On Tue, 2004-10-05 at 19:31, Brent Meeker wrote:
> >I always forget to reply-to-all in this list.
> >So below goes my reply which went only to Hal Finney.
> >-----Forwarded Message-----
> >> From: Eric Cavalcanti <[EMAIL PROTECTED]>
> >> > Think about if the odd number of players was exactly
> >one. You're guaranteed
> >> > to have the Winning Flip before you switch.
> No, you're guranteed NOT to be in the winning flip.
> >> >
> >> > 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.
> I think you've confused the definitions of "winning flip" and
> "losing flip". The "winning flip" is the *minority at the time of
> the flip* For N=3 you can't be in the winning flip with someone
> else at the time of the flip - but you can switch to it.
Yes, you're right.
Hal and I have confused the definitions. It is still
not a paradox, though. You are more likely to be
in the Losing Flip.
So that this could indeed be a Casino game.