A theoretical game
Todd and Mike are playing a game. Todd says to Mike:
"I'll give you 5 bucks if you flip a coin and do the following; if it's heads the bet is over. If it's tails you flip again and if it's heads you give me 1$. But if it's tails the second time you have to flip again and give me 2$ if it's heads the third time. If it's tails 3 times in a row and then heads you give me 4$ and so on."
Mike alwasy keeps his 5$
Examples:
T: Mike gives 0$ to Todd
HT: Mike gives 1$ to Todd
HHHT: Mike gives 4$ to Todd
HHHHT: Mike gives 8$ to Todd
Should Mike take the bet for 5$? If not, how much should Mike demand to get paid to take the bet?
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