# re: observation selection effects

At 10:35 AM 10/9/2004, Stathis Papaioannou wrote:
From the point of view of typical player, it would seem that there is not: the Winning Flip is as likely to be heads as tails, and if he played the game repeatedly over time, he should expect to break even, whether he switches in the final step or not.

That's not correct. While it's true that the Winning Flip is as likely to be heads as tails, it's not true that I'm as likely to be in the winning group as the loosing group. Look at the case when there are only three players. There are eight possible outcomes:

```Me: H  Player 1: H  Player 2: H - WF: T
Me: H  Player 1: H  Player 2: T - WF: T
Me: H  Player 1: T  Player 2: H - WF: T
Me: H  Player 1: T  Player 2: T - WF: H
Me: T  Player 1: H  Player 2: H - WF: T
Me: T  Player 1: H  Player 2: T - WF: H
Me: T  Player 1: T  Player 2: H - WF: H
Me: T  Player 1: T  Player 2: T - WF: H```

I am in the winning group in only two out of these eight cases. So my chances of winning if I don't switch are 1/4, and my chances of winning if I do switch are 3/4. There's no paradox here.

`-- Kory`

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