The Science of Winning

These series of articles are about probabilityBasil Nestor is the author of the new Playboy Complete Guide to Casino Gambling. This wonderful book teaches players how to avoid sucker bets and win more when playing gambling games.  He is also the author of The Smarter Bet Guide series for video poker, slots, craps, and many other books about gambling.  Basil's website is www.smarterbet.com  and how probability works in gambling.

If you’re not mathematically inclined, don’t panic. We won’t wade through complicated formulas or graphs.

But learning about randomness, probability, and what to expect from dice, cards, and wheels is important because an effective gambling strategy depends on you being able to reasonably predict certain outcomes. It might seem like magic to the uninitiated, but eventually you will be able to just look at a game and in most cases know how you can beat it (or if it can be beaten). This will be before you risk the first dollar. Cool, huh?

Yes, but to get to that ninja-like state of expertise we need to go through probability, and also game theory.

Heads vs. Tails

Take a quarter and flip it. Will George Washington be on top when the coin stops moving? There’s no way to know. That’s why they call it a “toss up.” Neither side has an advantage. Neither side can expect to win one decision or the majority of decisions. A lucky streak could favor George, or the streak could go the other way. A streak may never appear, or there may be many streaks. Anything is possible.

If the payoff on a heads-or-tails wager is 1:1 (one unit paid for every unit risked), then both players have an equal probability of earning a profit or suffering a loss. Remember that a bet requires two opposing persons or entities.

But let’s say the payoff goes higher or lower (1:2, 2:1, etc.). The true odds are still 1:1, but the payoff odds, or house odds, have been shifted. The player who is getting the extra money has a long-term positive advantage. This is called a positive expectation. The person who is giving the extra money has a disadvantage, a negative expectation.

The difference could be as little as one penny on a dollar wager, but that alone would do it. There is still no way to predict who will win most of the decisions, but one side will inevitably, inexorably, and permanently win more money as the flips continue.

It’s a mathematic fact, a rule of the universe. The person wagering the positive side could quit her job and retire if the other guy would just consistently and rapidly keep flipping and betting. This is how casinos earn a profit. They don’t have to win all the time. They don’t even have to win most of the time; they just need to have a positive expectation. This advantage is commonly known as the house edge, and it’s usually measured as a percent of the wager.

In the above example a one-penny difference in the payoff (ninety-nine cents paid instead of one-dollar) translates into a 0.5% house edge and a payback to the bettor of 99.5%. In other words, a typical bettor would lose once, win once, and be down an average one cent after two decisions or one-half cent after one decision.

Of course, it’s impossible to lose one-half cent in our flipping contest; a player either wins 99 cents or loses one dollar. And the flips are random, so there are streaks. A player might win twenty flips out of thirty, or lose thirty of fifty. Anything could happen in a few hundred or a few thousand flips, but over time the side with the negative expectation eventually will lose about one-half percent of all the money that is wagered. It doesn’t sound like a lot, but those giant palaces in Las Vegas and Atlantic City were built on similar minuscule advantages.

Does that mean everyone who plays against a casino is “doomed” to lose? Not necessarily. Luck plays a role, and so does strategy. But the positive effects of luck and strategy are diminished as the house edge grows. That’s why casinos work hard to entice you with games that have a big house edge.