there certainly is if you consider 50 moves rule.

And you can derive an easy upper bound from that as 50x8x8x2 (basically each 50 moves you make a pawn move)

if you only consider 3 moves repetition and not 50 move rule then this is harder and the number becomes one of those crazy combinatorical numbers.

The 50 moves rule doesn't have be considered as it is optional. The players may claim, but they don't have to. So the game can continue.

The 75 move rule is the exact same thing but mandatory. That has to be considered.

(same thing is true for 5 times repetition vs 3 times).

Captures also reset the counter, not only pawn moves.

> And you can derive an easy upper bound from that as 50x8x8x2 (basically each 50 moves you make a pawn move)

This is not high enough, because the 50 move rule also resets when a piece is captured.

The 50 move rule is a rule of chess so it must be considered.

The 3 repetition rule is an opportunity for one of the players to declare a draw, but games can continue beyond that. The mandatory draw rule is 5 repetitions. In any case, the 50 move rule is far more limiting as to the number of moves in a game, since repetitions are necessarily neither pawn moves nor captures (the whole point of the 50 move rule being limited to those is that they are irreversible).