If Ballmer is being adversarial, he won’t pick the number at the start, and always win.
Of course you can set up the game such that Ballmer has to commit on a number at the start of the game (by sealing it in an envelope or whatever), but that wasn’t specified.
Of course you can set up the game such that Ballmer has to commit on a number at the start of the game (by sealing it in an envelope or whatever), but that wasn’t specified.