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The game is as follows. You flip a coin.

H TH TTH TTTH ..........

$2 $4 $8 $16

If you flip heads, the game is over and you get the coressponding prize money. The question is, how much would you be willing to pay to play this game? Seeing that winning $2 is equally as likely as winning 4$, and winning 4$ is equally as likely as winning $8, ad infintium.

Any thoughts?