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The Science of Winning

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Revealing the secrets of cards, dice and wheels

by Basil Nestor

Why do coins flip the way they do? Why do cards fall a certain way? What combination of symbols will appear on the reels of a slot machine?

In this article I’m going to tell you about probability and how it works in gambling. If you’re not mathematically inclined, don’t panic. I won’t wade through complicated formulas or graphs.

Actually, it’s rather simple. An effective gambling strategy depends on you being able to reasonably predict certain outcomes. It might seem like magic to the uninitiated, but an optimal-strategy player can simply look at a game and in most cases immediately know how to beat it (or know if it can be beaten). This is before he risks a single dollar. Cool, huh?

Yes, but to get to that ninja-like state of expertise we need to go through probability. So let’s look at some practical applications.

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.

What if George hits a bad streak and loses five consecutive times. What’s the probability that the streak will extend to six?

Some folks would say that George is “due.” Others would say that the eagle (or state symbol) is “on a rush,” and betting the trend is the way to go. Which choice is correct?

They’re both wrong. It’s still a coin toss. The odds are exactly the same for every flip, always 50:50. History doesn’t matter.

There are situations when history will affect the future, but in most casino games this is not the case. Here’s why.

Deal yourself one card from a deck of cards. You have a 1 in 52 chance of receiving any particular card. Let’s say you draw the jack of diamonds. The chance of someone else drawing the jack of diamonds has dropped to zero. In addition, the chance of drawing another diamond has dropped to 12 in 51. In this situation the first decision (history) will affect subsequent decisions (the future).

Now put the card back and shuffle the deck. The chance of drawing the jack of diamonds is back to 1 in 52. The deck doesn’t remember your previous draw.

Spin a roulette ball. Let’s say red wins five consecutive times. Is red now less likely to hit? No. The wheel has no memory. Dice are the same. Gambling devices are not sentient. They do not say to themselves, “Hey, it’s time to average things out and end the trend.” They are inanimate and do not respond to history.

Misunderstanding this one truth has cost gamblers more money than all the unfavorable games and poor odds in the entire history of gambling. The error is known as gambler’s fallacy. Gambling systems based on this fallacy are doomed to fail. Why? Because they don’t accurately predict the probability of a win. Bets increase or decrease for no valid reason.

So remember this: A pattern of wins or losses generally tells you nothing about what will happen on the next decision. The only thing that matters are the actual odds. Nobody is ever “due” for a win or a loss.

So how do casinos earn money if everything is so unpredictable? Simple: They give themselves an edge.

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What Is the Edge?
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.
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 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 mathematical 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.
In the coin-flip example, a one-penny difference in the payoff translates into a 0.5 percent house edge and a payback to the bettor of 99.5 percent. 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, the flips are random, so there are streaks. Anything could happen in a few hundred or a few thousand flips. But over time the side with the positive expectation eventually will win about one-half percent of all the money that is wagered. It doesn’t sound like a lot, but it adds up. And it gets even better for casinos. Most people voluntarily play in a way that gives casinos an edge of between 2 and 15 percent. And many games “hide” an enormous edge by paying 1:1 or better but cleverly changing the “coin” so heads is harder to hit.

So How Do I Win?
First, you have to lose less. That means reducing the house edge whenever possible. Sometimes it’s as simple as choosing quarters over nickels, or a 3:2 payout for blackjack naturals over a 6:5 payout. Your potential for profitable luck increases as the casino’s edge decreases.

The best way to reduce the house edge, and sometimes even shift it to your side, is to use optimal strategies (such as the strategies in my Smarter Bet Guides). Optimal strategies tell you when to double down in blackjack. They tell you which cards to hold in video poker, or the advantage of the line over the field in craps.

About 90 cents of every dollar a casino wins comes from players who are not using optimal strategies. They either don’t know that a game strategy exists, or they think it’s too much trouble to learn. Some players prefer to rely on hunches and superstitions. That’s okay, but it’s expensive! Optimal strategies save you money, give your more playing time and give you more chances to walk away with a profit.
So really, the science of winning is about having more fun. Enjoy the game!Basil Nestor is author of The Smarter Bet Guide to Blackjack, The Unofficial Guide to Casino Gambling and other comprehensive gambling guides. Got a question? Visit and drop him a line.

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