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 head

so if you immediately get a head - I pay you 1 dollar

if you get a head on the second toss I pay you 2 dollars

if you get a head on the third toss I pay you 4 dollars

if you get a head on the fourth toss I pay you 8 dollars

if you get a head on the fifth toss I pay you 16 dollars

etc

Sounds like vegas, however I pay then i get head or tail

I'd pay $7 imo.


Just sounded like a nice figure to pay for nice game.

1$ Then I'd go over to the Red Dog table and play there

nevermind

ISAM

How much would I pay to go back in time and not open this thread?

two bits

I wish this thread was about giving head

1/2 of the time = $1
1/4 = $2
1/8 = $4
1/16 = $8
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(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).

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 answer

its funny how its ev is infinity though - i guess no one here plays poker for the math

Which, unfortunately, is also infinity.




Ah, there's the rub.


I knew exactly the answer to the question posed in the thread before I even opened it.

I changed my mind... I want my dollar back

double post...

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 - $x 3/4 = -$x
1/8 = $4 - $x 7/8 = -$x
1/16 = $8 - $x 15/16 = -$x
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1/2^27 = $67,000,000 - $x 1-(1/2^27) = -$x

Simplifying that, and solving for 0 you get:

0.499 - $x = 0

Breakeven point for the game approaches $0.50 - so if you can play it for less than that life is good.

It's a one time fee.

You pay $X and then flip until you hit heads.

EDIT: I'm slow

I'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.

Minimum payout is $1, so the breakeven point has to be at least $1.