Comment by chongli

Threefold repetition does not require the three positions to occur consecutively. So you could conceivably have a position repeat itself for first on the 1st move, second time on the 25th move, and the third time on the 50th move of a sequence and then players could claim a draw by threefold repetition or 50 move rule at the same time!

This means you do need to store the last 50 board positions in the worst case. Normally you need to store less because many moves are irreversible (pawns cannot go backwards, pieces cannot be un-captured).