Roulet Expected Payouts
By admin. Filed in Roulet |
In the early frontier gambling saloons, the house would set the odds on roulette tables at 27 for 1. This meant that on a $1 bet you would get $27 and the house would keep your initial dollar. Today most casino odds are set by law, and they have to be either 34 to 1 or 35 to 1. This means that the house pays you $34 or $35 and you get to keep your original $1 bet.
The house average or house edge (also called the expected value) is the amount the player loses relative to any bet made, on average. If a player bets on a single number in the American game there is a probability of 1/38 that the player wins 35 times the bet, and a 37/38 chance that the player loses their bet. The expected value is:
-1×37/38 + 35×1/38 = -0.0526 (5.26% house edge)
For European roulette, a single number wins 1/37 and loses 36/37:
-1×36/37 + 35×1/37 = -0.0270 (2.70% house edge)
The presence of the green squares on the roulette wheel and on the table are technically the only house edge. Outside bets will always lose when a single or double zero come up. However, the house also has an edge on inside bets because the pay outs are always set at 35 to 1 when you mathematically have a 37 to 1 chance at winning a straight bet on a single number. To demonstrate the house edge on inside bets, imagine placing straight $1 wagers on all inside numbers on a roulette table (including 0 and 00) to assure a win. You would only get back 35 times your original bet having spent $38. The only exception are the five numbers bet where the house edge is considerably higher (7.89% on an American wheel), and the ‘even money’ bets in some European games where the house edge is halved because only half the stake is lost when a zero comes up.
The house edge should not be confused with the hold. The hold is the total amount of cash the table changes for chips, minus the chips taken away from the table. In other words, the actual “win” amount for the casino. The Casino Control Commission in Atlantic City releases a monthly report showing the win/hold amounts for each casino. The average win/hold for double zero wheels is between 21-30%, significantly more than 5.26%/2.70% of all players money because players are making repeated bets after winning and losing portions of their total money. This is known in the casino gaming industry as “churning” and is especially true of slot machine players who statistically end up losing all their wagers.
A player with a certain total amount of money may not win or lose all their money instantly, such that the total of all bets they make will often be greater than the total of the money they actually started with. The house edge applies to each bet made; not the total money, which means the player can end up losing significantly more than 5.26% of his starting money. For example it is likely that a player with $100 making $10 bets on red will be able to bet more than 10 times, because sometimes he wins. He may end up betting a total of 20 times on red. This means the expected value is 20*$10*5.26% = $10.52, over 10% of his money is now in the ‘hold’ despite the game having a 5.26% house advantage. A player who continually bets until they run out of money will give the house 100% hold.
