# Re: S. Petersburg paradox

**From:** jem (*xxx_at_xxx.xxx*)

**Date:** 02/19/05

**Next message:**sigu4wa02_at_sneakemail.com: "Full conditional probability out of product of Gaussians?"**Previous message:**Alan Williams: "Re: Estimates of Weibull parameters based on maximum likelihood function"**In reply to:**beda pietanza: "Re: S. Petersburg paradox"**Next in thread:**Nuno T.: "Re: S. Petersburg paradox"**Reply:**Nuno T.: "Re: S. Petersburg paradox"**Messages sorted by:**[ date ] [ thread ]

Date: Sat, 19 Feb 2005 07:09:35 -0500

beda pietanza wrote:

*> "jem" <xxx@xxx.xxx> ha scritto nel messaggio
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*> news:zHlRd.82793$bu.13471@fed1read06...
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*>
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*>>beda pietanza wrote:
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*>>
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*>>>"Yan Zhang" <yanzhang@fas.harvard.edu> ha scritto nel messaggio
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*>>>news:cv2vd2$3lh$1@us23.unix.fas.harvard.edu...
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*>>>
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*>>>
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*>>>>beda pietanza wrote:
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*>>>>
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*>>>>
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*>>>>>Sunny wrote:
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*>>>>>
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*>>>>>
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*>>>>>
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*>>>>>>>>Since the Expectation value of the game is infinite, what is the
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*>>>>>>>>even bet a bettor should be willing to pay in order to play the
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*>>>>>>>>game?????
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*>>>>>>
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*>>>>>>Here's something off the top of my head:
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*>>>>>>The probability of winning 2^n units is (1/2)^n, so on average you
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*>>>>>>need to play 1/((1/2)^n) = 2^n times to win 2^n units. However to
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*>>>>>
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*>>>>>play
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*>>>>>
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*>>>>>
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*>>>>>
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*>>>>>>that many times, you pay x*2^n units in entrance fees, where x is the
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*>>>>>>entrance fee for one throw.. So for every amount you win from a draw,
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*>>>>>>you expect to have lost x*2^n units. So to come out on top, you'd pay
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*>>>>>>x<1 units to enter.
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*>>>>>>
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*>>>>>>There's probably some silly mistake there, but I'm sure someone will
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*>>>>>>point it out soon enough.
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*>>>>>>
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*>>>>>>-Sunny
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*>>>>>
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*>>>>>
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*>>>>>I am not sure I got your reasoning, I only point out to you that the
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*>>>>>SPP is meant to be played only once: the Expectation value of the game
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*>>>>>is said to be infinite and it is expected that a bettor should be
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*>>>>>willing to pay a infinite amount of money in order to play the game
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*>>>>>just once !!!
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*>>>>>
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*>>>>
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*>>>>I think the confusion here is using "expected value" too loosely as a
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*>>>>decision device in a situation where only one probabilistic check is
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*>>>>made. Consider the following simpler game:
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*>>>>
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*>>>>You flip a coin. On the 0.0001% chance it lands on its side, I give you
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*>>>>$100000000000000000. On the 99.9999% chance it lands heads or tails, you
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*>>>>give me $100. Now, you have no doubt that the expected value is positive
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*>>>>(huge in fact, but I don't feel like doing simple arithmetic since I'm a
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*>>>>lazy person), but are you really willing to play the game just once and
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*>>>>pay me, say, $1000000 to do it? I don't think so, though the expected
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*>>>>value is much higher than that!
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*>>>>
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*>>>>The St. Petersburg "Paradox" is not a paradox for the precise reason as
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*>>>>above. It has a high expectation value, infinite, actually. But you are
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*>>>>talking about a situation where we just play "once" and playing into
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*>>>>the psychological factors involved. There is no paradox though, for if
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*>>>>we keep playing, forever and ever, the player will indeed come out ahead
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*>>>>in the long run on average.
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*>>>>
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*>>>>-Yan Z.
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*>>>
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*>>>
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*>>>I don't think the SPP has really a infinite expectation value if you pay
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*>
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*> a
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*>
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*>>>infinite bet in order to play it once:
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*>>>the really payoff scheme for a infinite paid bet is :
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*>>>1° outcome payoff 1- infinite net win = -infinite
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*>>>2° outcome payoff 2-infinite net win = -infinite
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*>>>3° outcome payoff 4-infinite net win = -infinite
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*>>>and so on....
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*>>>if you pay a infinite amount of money you will loose it for sure
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*>>>and if you play N numbers of games you surely will loose N time
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*>>>the infinite bets you have paid.
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*>>
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*>>Nonsense. It's not possible to bet an infinite amount.
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*>
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*>
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*> You don't have to you only calculate it.
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*> In any case substituting infinite with a very large amount the destiny
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*> of the bettor doesn't changes.
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*>
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The amount of any bet is necessarily finite, and for any and all bets

the gambler's Expected gain is infinite.

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