Swain Scheps - Casino Gambling For Dummies

In order to have a realistic perspective of your chances in the casino, you need to view luck in rational and mathematical terms: Luck is a temporary fluctuation or deviation from the norm. In the short run, you may perceive that you got real lucky when the dealer busted eight hands in a row at blackjack. But in reality, such an event is just normal fluctuation — also known as a random walk — such as when the stock market drifts in one direction or another.

For example, in three-card poker, for every $100 you wager, you can expect to lose a little over two bucks. But remember, that’s an average loss over an infinite number of games. Over the short run, anything can happen. You may get lucky and finish the day ahead — or you may get unlucky and lose far more than $2.

In a purely mathematical sense, neither of these results has anything to do with luck. They are simply the normal consequences of fluctuation. For example, try flipping a coin. Half the time, it should be tails, and half the time, it will be heads. Flip it 1,000 times, and you’ll get close to 500 each. Now zoom in on any consecutive sequence of 20 coin flips out of that 1,000, and you’ll find sets of 20 that veer way off the path from 50 percent.

Millions of merry gamblers frequent casinos all over the world every day without a clear understanding of one important concept — probability. Mastering one of the more complex branches of mathematics isn’t necessary for successful gambling. But an elementary understanding of probability is certainly helpful in making sound gambling choices.

Probability is the study of the laws of chance and the identification of how often certain events can be expected to occur. To express the probability, or likelihood, that a coin will turn up heads, you can give the result in numerous ways, such as a

Ratio — 1 in 2 times

Fraction — ½ or half the time

Percentage — 50 percent

Decimal — .50, which is the same as 50 percent

Odds — 1-to-1 Odds is an overloaded word in casino gambling. In this case, it’s an expression of the number of times something won’t happen next to the number of times it will happen. So, 1-to-1 odds means an event is an even-money event; it has an equal chance of occurring or not occurring. But odds has another meaning: The amount of money you win compared to the money you risk. If a bet payoff is concerned, we’ll refer to it as the payout odds .

(If you’re champing at the bit to find out more in-depth info about probability, there’s a 100 percent chance you’ll love reading Probability For Dummies by Deborah Rumsey, PhD, [Wiley].) This section looks a bit closer at probability’s role in casino gambling.

Another important term to understand here is independent outcomes . Being independent has nothing to do with successfully ditching your loser boyfriend in the casino bar. In gambling, independent events are those where the probability of the outcome doesn’t change from one event to the next. Dice throws and roulette wheel spins are good examples of independent events; they aren’t affected by any previous results. Craps dice, roulette balls, and fair coins have no memory. Each new throw, spin, or flip is independent of all previous turns. In other words, the dice or ball doesn’t know what numbers are running hot or cold, so the probability of the outcome for each and every spin is exactly the same.

Slot games and other forms of automated and digital gambling inside a casino are also independent. Recent jackpots do not change the likelihood of the same combination coming up again. If your chances of lining up three cherries are 5,000-to-1, and you just hit the jackpot, the three cherries have exactly the same chances of appearing on the very next spin.

So, you may be asking yourself, what constitutes a nonindependent or dependent event? Dependent events are occurrences that are more or less likely based on the previous occurrences. Imagine a bag of five black balls and five red balls. Before you pull a ball out, you know you have a 50 percent chance of pulling out a black ball and the same odds of pulling out a red ball. Then you reach in and pull out one red ball and toss it aside. Now the odds have changed — you no longer have a 50 percent chance of pulling either ball. Because you’ve removed a red ball, your chances of pulling out a black ball are now greater (56 percent). In other words, the probability of a single pull is dependent on previous events.

So, in some situations, the past does affect the future. Another classic example is the game of blackjack, in which the composition of the remaining deck changes as cards are dealt out to players. As we’ll discuss in Chapter 7, your chances for getting a natural 21 get lower as more aces are dealt from the deck.

Almost all casino games consist of cards, dice, spinning wheels, or reels. These games almost always yield independent events. Blackjack is the rare exception, which is the main reason for its popularity.

To be a successful gambler, you must understand the intersection of statistics, probability, and the odds. In simple terms, that means you need to understand how often something is to happen ( statistics ), how likely that it can happen to you ( probability ), and what you’re going to get out of it if it does happen ( payout odds ). With a grasp of these concepts, you’re ready to tackle the casino with realistic expectations, and you can understand why some games should be avoided.

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.

Odds is a word with two meanings in the casino. Don’t confuse payout odds with odds in the probability sense, which will sometimes be referred to as true odds . And when you start comparing payout odds with true odds, you’ll start to understand how casinos can afford lavish lobbies and waterfalls and Bengal tigers.