## Casino, Sports Betting, and Lottery – A Comparison of the House Edge

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The house edge, which is the commission that a gambling agent such as a casino, a sportsbook (bookmaker), or a lottery administrator charges, is a yardstick that measures how a specific gambling game is fair and reasonable. It is one of the most important factors that every player should consider whenever he/she is engaged in any type of gambling, inasmuch as it indicates how much of the money wagered goes to the gambling agent’s pocket and how much is redistributed to the winners.

Indeed, a house edge cannot be zero since casinos, sportsbooks, and lottery administrators have to make some money in order to cover their expenses, and to make some profit as well. Yet, a high house edge simply means that the players are unecessarily being ripped-off, and as a result, any gambling game with a high house edge should certainly be avoided by a knowledgeable gambler.

In this article, we shall compare, in the simplest way possible, the house edges of a roulette, an evens-odd betting, and a Cash 3 lottery game as representatives of the three major gambling categories.

The Equation

The easiest way to compute a house edge is to compare the actual winnings that are paid by the respective agents to the winnings that would be paid in a fair game or bet. A fair game or a fair bet is one in which no commission is involved; an obvious model is a game between friends. Therefore, in percentage form, the house edge is obtained by subtracting an actual game winning from a fair game winning and dividing the result by the fair game winning, finally multiplying by 100. Thus,

House Edge = [ (fair game winning – actual game winning) / fair game winning ] * 100

Roulette

Because of its simplicity and popularity, we shall consider the roulette as a representative casino game. A European roulette wheel has grooves marked by the numbers 0 to 36; the American wheel (also called Las Vegas wheel) has an additional groove marked as ’00’. So, the European wheel has a total of 37 numbers, while the American wheel has 38. Internet casinos usually make available the option to select the type of wheel the customer prefers, but the brick and mortar casinos normally offer only one type. The winning number in a roulette game is the number corresponding to the groove where a spinning ball lands.

Now, consider a fair game in which 38 friends are playing the roulette at home, and each one selects a number and places a $1 bet on the number (no two or more players wagering on the same number). When the ball is spun and lands in a groove, the number marking that groove will be the winning number. The person who has selected this winning number collects all the money on the table thus making him win $37. On the other hand, if the game were conducted in a casino, the winner would be paid only $35. The difference between the two winnings applied in the above equation gives us the house edge of a roulette game as

( 37 – 35 ) / 37 * 100 = 2 / 37 * 100 = 5.4%

This means that every time you spend a $100 on an offline or online casino roulette, $5.40 goes to the casino and the rest is redistributed to the winners. Evidently, there are quite a number of casino games and the house edge varies from game to game, many of them having a house edge less than that of the roulette. For obvious reasons, a good gambler always prefers games that have low house edges, while the casino itself loves those games with high house edges. For example, the house edge of craps is 1.4% which makes it one of the most preferred casino games by the players.

Even-odds Sports Betting

Again, because of its simplicity, we shall consider an even-odds betting as a representative of this category of gambling. By even-odds we mean that the event (usually a sports game) has equal chances of going either way. *An example is a tennis match between two competitive players each of which has an equal chance of winning the match. A fair bet, in this case, is just a simple bet between two friends who just pick one of the tennis player as winner.* If these two friends wager $1 each, the winner will collect $2, thus winning $1. If instead the bets are placed through a sportsbook, the winner will collect only $1.91, since the odds of an evens game at most bookies and online sportsbooks is 1.91. If you are not familiar with the decimal representation of odds, 1.91 is the same as 10/11 in UK notation and -110 in US odds notation. Odds of 10/11 mean that you’ll win $10 when you wager $11; and odds of -110 mean that you have to wager $110 in order to win $100. Anyway, since the winnings paid by a sportsbook is only $0.91, the house edge of an even-odds betting will therefore be

( 1 – 0.91 ) / 1 * 100 = 0.09 * 100 = 9%

So, this is how sportsbooks make a living. Since several internet sportsbooks offer odds higher than 1.91 in order to lure bettors, the house edge could be smaller than 9%, which is one of the things that the bettor should be looking for when searching for a sportsbook. On the other hand, if the bettor is wagering on parlays the house edge would be significantly higher than 9%; for big parlays, it could go as high as 40%.

It should be apparent by now that the gambler is better off with casino games than sports betting. It should also be noted that while the house edge could be a major factor to consider while selecting a gambling game, it is by no means the only one. For instance, one should consider the fact that casino games are mostly games of chance, while sports betting also involves a learned decision in selecting a pick, consequently leading to a higher probability of winning a bet.

Cash 3

Depending on the state you are in, this lottery game may be known by a different name such as Pick 3, Play 3, Daily 3, etc. In this game, the player selects a three-digit number from 000 to 999, and plays the number as a straight or as a box. A straight play is a prediction that the number will come exactly as selected while a box is a prediction for the number to come in any order. For instance, if a player selects the number 672 and plays it straight, he/she will win if the number drawn is exactly 672. Instead, if the player plays 672 as a box, he/she will win as long as the drawn number contains a 6, a 7 and a 2, in any order (276, for example). Obviously, a straight game pays much more than a box game for the same amount wagered.

Now consider 1000 friends (maybe in a club) selecting a number as a straight, each for $1, so that all the 1000 possible numbers are covered. When the winning number is drawn, the person who has selected that lucky number will be deemed a winner and will cash in all the $1000 collected, so making him win $999. This is a fair game. In the case of state lotteries, however, the winner will be paid only $500 in most states. Some states may pay a little bit less, others may pay a little bit more, but $500 is more or less the standard. The winner therefore wins $499. The house edge for a Cash 3 game will therefore be

( 999 – 499 ) / 999 * 100 = 500 / 999 * 100 = 50%

This house edge applies not only to the Cash 3 game but also to all state lottery games such as Play 4, Cash 5, Mega, Fantasy 5, Lotto, Power Ball, etc. So, whenever you are playing the state lottery, remember that you are wagering only half of your money on the actual lottery; the other half, you are just giving it away. Where this other half goes is not the gambler’s concern, since his/her main objective is to win some money in order to pay the ever present bills, or to get out of a miserable life, or to change his/her 20-year-old car. As regards contributing to education and other noble causes, there are other means of collecting money called taxes and charities.

Unfortunately, many states do not allow casino games, and furthermore, sports betting is illegal in the United States. The player is therefore left with no choice but to cross state borders in search of a casino, or more recently, to engage in online sports betting through the several offshore internet sportsbooks. Nowadays, there is a plethora of trustworthy online casinos and sportsbooks operating from Canada, the UK, Antigua, Costa Rica, and so on.

The Conclusion

As far as the house edge is concerned, it has been shown that casino games are the best choice for the gambler. On the other end, any state lottery is a pretty miserable game to play. Nevertheless, besides the house edge, there is also the possibility of winning to consider.

Casino games, like lotteries are mostly games of chance; the player just selects a number or numbers and waits to see what luck brings him/her. There is absolutely no basis to prefer one number to others. Some people try to analyze previously drawn numbers in order to see the trend and predict the next numbers. This strategy may work a few times, but not always. Keep in mind that it is the players, and not the machines, who remember the previous numbers. In short, the possibility of winning a roulette or the lottery entirely depends on luck.

While there is little or nothing that a roulette or a lotto player can do to initially select a possible winning number, the situation could be quite different in the case of betting. With a lot of information and some assistance from sports handicappers, it is possible to predict the outcome of a sports event with more certainty than predicting a Cash 3 number.