I once studied the expected remaining length of a game of chess, as a function of moves played: https://chess.stackexchange.com/questions/2506/what-is-the-a...
What was interesting is that for the first 20 moves (40 half moves) the expected remaining length will decrease at a near linear rate, but then it levels off at about 25 remaining moves, and after 45 moves every move played will _increase_ the expected remaining length.
At the time it surprised me, but of course it is natural to expect long games to be long.
At the time it surprised me, but of course it is natural to expect long games to be long.