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Monty Hall Spinoff Thread: St. Petersburg Paradox
Posted on 8/12/17 at 4:40 pm
Posted on 8/12/17 at 4:40 pm
Let's say you have the opportunity to play a coin flip game. If you get heads, you win $1. If you get two heads in a row, you get $2. To generalize, for however many heads in a row you get, the amount you win doubles with each head. If you get a tails at any time, the game ends and you get the amount of money you won so far.
The issue comes when deciding what is a fair price to play such a game. You have a 1/2 chance of winning $1, a 1/4 chance of $2, a 1/8 chance of $4, and so on. As the chance of continuing the game decreases at the same rate the amount of winnings increases, the expected value of such a game is infinite.
How much would you pay to play?
The issue comes when deciding what is a fair price to play such a game. You have a 1/2 chance of winning $1, a 1/4 chance of $2, a 1/8 chance of $4, and so on. As the chance of continuing the game decreases at the same rate the amount of winnings increases, the expected value of such a game is infinite.
How much would you pay to play?
This post was edited on 8/12/17 at 4:43 pm
Posted on 8/12/17 at 4:44 pm to STLDawg
quote:hosted Let'sa maka deala
Monte Carlo
![](https://i.imgur.com/2TnoF.jpg)
Posted on 8/12/17 at 4:45 pm to STLDawg
quote:
How much would you pay to play?
about tree fiddy
Posted on 8/12/17 at 4:47 pm to STLDawg
Col. Mustard in the study with the wrench.
This post was edited on 8/12/17 at 4:48 pm
Posted on 8/12/17 at 4:58 pm to KosmoCramer
quote:
Expected Value
infinity
Posted on 8/12/17 at 5:25 pm to STLDawg
Idk, probably like a dollar.
It doesn't matter if you flip 10000 heads in a row, the chance of the next flip is still 50/50. Odds are you wouldn't win more than a few bucks so I certainly wouldn't put much into it.
It doesn't matter if you flip 10000 heads in a row, the chance of the next flip is still 50/50. Odds are you wouldn't win more than a few bucks so I certainly wouldn't put much into it.
Posted on 8/12/17 at 5:36 pm to STLDawg
Whatever the calculated average winnings are, Vegas would set the entry to be much higher than that.
Say, your average payout is $5 in this game. Vegas would probably charge $8 to play.
$3 average profit for every time played.Vegas wins again and builds another billion dollar casino, using 0 tax dollars.
Say, your average payout is $5 in this game. Vegas would probably charge $8 to play.
$3 average profit for every time played.Vegas wins again and builds another billion dollar casino, using 0 tax dollars.
Posted on 8/12/17 at 5:46 pm to STLDawg
quote:
You have a 1/2 chance of winning $1, a 1/4 chance of $2, a 1/8 chance of $4, and so on.
That isn't right. Each flip of the coin is 50/50. The coin has no memory nor control over the flip.
quote:
As the chance of continuing the game decreases at the same rate the amount of winnings increases, the expected value of such a game is infinite.
No it is the same odds for every flip.
Posted on 8/12/17 at 5:49 pm to Gray Tiger
quote:
No it is the same odds for every flip
So by the odds of flipping tails once, and flipping it 100 times in a row is the exact same.
Got it.
![](https://media.giphy.com/media/Fml0fgAxVx1eM/giphy.gif)
Posted on 8/12/17 at 5:50 pm to Gray Tiger
Probably a couple hundred dollars
Posted on 8/12/17 at 5:55 pm to Gray Tiger
Actually depends on the coin. Heads is heavier than tails in the case of a quarter
Posted on 8/12/17 at 5:59 pm to Kafka
quote:
Monte Carlo
hosted Let'sa maka deala
I did upvote
Posted on 8/12/17 at 5:59 pm to STLDawg
quote:
The issue comes when deciding what is a fair price to play such a game. You have a 1/2 chance of winning $1, a 1/4 chance of $2, a 1/8 chance of $4, and so on.
Nope.
Posted on 8/12/17 at 6:13 pm to KosmoCramer
I think he's saying the odds for each individual flip are 50/50.
The probability that you do it 100 times in a row are 1 in 1,267,650,600,228,229,401,496,703,205,376.
I feel pretty confident on this as I recall reading this from Marilyn vos Savant years ago but my track record today has not been great, as you can testify.
![](https://images.tigerdroppings.com/Images/Icons/IconLOL.gif)
The probability that you do it 100 times in a row are 1 in 1,267,650,600,228,229,401,496,703,205,376.
I feel pretty confident on this as I recall reading this from Marilyn vos Savant years ago but my track record today has not been great, as you can testify.
![](https://images.tigerdroppings.com/Images/Icons/IconLOL.gif)
Posted on 8/12/17 at 6:19 pm to mdomingue
This poster said in regards this previous post:
That's wrong. Each flip is 50/50 but the series of events isn't. The poster above is confused.
quote:quote:
You have a 1/2 chance of winning $1, a 1/4 chance of $2, a 1/8 chance of $4, and so on.
That isn't right. Each flip of the coin is 50/50. The coin has no memory nor control over the flip.
That's wrong. Each flip is 50/50 but the series of events isn't. The poster above is confused.
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