keith crime 8 Posted January 19, 2008 Share Posted January 19, 2008 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 Link to post Share on other sites
TheRake_MD23 0 Posted January 19, 2008 Share Posted January 19, 2008 Sounds like vegas, however I pay then i get head or tail Link to post Share on other sites
James D 0 Posted January 19, 2008 Share Posted January 19, 2008 I'd pay $7 imo.Just sounded like a nice figure to pay for nice game. Link to post Share on other sites
HollywoodAFD 0 Posted January 19, 2008 Share Posted January 19, 2008 1$ Then I'd go over to the Red Dog table and play there Link to post Share on other sites
Balloon guy 158 Posted January 19, 2008 Share Posted January 19, 2008 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 dollarsetcnevermindISAM Link to post Share on other sites
Ron_Mexico 4,219 Posted January 19, 2008 Share Posted January 19, 2008 How much would I pay to go back in time and not open this thread? Link to post Share on other sites
runthemover 39 Posted January 19, 2008 Share Posted January 19, 2008 How much would I pay to go back in time and not open this thread?two bits Link to post Share on other sites
donk4life 34 Posted January 19, 2008 Share Posted January 19, 2008 I wish this thread was about giving head Link to post Share on other sites
simo_8ball 0 Posted January 19, 2008 Share Posted January 19, 2008 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 dollarsetc1/2 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). Link to post Share on other sites
simo_8ball 0 Posted January 19, 2008 Share Posted January 19, 2008 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. Link to post Share on other sites
keith crime 8 Posted January 19, 2008 Author Share Posted January 19, 2008 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 Link to post Share on other sites
LongLiveYorke 38 Posted January 19, 2008 Share Posted January 19, 2008 Our average return is $infinity.That means theoretically we should pay anything up to infinity-1 to play the game just onceWhich, 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. Link to post Share on other sites
HollywoodAFD 0 Posted January 19, 2008 Share Posted January 19, 2008 I changed my mind... I want my dollar back Link to post Share on other sites
SpiderGuard 0 Posted January 20, 2008 Share Posted January 20, 2008 double post... Link to post Share on other sites
SpiderGuard 0 Posted January 20, 2008 Share Posted January 20, 2008 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. Link to post Share on other sites
simo_8ball 0 Posted January 20, 2008 Share Posted January 20, 2008 It's a one time fee.You pay $X and then flip until you hit heads.EDIT: I'm slow Link to post Share on other sites
SpiderGuard 0 Posted January 20, 2008 Share Posted January 20, 2008 It's a one time fee.You pay $X and then flip until you hit heads.EDIT: I'm slowI'm the slow one who misread it in the first place...I just happened to beat you to the edit ;)Second post fixed to represent the real rules of the game. Link to post Share on other sites
simo_8ball 0 Posted January 20, 2008 Share Posted January 20, 2008 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. Link to post Share on other sites
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