Re: S. Petersburg paradox

examachine_at_gmail.com
Date: 02/15/05 

Date: 15 Feb 2005 06:30:46 -0800

beda pietanza wrote:
> <examachine@gmail.com> ha scritto nel messaggio
> news:1108389275.221128.238670@g14g2000cwa.googlegroups.com...
> > This is not a paradox AFAICT.
> >
> > It's simply that the casino proof works only asymptotically, I
think
> > it's in the introductory chapters of a common textbook for
randomized
> > algorithms. So, don't sit at a roulette table thinking of this.
> >
> > Cheers,
> >
> > --
> > Eray
> >
> Can you explain it better: what is the casino proof ???
>

Well, I suppose you want to increase the amount invested in a binary
bet, like in the red/black game on the roulette table. What happens if
you double the bet every time you _lose_? You would definitely win the
game at some unknown distant horizon. The unfortunate thing is that
such a strategy is worthless in practice, because you can double your
bet only so few times.

Given that you don't have unbounded wealth, and that there is non-zero
probability of losing, the odds aren't good that you are going to
"actually" win. (Even if you have more wealth than the house!) An
interesting problem would be of course to study "unfair" roulette
tables on which multiple games are going on at once. In some ways, this
is reminiscient to certain underinvestigated stock market prediction
problems which depend on huge computational power to accomplish (I
think). There are interesting possibilities for a computer player when
it goes online, I believe. (But I'd rather not go into details)

The relation to randomized algorithms is not too clear to me either, a
friend had mentioned it, I don't think I read that textbook, but in
this case, it seems plain expected cost analysis, it doesn't even have
much to do with algorithms, but surely similar ideas are used
frequently in the analysis of randomized / amortized algorithms... This
is the simplest mathematical idea that Sum{k=0 to n}2^k + 1 = 2^{k+1},
no you wouldn't even win a lot, even if you won, so of course doubling
the money probably isn't a good idea if you want to win a huge amount
of money (which kind of runs contrary to the idea of a casino :) On
newsgroups, I'd heard that "counting cards" was illegal in some US
states, so figure...

The conclusion, if you like gambling with dice: make sure you
absolutely know how to trick the dice. :)

Cheers, 

--
Eray
PS: I'm not a gambler, as you can tell. I can't take that many risks.

Relevant Pages

  • Re: S. Petersburg paradox
    ... >> It's simply that the casino proof works only asymptotically, ... >> algorithms. ... don't sit at a roulette table thinking of this. ... like in the red/black game on the roulette table. ...
    (sci.stat.math)
  • Re: S. Petersburg paradox
    ... >> It's simply that the casino proof works only asymptotically, ... >> algorithms. ... don't sit at a roulette table thinking of this. ... like in the red/black game on the roulette table. ...
    (sci.physics.relativity)
  • Re: S. Petersburg paradox
    ... >> It's simply that the casino proof works only asymptotically, ... >> algorithms. ... don't sit at a roulette table thinking of this. ... like in the red/black game on the roulette table. ...
    (sci.econ)