# The FLip Flop Game

```In one version of Flip Flop, each of an odd number of players simply flips a
coin.  The majority result, heads or tails, pays the casino \$1 each while
the minority result gets paid \$2 each.  Based on these rules, I worked out
Kory's tables for 3, 5, 7 and 9 players.```
```
The results show that the player's expectation changes according to how many
players there are.

For example, if there are 3 players then the long-term odds are that each
game costs each player 25 cents.  If there are 5 players, the average cost
goes down to 6.3 cents per game.  If there are 7 players, they make on the
average 3.1 cents per game.  If there are 9 players  they make about 9 cents
per game.

It isn't clear to me why this should be so.
Norman
----- Original Message -----
From: "Kory Heath" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Sunday, October 10, 2004 5:32 PM
Subject: Re: observation selection effects

At 07:17 PM 10/10/2004, Kory Heath wrote:
>We can also consider the variant in which the Winning Flip is determined
>after people decide whether or not to switch.

In a follow-up to my own post, I should point out that your winning chances
in this game depend on how your opponents are playing. If all of your
opponents are playing randomly, then you have a negative expectation no
matter what you do. If your opponents are not playing randomly, then you
may be able to exploit patterns in their play to generate a positive
expectation.

-- Kory

```