Thanks, Kory, that takes care of my confusion. The same to Jesse's post. John Mikes ----- Original Message ----- From: "Kory Heath" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Sunday, October 10, 2004 7:17 PM Subject: Re: observation selection effects
> At 02:57 PM 10/10/2004, John M wrote: > >Then it occurred to me that you made the same > >assumption as in my post shortly prior to yours: > >a priviledge of "ME" to switch, barring the others. > > I think this pinpoints one of the confusions that's muddying up this > discussion. Under the Flip-Flop rules as they were presented, the Winning > Flip is determined before people switch, and the Winning Flip doesn't > change based on how people switch. In that scenario, my table is correct, > and there is no paradox. > > We can also consider the variant in which the Winning Flip is determined > after people decide whether or not to switch. But that game is functionally > identical to the game where there is no coin-toss at all - everyone just > freely chooses Heads or Tails, then the Winning Flip is determined and the > winners are paid. Flipping a coin, looking at it, and then deciding whether > or not to switch it is identical to simply picking heads or tails! The > coin-flips only matter in the first variant, where they determine the > Winning Flip *before* people make their choices. > > In this variant, it doesn't matter whether you switch or not (i.e. whether > you choose heads or tails) - you are more likely to lose than win. We can > use the same 3-player table we've been discussing to see that there are > eight possible outcomes, and you only win in two of them. Once again, > there's no paradox, although you might *feel* like there is one. You might > reason that the Winning Flip is equally likely to be heads or tails, so no > matter which one you pick, your odds of winning will be 50/50. What's > missing from this logic is the recognition that no matter what you pick, > your choice will automatically decrease the chances of that side being in > the minority. > > -- Kory >
