Easier explenation There are 16 possibilities A Alice's coin Ac Alice's choice B Ben's coin Bc Ben's choice They win if A's and Bc's OR B's and

Easier explenation There are 16 possibilities A Alice's coin Ac Alice's choice B Ben's coin Bc Ben's choice They win if A's and Bc's OR B's and Ac's are the same A Ac B Bc T T T T W H T T T W T H T T W H H T T L T T H T W H T H T L T H H T W H H H T W T T T H W H T T H W T H T H L H H T H W T T H H L H T H H W T H H H W H H H H W It's easier to check for when they are losing: A Ac B Bc H H T T |they both stick to their choices H T H T |they both flip T H T H |they both flip T T H H |they stick So the winning strategy is if one of them sticks to his choice and other flips it's choice.