Slightly late to point this out, and not sure if an edit can be made now, but I feel the third of your nrich articles linked from your main page has a misleading point at the start. It says that in games including Nim, the first move is decisive. The fact is that in Nim, whether the last person to play is defined to be the loser or the winner, "balanced" Nim positions with at least one pile with more than one matchstick are won by the second player. The game {3,2,1} is an example, where the first player is doomed whatever he does. After all 6 possible first moves, the second player can choose to force the first player to make the final move or choose to force him to make the penultimate move.