Alex and Bert are going to play a variation of Two players, two pots
. This time there are three pots and the pots start with 58, 62, and 68 stones.
A legal move consists choosing two of the pots and of emptying one of them and then splitting the stones from the second chosen pots among the two pots so that each pot contains at least one stone. The third pot is untouched.
Alex and Bert alternate their moves and Alex is the first to make a move. If a player is unable to make a legal move then he loses.
Who wins this game and what is his optimal play strategy?