Thanks, Kory, that takes care of my confusion.
The same to Jesse's post.
----- 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
> 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
> 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