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Calculating House Edges in Casino Games

By: Ryan Alders, Monday September 22nd 2008
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Very often while reading reviews of games one comes across statements like "so-and-so game has a very high house edge therefore it should be avoided" or "so-and-so game has a low house edge and therefore should be played". It is essential to have a clear understanding of what house edge is.

House edge is the average percent of each wager placed that goes to the online casino. Sometimes players win and the casino loses money, other times the players lose and the casino makes money. If these wins and losses are averaged over a large number of bets then one will find that the casino always makes money, because that is how they stay in business. Different casino games have different house edges. Also different wagers in games like craps have different house edges. No online casino offers information on game wise or wager break up of house edges. The onus is on the player to find out what the house edge for a particular wager is. The simplest way is to search literature and memorize the house edges for different games and different bets. But the online casinos are one step ahead. The continuously introduce variations thereby making memorized knowledge worthless. And if an online player is going to spend time and money on online casinos he may as well understand how house edges are calculated.

Take for example the bet "Any 7" in craps. This bet wins if the sum of the two dice rolled is 7. The first step in calculating house edge is calculating the probability of getting a 7. When two dice are rolled the total number of outcomes is 36. 6 of these outcomes lead to a total of 7. Therefore the probability of getting a 7 is 6/36 or 1/6. The probability of not getting a 7 is therefore 5/6.

The next step is to calculate the expectation. Expectation is a mathematical term for what the player can expect to win or lose in the long run. "Any 7" pays out at 4 to 1 in most online casinos. If the player wagers $1 and wins he gets $4, if he loses then he loses his $1 wager.

Given that the probability of winning is P and the odds are W to 1, the expectation E is given by E = P*W - (1 - P)*1. For "Any 7" bet P = 1/6 and W = 4.

Therefore E = (1/6)*4 + (5/6)*1 = -(1/6) = - 0.17

This implies that for every dollar wagered the player expects to lose 17 cents in the long run.

The house edge is simply the numerical value of the expectation per dollar wagered expressed as a percentage. Or when the expectation is calculated for a wager of $1, the house edge is the numerical value of the expectation calculated as a percentage.

Therefore for "Any 7" bet in craps the house edge is 17%.

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Comment by: Dilbert Jones On: December 26, 2009
Good article but I just want to play and not overburden myself with the math aspect of play. I think that there's really two types of players out there those that want to beat the casino and those that just wanna have some fun and have a chance at winning. I'm definitely the second type but I'm sure there's plenty of both.
Comment by: sadie777 On: September 02, 2009
There's no definite way to calculate house edge in games like slots as the slots payouts change from slot game to slot game. I think that with other games like craps there are formulas to know the exact payouts on the game. Same goes for games like craps. Blackjack in addition to the others is also a game where you can somewhat determine the payout. It's really based on how well you play and follow basic blackjack strategy. If for example in blackjack you play an optimal strategy based on the blackjack variation you're playing you could very well lower the house edge in the game to less than 1%.

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