# Maximum number of chess moves

Chess has a limited number of maximum moves because of the 50-move rule (50 moves without any captures or pawn moves results in a draw). There are 30 capture-able pieces, and I've figured out that the number of pawn moves can be maximized in this way:

• Each white pawn moves up to right in front of a black pawn (4 moves)
• The black pawn to its right/left captures it (1 move, but we don't count it because it's also a capture)
• The pawn that just captured moves all the way to the end of the board (5 moves)
• The other black pawn moves all the way to the end of the board (6 moves)
• The white pawn whose column is freed up moves to the end of the board too (6 moves)

So there are 21 pawn moves for each group of 4 pawns, so 84 pawn moves in total. This added to the number of captures gives us 114 events that can reset the 50 move counter, so 115 groups of 50 moves, giving us a total of 5750 moves.

Is this calculation correct?

Edit: I've just realized that the number of pawn moves could be increased to $5\ast8 + 6\ast8 = 88$ by having the pawns capture non-pawn pieces and be able to all move all the way to the end of the board, giving us 5950 moves.

• This blog post discusses this problem. – JimmyK4542 Jul 28 '15 at 3:01
• Also, this might be a duplicate of this question, although none of the answers give an achievable upper bound. – JimmyK4542 Jul 28 '15 at 3:08

Each pawn can make $6$ moves and be queened. You can arrange that all pawns are queened by having some of them capture pieces. This requires capturing eight pieces, where these captures are also pawn moves. There are then $30-8$ captures available that are not pawn moves to reset the counter. This gives $16\cdot 6 +30-8=118$ moves that reset the $50$ move timer. After the last capture you just have two kings left, so a draw can be claimed due to insufficient material for checkmate. You can then have $50 \cdot 118=5900$ moves before a draw can be claimed where the last half-move of the $50$ is one that prevents a $50$ move rule claim.