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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
11
Posted on 8/12/17 at 4:43 pm to STLDawg
You said spinoff.
Posted on 8/12/17 at 4:44 pm to STLDawg
quote:hosted Let'sa maka deala
Monte Carlo
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 4:46 pm to STLDawg
50 cents
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 4:48 pm to STLDawg
Expected Value
Posted on 8/12/17 at 4:49 pm to High C
More like a flipoff.
Posted on 8/12/17 at 4:58 pm to KosmoCramer
quote:
Expected Value
infinity
Posted on 8/12/17 at 5:00 pm to STLDawg
42
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.
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.
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.
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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