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What is the most moves you can make in a chess game without it being draw?

wismuth.com/chess/longest-game.html

see the position at "phase 4" after >8000 moves. In the example it ends in a draw, but with K / KR white could also win at around the same number.

Note:this works on the assumption that it is a "forced" draw only after 75 moves, not 50 as is customary. Not sure what the correct interpretation of the rules is here....
Depends on the FIDE rule:

-50 moves rule say 5800 moves
-75 moves auto-claim say 8800 moves
For the 50 move, it is actually 5798 moves.
So a player can promote to a N, move it to every unoccupied square, do the whole thing a second time (short of a third time repetition), then move one other piece (or the same piece to a different square), then begin again, moving the N again to every unoccupied square (or maybe capture a piece), repeat the whole thing again, then move another piece, then move the N again to every unoccupied square, twice, finally when every permutation of this is exhausted, promote another pawn and begin again. Meanwhile the opponent alternates the same process. The sheer number of permutations is mind-boggling. I wonder how the program calculates it.
My thinking on this:

The boring answer is infinitely as if no player claims a draw it will go on.

With the 50 move rule:

I ignore a ply till later.

To promote all 16 pawns you have to capture total of 8 pieces at the 5th pawn move.
These 8 pieces makes 250 moves each before capture.
Then you have 8 times 50 moves before the capturing pawns promote.
Then you have 8 times 6 times 50 moves before the other 8 pawns promote.
After that you have 22 pieces making 50 moves each before capture.
So, 8 x 250 = 2000.
8 x 50 = 400.
8 x 6 x 50 = 2400.
22 x 50 = 1100.
- 86 ply = 43 moves.
2000 + 400 + 2400 + 1100 - 43 = 5857 moves.
Close to #3 and #4. Please correct my thinking here.
@what_game_is_this

Without a move limit, the maximum number of moves in NOT infinite. The number of possible permutations is finite because the number of pieces and squares is finite. Eventually there would be a forced third repetition of a position.

I don't follow some of your calculations, and you seem to ignore that every position can be repeated once.
You could literally never trade pieces and do it on purpose but also if there is 0 as increment in any time control the time doubled would be the time the game ends like 5:00 would end with 10 mins

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