on it (6 vertical + 6 horizontal + 11*2 diagonal).

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    $\begingroup$ You could, of course, replace the corners with bishops and get the same result. $\endgroup$ – Kevin Jul 9 '14 at 1:10

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