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How Much Would You Pay To Play This Game?


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How much would you pay to play this game?You get to flip a coin until you get a head and in return I pay you 2 to the nth power with n being the number of tails you get before you get a headso if you immediately get a head - I pay you 1 dollarif you get a head on the second toss I pay you 2 dollarsif you get a head on the third toss I pay you 4 dollarsif you get a head on the fourth toss I pay you 8 dollarsif you get a head on the fifth toss I pay you 16 dollarsetc

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How much would you pay to play this game?You get to flip a coin until you get a head and in return I pay you 2 to the nth power with n being the number of tails you get before you get a headso if you immediately get a head - I pay you 1 dollarif you get a head on the second toss I pay you 2 dollarsif you get a head on the third toss I pay you 4 dollarsif you get a head on the fourth toss I pay you 8 dollarsif you get a head on the fifth toss I pay you 16 dollarsetc
nevermindISAM
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How much would you pay to play this game?You get to flip a coin until you get a head and in return I pay you 2 to the nth power with n being the number of tails you get before you get a headso if you immediately get a head - I pay you 1 dollarif you get a head on the second toss I pay you 2 dollarsif you get a head on the third toss I pay you 4 dollarsif you get a head on the fourth toss I pay you 8 dollarsif you get a head on the fifth toss I pay you 16 dollarsetc
1/2 of the time = $11/4 = $21/8 = $41/16 = $8...(1/2 x 1) + (1/4 x 2) + (1/8 x 4) + .... = 1/2 + 1/2 + 1/2 + 1/2 + .... --> infinity.Our average return is $infinity.That means theoretically we should pay anything up to infinity-1 to play the game just once (if we ignore the utility of money).
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27 flips will get us to $67m. If we assume that any more is almost irrelevant to our lives ($100bn = $67m in utility), then:50c x 27 = $13.5.We should pay at most $13.5 to play the game.If you up that to $1bn being your utility 'cap', so to speak, that's 31 flips, so you should pay at most $15.5.

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27 flips will get us to $67m. If we assume that any more is almost irrelevant to our lives ($100bn = $67m in utility), then:50c x 27 = $13.5.We should pay at most $13.5 to play the game.If you up that to $1bn being your utility 'cap', so to speak, that's 31 flips, so you should pay at most $15.5.
excellent answerits funny how its ev is infinity though - i guess no one here plays poker for the math :club:
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Our average return is $infinity.That means theoretically we should pay anything up to infinity-1 to play the game just once
Which, unfortunately, is also infinity.
(if we ignore the utility of money).
Ah, there's the rub.I knew exactly the answer to the question posed in the thread before I even opened it.
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So yeah...changing the assumption to the idea that you don't have to pay for every flip changes how much I choose to play:1/2 the time your EV is $1 - $x (whatever you paid to play)1/4 = $2 - $x 3/4 = -$x1/8 = $4 - $x 7/8 = -$x1/16 = $8 - $x 15/16 = -$x...1/2^27 = $67,000,000 - $x 1-(1/2^27) = -$xSimplifying that, and solving for 0 you get:0.499 - $x = 0Breakeven point for the game approaches $0.50 - so if you can play it for less than that life is good.

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So yeah...changing the assumption to the idea that you don't have to pay for every flip changes how much I choose to play:1/2 the time your EV is $1 - $x (whatever you paid to play)1/4 = $2 - $x 3/4 = -$x1/8 = $4 - $x 7/8 = -$x1/16 = $8 - $x 15/16 = -$x...1/2^27 = $67,000,000 - $x 1-(1/2^27) = -$xSimplifying that, and solving for 0 you get:0.499 - $x = 0Breakeven point for the game approaches $0.50 - so if you can play it for less than that life is good.
Minimum payout is $1, so the breakeven point has to be at least $1.
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