games almost always yield independent events. Blackjack is the rare exception, which is the main reason for its popularity.
Factoring in the odds
Let’s return to our trusty coin flip. You probably know that heads and tails each have a 50-50 shot at turning up. You can communicate the probability of the flip in terms of odds. In the case of a two-sided coin, your odds of flipping heads are 1-to-1. In other words, with two possible events (outcomes), you have one chance to fail and one chance to succeed. Clear as mud? Here’s another example. Consider rolling a 6-sided die. What are the odds that you’ll roll a 3? The ratio is 1-in-6, so the odds are 5-to-1.
When the true odds are greater than 1-to-1, that event has a less than 50 percent chance. The higher the first number, the lower the chance, so a 500-to-1 event is much less likely to turn up than a 10-to-1 event. You can also express odds for events that have a greater than 50 percent chance of occurring. If you had a bag with three black balls and one red ball, your true odds of pulling a black ball would be expressed as 1-to-3.
Examining How Casinos Operate and Make Money: House Edge
Bad news: Casinos aren’t in the charity business. In fact, they exist to make money. Like all successful enterprises, they follow reliable business models. And the casino business model is one of the simplest and most successful of all time. With their intimate understanding of probability (and human nature), casino owners have created a catalog of entertaining games that are mathematically guaranteed to keep their pockets full and their bottom lines healthy.
To put it a different way, casinos expect to pay out slightly less money to winning bettors than they take in from losing bettors. The laws of probability tell casinos how often certain bets win relative to how often they lose. Casinos then define the payout odds based on the winning probabilities — the true odds. The payouts are invariably smaller than the true odds, ensuring that, with enough betting action, the casino will take in a certain amount with every dollar wagered.
Table 3-1 shows the house edge for popular casino games and how much you can expect to lose for an average three-day weekend of playing $10 a hand on the most popular table games. As you can see, the higher the house edge, the more you can expect to lose. For example, you cut your losses by 80 percent if you switch from roulette to baccarat!
This table makes a few assumptions. First, it assumes you’re playing the most advantageous bets for games like baccarat and craps. Second, it assumes optimal gameplay rules and payout odds for games like blackjack and video poker. Finally, you’re playing optimal strategy, which has a big impact on house edge in games like Let It Ride, three-card poker, and blackjack. (Check out the specific chapters later in this book for detailed strategies.) This next section looks at the three methods that casinos utilize to assist themselves in performing profitably.
TABLE 3-1 The Minimum House Edge for Popular Casino Games
| Game | House Edge | Loss per $8,000 in Total Bets |
|---|---|---|
| Baccarat | 1.06 percent | $85 |
| Blackjack | 0.50 percent | $40 |
| Craps | 1.36 percent | $109 |
| Caribbean Stud Poker | 5.22 percent | $418 |
| Let It Ride | 3.51 percent | $281 |
| Pai Gow Poker | 2.54 percent | $203 |
| Roulette | 5.26 percent | $421 |
| Three-Card Poker | 3.37 percent | $270 |
| Video Poker | 0.46 percent | $37 |
Charging a fee
With some games, casinos charge a fee or commission. Baccarat is a perfect example. If you bet on the banker’s hand and win, a 5 percent commission is deducted from your winning bet. This fee tilts the odds slightly in favor of the house and ensures that the casino makes a profit at this popular table game. Other examples of the house charging a commission for a bet are the buy and lay bets in craps, where the payout odds are the same as the true odds, but the player must return 5 percent (or so) of their winnings.
Paying less than the true odds
Another way the casino makes money is to pay out less than the true odds (see the earlier section “Factoring in the odds”). Take roulette: With 38 numbers on the wheel, your odds of guessing the winning number are 37-to-1. So, you bravely place a $100 bet on a single number and hit it. Congratulations! After you quit jumping up and down and kissing the cocktail server, dealer, and anyone else who couldn’t quickly escape, you collect $3,500.
But, wait a minute. $3,500 means a payoff of 35-to-1. What happened to the true odds of 37-to-1? The fact is, even though you win, your payoff is less than the true odds. The bottom line? Casinos take $200 out of every $3,800
