Pricing a coin flip
Suppose a casino has created a new game, determined via coin toss. If the coin is tails, the individual is paid $1, and if the coin is heads it's tossed again. On the 2nd toss (assuming heads on first toss), the individual will be paid $2 if tails, otherwise if it's heads we continue, doubling each time to $4, $8, $16 etc for each tails. What price should the casino charge to play this game, assuming you only want to break even?
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