You and a friend play a game in which there are an odd number of rocks. You can take 1, 2 or 3 rocks on your turn (alternating turns with your opponent); when all rocks have been taken, the person who has taken an odd number of rocks is the winner.
If you are the first to go, what strategy should you use in order to have the best chance of winning?
(In reply to strategy
So, Charlie, if you play a game with 5 initial rocks, and you move first, how many do you take?
A similar question is... for what values of N (= the initial rocks) can one guarantee a win?