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I am going to keep flipping a coin until I get a heads, for every tails I get in a row before that first heads, I will double the amount of money I will give you. So if it lands on heads first, you get $1. One tails and then a heads, you get $2. Two tails and then a heads, you get $4... Here's how you figure out how much the game is worth, consider you chance of getting a certain amount of tails in a row, and then the payout if this is to occur, then add up the amounts you get for all the different options, and you have the value of the game. In probability, this is called the expected value, the average amount the game would pay out if you played it an infinite amount of times... You have a 1/2 chance (no tails before heads) of winning $1, so this outcome is worth $0.50.