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... :)


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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