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Alan tosses a coin 20 times. Bob pays Alan $1 if the first toss falls heads,...

Alan tosses a coin 20 times. Bob pays Alan $1 if the first toss falls heads, $2 if the first toss falls tails and the second heads, $4 if the first two tosses both fall tails and the third heads, $8 if the first three tosses fall tails and the fourth heads, etc. If the game is to be fair, how much should Alan pay Bob for the right to play the game?

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