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 > >
