Consider the following two-player game, Don't be Greedier, that involves players taking alternate turns removing pebbles from one pile of pebbles, subject to the following rules:
(1) The player to remove the last pebble or pebbles from the pile wins the game.
(2) On the very first move of the game, the player to play is not allowed to remove all the pebbles and win immediately (that would be greedy).
(3) After the first move, the number of pebbles removed can't be more than the number of pebbles removed in the turn immediately prior (that would be greedier). That is, the sequence of numbers of pebbles removed on each turn is a monotonically non increasing sequence.
Starting with a pile of 12 pebbles, which player would win a game of Don't be Greedier, assuming optimal play?