[iainmerrick]

Right! I'm not sure if that's actually what he had in mind, but if he did, it's funny because it makes all this mathematical analysis completely pointless.

The OP has a complex randomized strategy that guarantees to average at least $0.07 against any adversary; meanwhile, just by delaying his "pick" and stringing you along, Ballmer makes you take seven guesses and owe him a dollar each time.

If you were expecting to win $0.07 on average, how many rounds would you play before you realise you're being scammed?