Sam And Ray

This last weekend, I was finally able to solve a logic problem that I learned some time ago over at the xkcd forums. Frequently when I tell people this problem, I manage to slur the words "Sam And Ray" into something sounding like "salmon ray" causing much confusion and hilarity for all.

Alright, the problem is:
Two players, Sam and Ray, will play a cooperative game. There is a list of zeros and ones, and Sam and Ray must simultaneously guess the next number in the list starting from the first one, they must guess either 0 or 1. They can see what the other one guessed, and what the correct answer was. If they are both correct, they win $1, if either or both of them are wrong, they lose $2. They may play as long as they like, the list of numbers is arbitrarily long.

Before the game, Sam will be given access to the complete list of numbers, he knows every correct answer. Before Sam is given the list, the two of them may meet up to strategize. Come up with a strategy that guarantees that they can win a positive amount of money before quitting.

Of course, one could ask you to make a strategy that wins, say, $100, but once you have a strategy that is guaranteed to get $1, you can just repeat it as many times as needed.

I'll post the solution later.

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