House Edge on Roulette

The house edge, which is closely related to the concept of expected value, is the amount of money that a player will lose relative to any bets which are made. In the early days of roulette, house odds were often set at 27 to 1. This meant that if a player made a winning bet, he or she would receive $27 for each $1 wagered (with the house keeping the initial dollar).

In modern times, odds are usually set by law, with the most common being 34 to 1 or 35 to 1. In these cases, the player gets to keep their original bet, plus they receive either $34 or $35 (depending on the odds).

Determining the House Edge

In a game of European roulette (single zero), the player betting on one number has a 1 in 37 chance of winning and a 36 in 37 chance of losing. This can be expressed by the following mathematical formula:

-1x36/37+35x1/37=-0.0270 (This formula results in a house edge of 2.70%.)

For a game of American roulette (double zero), the player has a 1 in 38 chance of winning on a single number and a 37 in 38 chance of losing. This can be expressed by the following:

-1x37/38+35x1/38=-0.0526 (This formula shows that the house has a 5.26% edge in American roulette.)

The Hold

Some players will confuse the “hold” with the house edge, but they are two different things. The hold is the amount of cash exchanged for chips, minus the chips that are taken away from the table. This number represents the actual profit for the roulette table on behalf of the casino.

Both the win and hold amounts are constantly monitored by the Casino Control Commission, and the win/hold amounts for each American casino are released in a monthly report. In Atlantic City, for example, it has been found that, on average, a double zero roulette table takes in more money than the house edge of 5.26% would indicate.

This is often due to players winning and then turning around and losing those same winnings on subsequent wagers. In the industry, this is known as “churning.” It is often seen with slot machines, as players will slowly lose any accumulated winnings over a long session of playing. Needless to say, churning is a very popular concept within the casino industry.

When calculating the house edge, it is applied to each bet which is made. Just because the house has a 5.26% edge on American roulette, does not mean that it will only win that amount of the player’s starting bankroll. In fact, if a player stays at the table and wagers until they run out of money, then the house is said to have a hold of 100%.

Numbers Which Grant a House Edge

Technically, the zero and double zero are supposed to be the only numbers which grant a house edge over the player. This is because all outside bets (including even/odd, black/red, 1 to 18, etc.) will immediately lose when a single or double zero turns up.

Since the house pays out at 35 to 1, they also have an advantage on the inside bets. For example, let’s say you wagered $1 on all of the numbers on the roulette table (which would include the zero and double zero). In doing this, you would have risked $38 to guarantee a win. Unfortunately for you, the house only pays out at 35 to 1, so you still end up losing a couple of dollars. Over a lengthy gaming session, this seemingly small advantage can take a toll on even the most determined of roulette players.

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