Hi Eric,
    I'm laughing, not at you, but at the tendency we may have to see what we 
want to see and not what's really there!  Kory's explanation is a good one. 
Maybe this even has something to do with Observation Selection Effects!
Norman
----- Original Message ----- 
From: "Eric Cavalcanti" <[EMAIL PROTECTED]>
To: "Kory Heath" <[EMAIL PROTECTED]>
Cc: "Everything List" <[EMAIL PROTECTED]>
Sent: Monday, October 11, 2004 1:15 AM
Subject: Re: The FLip Flop Game


AAArrrrghhh!!!
I didn't read it carefully again!!!
Yes, it is not even-money. In the infinite
players case, even though you are equally
likely to win or lose, you win money in the
long run.

I am going to sleep... :)

Eric.

On Mon, 2004-10-11 at 17:52, Kory Heath wrote:
> At 12:20 AM 10/11/2004, Norman Samish wrote:
> >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.
>
> The issue is in the payout structure you suggest, which is that if you win
> you get $2, and if you lose, you pay $1. This is not an even-money
> proposition. If your chances of winning are exactly 1/3, then for every
> three times you play you will (on average) pay $1 twice and win $2 once,
> which is break-even. Therefore, you have a positive expectation if your
> winning chances are any greater than 1/3.
>
> In three-player Flip-Flop, your winning chances are only 1/4, so the
> three-player game is a bad bet even given this generous payout structure.
> However, as you add players, your chances of winning tend towards 50% (but
> never quite reach it). Very quickly, your winning chances will become
> greater than 1/3, and the game will suddenly have a positive expectation
> for you, and a negative one for the house.
>
> If the casino wants to guarantee profits, it must adjust its payout
> structure to an even-money proposition. In other words, losers pay $1, and
> winners get $1. As you add more players, your winning chances improve, but
> they're still always slightly less than 50%, so the game will always have 
> a
> negative expectation for the players.
>
> As a side note, the common parlance in betting is that you pay a certain
> amount up front (the "bet"), and then if you win you get a certain amount
> back, while if you lose you get nothing. In this way of speaking, an
> even-money proposition would be to bet $1 and get $2 back if you win. The
> bet that you proposed was equivalent to betting $1 and getting $3 back 
> when
> you win, which is better than even-money.
>
> -- Kory
>
>


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