A game of 11 marbles wherein each player can either pick one or two marbles from the total. Starting from Player A & then Player B alternatively. This continues till all the marbles are picked. The winner is the one having odd number of marbles.

What is the strategy to be followed for Player A & B to win?. What happens for higher total number of marbles (13, 15 etc )?

(In reply to

Trial and error by TamTam)

If my strategy is right, the last comment ("if you start, the amount you take is irrelevant") is correct, but I'd object to the first part of the same paragraph.

Suppose you have 5 marbles, there are 3 marbles on the table, and the other player has 5 marbles, AND PICKS 1. You win if you take TWO, not one, so "do the same as the other did" doesn't work here.