About whether A has an "always win" strategy or not
There's a funny point within the rules, and that is that player A technically doesn't have to choose the number in advance even though the rules say the player must. Player A realistically only has to choose N, and keep track of what the valid possibilities for the starting number are as the questions are being answered. Player B cannot distinguish whether or not player A really chose the number in advance or not.
So actually, if player A does this, player B simply cannot 'get lucky', and may in fact have an "always win" strategy. --Chouepm 18:41, 27 July 2012 (UTC)