Fair Games

[Treadstone 71]

Is is possible for a game to be fair (http://mathworld.wolfram.com/FairGame.html) but not futile (http://mathworld.wolfram.com/FutileGame.html)?

[matt grime]

Of course. Scissor paper stone is one that is fair but not futile (there is no strategy that forces a draw).

[Treadstone 71]

Thanks. Here's a follow up: If a game allows the first player to forfeit his first move, then there cannot be a winning strategy for the second player, right? Since if there is such a strategy for player 2, then player 1 could simply forfeit the frist move and adopt the strategy of player 2.

[matt grime]

That assumes that the same options are open to all players at all times (apart from the first move). It is trivial to give a (trivial) game where 'player 2' has a winning strategy; forfeiting your first move *is still a move*.