I always forget to reply-to-all in this list.
So below goes my reply which went only to Hal Finney.
> From: Eric Cavalcanti <[EMAIL PROTECTED]>
> To: "Hal Finney" <[EMAIL PROTECTED]>
> Subject: RE: Observation selection effects
> Date: Tue, 05 Oct 2004 12:57:14 +1000
> On Tue, 2004-10-05 at 10:20, "Hal Finney" wrote:
> > 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.
It is interesting to note that, even though you are
more likely to be in the Winning Flip, there is no
disadvantage in Switching. To understand that, we can
look at the N=3 case, and see that if I am in the
Winning Flip with someone else, then if I change I
will still be in the Winnig Flip with the other person.
As opposed to Stathis initial thought, even though the
Winning Flip is indeed as likely to be Heads as Tails,
each individual is more likely to be in the
Winning Flip as in the Losing Flip in any given run.
So that this would never make it into a Casino game,
because the house would lose money in the long run.