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House Edge & Expectation in Gambling

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How the Casino Makes Money

House Edge and Expectation in GamblingThe casino makes money because of the house edge, which is an unstoppable force, like compound interest. The house edge is the difference between the true odds offered by a bet and the actual odds that the bet payouts out.

House edge is normally stated as a percentage, and it's an indicator in some ways of whether or not a bed is a good or a bad one.

A Roulette House Edge Example

In roulette, a red or black bet pays even odds. For every unit you bet, you win 1 unit if you get the correct outcome.

There are 38 colored numbers on a roulette wheel. 18 of them are red, and 18 of them are black. 2 of the numbers on the roulette wheel are green. (The "0" and the "00").

The odds of getting a red outcome is 18/38, or 9/19, or 47.36%. Or, in this case, it might be better to state the odds as 19 to 9.

The bet pays off at even money, or 1 to 1, which converts to a probability of 1/2.

1/2 - 9/19 = the house edge.

Or you could state it as a decimal or percentage:

50% - 47.36% = 2.64%

Since the black bet has the same house edge, the actual house edge for that game is 5.28%.

What the House Edge Means to You

In the long run, the house edge will eat up its percentage of your wager amount. In a game where the house edge is 5.28%, you can expect, long term, to lose $5.28 for every $100 bet that you place. On a roulette wheel, there might be 50 or so spins per hour. If you're betting $100 per spin, you could expect to lose a total of $264 per hour.

Anything can happen in the short term though, so you could win or lose over the course of an hour. But over the course of 1000's of bets over 1000's of hours, the casino will make the house edge. And the more bets and action the casino receives, the house edge will more accurately be reflected in the casino's actual winnings.

Another way of stating this is by calling it expectation.

More articles about odds and probability in gambling:

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