It shouldn't be too much extra state. I assume that 2 bits should be enough to cover castling rights (one for each player), whatever is necessary to store the last 3 moves should cover legal en passant captures and threefold repetition, and 12 bits to store two non-overflowing 6 bit counters (time since last capture, and time since last pawn move) should cover the 50 move rule.
So... unless I'm understanding something incorrectly, something like "the three last moves plus 17 bits of state" (plus the current board state) should be enough to treat chess as a memoryless process. Doesn't seem like too much to track.
So... unless I'm understanding something incorrectly, something like "the three last moves plus 17 bits of state" (plus the current board state) should be enough to treat chess as a memoryless process. Doesn't seem like too much to track.