Thanks Hal, you're right, of course (except that you have transposed Winning
Flip for Losing Flip). The fact that you know the result of your own coin
flip changes the probabilities - it is no longer 50/50, and the smaller the
number of participants, the more obvious this effect becomes. This is the
same effect noted by Eric Cavalcanti in his post yesterday (4/10/04), and
applies to the room and the traffic examples as well. A little
disappointing, perhaps: there isn't a paradox after all. I have been
inspired by this thread to order Nick Bostrom's book (unreasonably expensive
though it is, in my opinion), which is based on his PhD thesis and discusses
the self-sampling assumption as applied to, among many other things, the
infuriating Doomsday Argument.
Stathis Papaioannou
>From: hal.domain.name.hidden ("Hal Finney")
>To: everything-list.domain.name.hidden
>Subject: RE: Observation selection effects
>Date: Mon, 4 Oct 2004 17:20:49 -0700 (PDT)
>
>Stathis Papaioannou writes:
> > In the new casino game Flip-Flop, an odd number of players pays $1 each
>to
> > individually flip a coin, so that no player can see what another player
>is
> > doing. The game organisers then tally up the results, and the result in
>the
> > minority is called the Winning Flip, while the majority result is called
>the
> > Losing Flip. Before the Winning Flip is announced, each player has the
> > opportunity to either keep their initial result, or to Switch; this is
>then
> > called the player's Final Flip. When the Winning Flip is announced,
>players
> > whose Final Flip corresponds with this are paid $2 by the casino, while
>the
> > rest are paid nothing.
>
>Think about if the odd number of players was exactly one. You're
>guaranteed
>to have the Winning Flip before you switch.
>
>Then think about what would happen if the odd number of players was three.
>Then you have a 3/4 chance of having the Winning Flip before you switch.
>Only if the other two players' flips both disagree with yours will you not
>have the Winnning Flip, and there is only a 1/4 chance of that happening.
>
>Hal Finney
>
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Received on Tue Oct 05 2004 - 03:37:22 PDT