House Edge

     

Some casino games are fairer than others. This is determined in large part by the house's edge on the particular game. The house edge can be calculated by comparing the real odds (or true odds) of winning to the payoff odds of the game. (* The most common method however, is to calculate the expected loss and divide by the average wager.)

In order to demonstrate house edge, let's make up a hypothetical game called BIG FAT LOSER, or BFL for short. Let's say that in BFL there are ten numbers to choose from, 1-10. To play the game, you simply place a $5 poker chip on the number of your choice. Let's further say that the dealer spins a little wheel with the ten numbers on it. If your number comes up on the wheel, the dealer will pay you at a rate of 8:1. If not, he will take your $5 chip. For this example, let's say we won. The dealer will pay us 8 times our bet of $5 = $40. He also does not take our original $5, so now we have a total of $45. Our real odds of winning this game is 9 to 1 because there are 10 possible combinations of which we have chosen 1. In other words, 9 combinations we did not choose vs. the 1 combination we did choose. If BFL paid the true odds of 9:1, the casino and player would break even over the long run. Therefore, the casino must pay less than 9:1 in order to make a profit. In this case they chose to pay 8:1. The problem with this payoff is that it is a ten percent reduction over the true odds. The house edge in this case would be 10%, which is way to much.

(* Expected loss for this game would be 9/10 * 5 - 1/10 * 40 = $.5 with an average wager of $5 such that .5/5 = .1 or 10%)

Another way to understand this is to imagine that you place a bet on every possible combination. 10 combinations with $5 on each = $50. The dealer spins the wheel and it stops on number 7. You lose the $5 chips you had on numbers 1, 2, 3, 4, 5, 6, 8, 9, and 10 = $45. You were paid $40 for your win on number 7. You also keep the $5 you placed on number 7 which brings the total amount of chips after the spin to $45. Before the spin = $50; after the spin = $45 which is a $5 loss. It also represents an overall loss of ten percent because $5 is 10% of $50. And here in lies the devilry of casino gambling known as the HOUSE EDGE.

To continue, our hypothetical game of BFL will consistently lose money for the player. A player can expect to lose $10 for every $100 bet over the long run. So, if over the course of an evening of play we were to wager a $1000 (not lose a thousand or bet a thousand at one time, simply playing most of the same poker chips over and over for a total of $1000 bet), our expected loss would be $100. Of course, we may not always do as expected. We may play BFL one evening and walk away with $10,000 in profit. It is important to recognize that, although we may sometimes beat our expectation by winning instead of losing, we will as often exceed our expectation by losing more than we were expected to. In other words, losing $10,000 in this game would be slightly more likely than winning $10,000 because our expectation is a net loss. However, statistically, players in a negative expectancy game will have a few big wins offset by a few big losses while losing at a certain percentage (house edge) over time.