Cointoss game - how much would you pay to play it? - TennisForum.com
View Poll Results: How much are you willing to pay to play the game?
Just $1 (meaning that you couldn't lose any money) 3 27.27%
$2 3 27.27%
$3 1 9.09%
$5 0 0%
$10 0 0%
$25 0 0%
$100 0 0%
$1000 0 0%
$100,000 2 18.18%
Other (please specify) 2 18.18%
Voters: 11. You may not vote on this poll

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post #1 of 29 (permalink) Old Dec 16th, 2006, 10:16 PM Thread Starter
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Cointoss game - how much would you pay to play it?

The game is very simple:

I flip a coin.

If it's heads, you win $1 and the game ends.
If it's tails, I flip it again.

If it's heads, you win $2 and the game ends.
If it's tails, I flip it again.

If it's heads, you win $4 and the game ends.
If it's tails, I flip it again.

Heads on 4th flip: $8
Heads on 5th flip: $16
Heads on 6th flip: $32

And so on.

Question: What is the maximum amount of money you would be willing to pay to play this game?
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post #2 of 29 (permalink) Old Dec 16th, 2006, 10:56 PM
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Re: Cointoss game - how much would you pay to play it?

50 cents?
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post #3 of 29 (permalink) Old Dec 16th, 2006, 10:58 PM
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Re: Cointoss game - how much would you pay to play it?

you've already made $200,000 off these people, how about you cut me in and I'll arrange some advertising?
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post #4 of 29 (permalink) Old Dec 17th, 2006, 12:00 AM Thread Starter
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Re: Cointoss game - how much would you pay to play it?

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Originally Posted by controlfreak View Post
you've already made $200,000 off these people, how about you cut me in and I'll arrange some advertising?
I wish it were so.
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post #5 of 29 (permalink) Old Dec 17th, 2006, 12:09 AM
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Re: Cointoss game - how much would you pay to play it?

surely, no matter how much money you pay, you will ALWAYS win it back, the minimum amount of winnings you will get (and that is gaurenteed) is what you started with, so in theory, play with every thing you own.


Is that correct or am I missing something?
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post #6 of 29 (permalink) Old Dec 17th, 2006, 12:10 AM
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Re: Cointoss game - how much would you pay to play it?

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Originally Posted by TomTennis View Post
surely, no matter how much money you pay, you will ALWAYS win it back, the minimum amount of winnings you will get (and that is gaurenteed) is what you started with, so in theory, play with every thing you own.


Is that correct or am I missing something?
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post #7 of 29 (permalink) Old Dec 17th, 2006, 12:11 AM
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Re: Cointoss game - how much would you pay to play it?

LMAO, we did this in uni. It was an example. He started to go off about Utility Theory and I think he somehow may have used a Monte Carlo simulation. Or maybe a mathematical equation dealing with Utility and stuff.

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post #8 of 29 (permalink) Old Dec 17th, 2006, 12:19 AM Thread Starter
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Re: Cointoss game - how much would you pay to play it?

I just realise that I omitted a crucial information: I have an infinite amount of money and can pay out every possible win.
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post #9 of 29 (permalink) Old Dec 17th, 2006, 12:25 AM
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Re: Cointoss game - how much would you pay to play it?

ok, I just looked at my notes and it's called St Petersburg Paradox. I'll look for the solution afterwards (I think we did it)

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post #10 of 29 (permalink) Old Dec 17th, 2006, 12:28 AM
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Re: Cointoss game - how much would you pay to play it?

lol ok, my notes say:

Quote:
The paradox states that Expected Utility is infinity, so we should bet everything we have

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post #11 of 29 (permalink) Old Dec 17th, 2006, 12:29 AM
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Re: Cointoss game - how much would you pay to play it?

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Originally Posted by ~*Supernova*~ View Post
lol ok, my notes say:
So you would bet everything you have to have a 50% chance to win 1$.
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post #12 of 29 (permalink) Old Dec 17th, 2006, 12:31 AM
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Re: Cointoss game - how much would you pay to play it?

I don't get what would be the point to bet more than 1$???
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post #13 of 29 (permalink) Old Dec 17th, 2006, 12:32 AM Thread Starter
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Re: Cointoss game - how much would you pay to play it?

Quote:
Originally Posted by King of Prussia View Post
So you would bet everything you have to have a 50% chance to win 1$.
But, there's also a 25% chance to win $2, and a 12.5% chance to win $4, and a 6.25% chance to win $8, and ...
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post #14 of 29 (permalink) Old Dec 17th, 2006, 12:33 AM
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Re: Cointoss game - how much would you pay to play it?

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Originally Posted by GoDominique View Post
But, there's also a 25% chance to win $2, and a 12.5% chance to win $4, and a 6.25% chance to win $8, and ...
But you get the same odds by betting 1$... Or am I missing something?
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post #15 of 29 (permalink) Old Dec 17th, 2006, 12:34 AM Thread Starter
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Re: Cointoss game - how much would you pay to play it?

Quote:
Originally Posted by King of Prussia View Post
I don't get what would be the point to bet more than 1$???
You need to bet more than $1 if the game organiser (= me) demands it.
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