50 moves without a pawn move or a capture and you can claim a draw.
stale mate or draw
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There is the 50 moves rules after the last capture. Ok MathSlayer just answered before me, I had not seen that while posting.
Just copying and pasting the rule from fide:
The game may be drawn if each player has made at least the last 50 consecutive moves without the movement of any pawn and without any capture. (See Article 9.3)
If i only have king left how many moves left does my oppenent have to check mate me before its considered a draw or stale mate?