Can Games Be Fair AND Not Futile?

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Is is possible for a game to be fair but not futile?
 
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Of course. Scissor paper stone is one that is fair but not futile (there is no strategy that forces a draw).
 
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.
 
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*.
 

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