# House Edge

The house edge is a mathematical advantage that the casino has over the player in a given game of chance. Along with the rake in poker and baccarat and the vigorish in sports betting, the house advantage is the reason casinos make profits. With the legal right to set a house edge on its games, a gaming company makes enough profits to afford large gaming staffs, opulent hotels, tourist attractions, concerts, and shows. It is the profit engine of the casinos. The house edge deals with probability, so any given card hand, throw of the dice, of spin of the wheel/reels is unpredictable.

Because gamblers do not understand the house edge fully, a number of myths and misconceptions have arisen about the concept. Having a better understanding of the casino’s advantage makes you a more informed gambler. Not only does knowing the house edge improve your chances of winning in many cases, but it also helps you avoid the logical fallacies which can lead to problem gambling. Today, I provide a detailed explanation of the house edge in gambling.

## How It Is Calculated

House edge is expressed as a percentage. The percentage indicates how much a player expects to win in payouts when the player wagers a theoretical \$100. If a player expects to win back \$99, then the player would be expected to lose \$1 and the house edge would be calculated at 1%. If a player expects to win back \$93.50 for every \$100 wagered, then the casino would be expected to win \$6.50 and the house edge would be expressed as 6.5%. If a player expected to win back \$101 for every \$100 wagered, this would be stated as a 101% expected return. No house edge would exist.

## Positive and Negative Expectation

The player would have the advantage over the casino at this point. When the expected return is greater than 100%, then it is considered a positive expectation game. This only happens when video poker uses the full-pay paytable, a player is successfully counting cards in blackjack, or a progressive jackpot has grown to such proportions that the amount won is greater than the amount which would need to be wagered to expect a 50% chance of winning that jackpot. Again, these are rare cases. Most players should expect to gamble on negative expectations games. In these cases, they will face the house edge.

## Connection to Expected Return

The house edge is connected to the payout percentage. Among manufacturers of gaming machines, the payout percentage is also called the “return-to-player” or “RTP”. The RTP is expressed as the amount the casino returns to the player or, perhaps better explained, the amount of a wager the player expects to win back from the casino.

Let’s return to our earlier examples. In the case where the player expects to win back \$99 of a theoretical \$100 wagered, then the expected return would be 99%. When the player expects a return of \$93.50, then the RTP or expected return would be 93.5%.

An easy way to picture the connection between the return-to-player and the house edge is to add them together. When playing a negative expectation game, the house edge and the payout percentage add up to 100. If you have a 99% return to player, then the house edge would be 1% for a total of 100%.

## Variance in Casino Gambling

Even though the casino has a probabilistic advantage, we are dealing with probabilities, not certainties. Variance happens in the course of any casino game. Variance is how much the results differ from the expectations.

This can be measured, but in the simplest terms, variance means sometimes you will win back more than 100% of what you wagered (and thus have a winning session) and sometimes you will lose a whole lot more than what you expected to lose. As the saying goes, results will vary.

## Odds Versus Results

In real life, the results are going to differ from the predicted house edge most of the time. These deviations should be expected when looking at short term results. The longer a gambler bets, the more likely the real life results will converge with the odds of winning and losing. If you played a billion hands of blackjack, then your results would conform pretty closely to the odds of the game.

What sometimes trips up gamblers is their perception of the terms “long term” and “short term”. Players often assume a few thousands hands (or spins or dice throws) represent long term results. In truth, a few thousand bets is a pretty small sampling.

## Misconceptions and Fallacies

That misconception can lead to major fallacies. Con artists often use players’ perceptions and common sense observations against them. For instance, when using a progressive betting technique like the Martingale system, that system is likely to work out pretty well with any sampling of a thousand bets. That’s because Martingale betting provides for a lot of small wins, but with one large, catastrophic loss. So long as that big ruinous bad luck streak doesn’t fall within the thousand-wager sample, the system appears to work like a charm. It appears you’ve found a way to beat the house edge.

In truth, there is no way to beat the house edge–not in the long run. The only way to beat the mathematics of gambling is to get lucky. The more bets you place, the luckier you have to be. That’s the essence of probability when it comes to gambling: shorten your gambling sessions and you should be pleased with your results. Conversely, if you lengthen your gambling excursions, you are likely to be less pleased with your results. Extend them long enough and you become a problem gambler, all because of the house edge.