Penney's game

[Steven G]

I recently have an interest in Penney's game (http://en.wikipedia.org/wiki/Penney's_game). The best tragedy is for the 2nd player to base their bet on what the 1st player said. There is a simple algorithm for this. One can find all the probabilities for this game and arrive at the same algorithm. My question is there a mathematical argument for this algorithm that does not result from looking at the probabilities? (for Dennis: if yes, then please do not just say yes)