Alice and bob can then either do one of 3 (rational!) things - stick to a prior choice, guess their flip result, or guess the opposite of their flip result. Bo

Alice and bob can then either do one of 3 (rational!) things - stick to a prior choice, guess their flip result, or guess the opposite of their flip result. Both of them sticking to prior choice was shown not to work, leaving 8 permutations to investigate at most. But it is easier than that. I started by assuming Alice will guess her flip result. Looking at the truth table A B h h :-) h t :-( t h :-( t t :-) This means the only losing possibilities are when the coins are different. Therefore Bob must guess the opposite of his flip result, to ensure no losing possibilities at all.