Statistics for Dummies (22 page)
Gambling to Win
Las Vegas is one of the most exciting hotspots in the world. I have a feeling though, that the cheap all-you-can-eat buffets and the majestic Roman gladiators that roam Caesar's Palace aren't the main attractions (although I highly recommend both!). Las Vegas is arguably a gambler's paradise; the place to go when you're feeling lucky and want to win big. The fact that the vast majority of folks who gamble in Las Vegas come out losers isn't important to that new crop of potential winners who board the planes each day heading toward Nevada with a feeling of hope and exuberance. After all, someone has to win, right? It may as well be you. While I can't promise that this chapter is going to make you a big winner in Vegas (or any place else you may choose to try a round with Lady Luck), I can say that it will help you understand what you're up against, give you some tips to gain a possible edge, and at the very least, help you not lose quite so much.
Casinos are beautiful places; they have exciting atmospheres with brightly colored machines, blinking lights, exciting sounds, happy dealers and servers, and no clocks or windows anywhere in the place (they don't want you to realize how much time you've been spending there). Everything is well thought out, from the layout of the building (to get to any restroom you must go past tons of slot machines) to the patterns chosen for the carpet (the patterns are
intentionally busy and hard on the eyes, because the owners don't want you to look down but instead want you to always be looking up at the action and moving toward your next adventure).
The gaming industry has its act down to a science, and those who run gambling houses are very good at what they do. They offer you great entertainment and a chance to win some big money; all you have to do is play. Many people are lured by the chance to win thousands of dollars or a new car with just one pull of a slot machine or just one perfect hand of blackjack. Of course that chance exists, but if everyone won big money, the casinos couldn't afford to stay in business. So they have to find ways to take your money, and they do that by setting game rules that give them a tiny edge during each round of play; by making sure that when someone does win, he or she wins big (so word gets around); and by encouraging you to stay in the casinos as long as possible. They know that the longer you play, the greater their chances of taking your money.
Hundreds of books have been written about how to beat the casinos at most any game offered. Each author wants you to believe that his own strategy is going to make you win big. The truth is, the best these books can do is to help you not lose so much, because the way the games are set up, the house (the casino) always has an advantage. This advantage is smaller with certain games, such as Blackjack, and larger with other games, such as slot machines, which, according to rumors, generate up to 80% of the total profits for some casinos. The most important thing to remember in any gaming situation (
gaming
is the casino industry's softer word for gambling) is to quit while you're ahead. If everyone did that, the casinos would be out of business. But of course, that won't happen because quitting while you're ahead is hard to do.
On the other side of the coin, another good strategy is to cut your losses and quit before you lose too much, instead of figuring that the odds will eventually turn back in your favor, and you'll win all your money back. That approach often turns out to be a lose-lose situation. Casinos bet that you will stay and play no matter what, increasing their chances of eventually getting more and more of your money. Looking at the lavish casinos now being built in Las Vegas, it seems that their bets are paying off.
| REMEMBER | What can you do to minimize your chance of losing, or of losing too much? Set up some boundaries for yourself before you even walk into the gaming situation (for example, quit playing when you're ahead or down by a certain amount), and then stick with those boundaries. When gambling (excuse me — gaming), quit while you're ahead or before you get too far behind. Set your limits before you start. |
Two of the most important tools you can use in any gaming situation are information about your chances of winning and a true understanding of what those chances mean. Probability can certainly go against your intuition, and you don't want to let your intuition get in the way of keeping your money. (See
Chapter 6
for a more in-depth discussion of the use of probability in statistics.)
Here are some of the most common
misconceptions
about probability:
Any situation that has only two possible outcomes is a 50-50 situation (50% chance of winning, 50% chance of losing).
A combination of lottery numbers like 1-2-3-4-5-6 can never win; those numbers aren't random enough.
Buying 100 lottery tickets instead of just one is a great idea; it gives you such a better chance of winning.
If Joe and Sue have three girls already, the chance that they will have a boy next time has to be pretty good.
The longer you play this slot machine, the better chance you have of coming out ahead.
In this section, I break down each of these misconceptions so that you can be informed about the reality of any gaming situation, have a better understanding of what to expect, and plan accordingly. This may ruin some of the magic and excitement that comes with gaming, but then again, it probably explains why you can't find statisticians (certainly none that I know) who are either professional or compulsive gamblers. In fact, Las Vegas won't really mind if statisticians don't hold a conference there any more, because they didn't spend much money in the casinos the last time they were there! (I, myself, play only nickel slot machines, one nickel at a time. At least my $20 will last longer.)
You're going to flip a fair coin (that is, a coin that hasn't been tampered with); it has heads on one side, tails on the other. What's the chance that a head will come up? Fifty percent. What's the chance that a tail will come up? Fifty percent. If you were to bet on the outcome of this coin flip, you would have a 50-50 chance of winning (versus losing). Why is that? Because you have two
possible outcomes, heads and tails, and each of these outcomes has an equal chance of occurring. You know a couple that is going to have a baby. They, of course, can have either a boy or a girl. Each of these outcomes is equally likely, so the couple's chances of having a girl (versus a boy) is 50-50. On the other hand, if you buy one of 1,000 raffle tickets for a motorcycle, you have two possible outcomes, win or lose the motorcycle. Does that mean that your chance of winning is 50-50? No. Why not? Because you aren't the only person who bought a ticket!
Four rules of probability may help break these ideas down a bit:
The probability that a certain outcome will happen is the percentage of times that the outcome is expected to happen in the long term, if the exact same conditions were repeated over and over.
Any probability is a number between 0 and 1. A probability of 0 means that the outcome is not even possible. A probability of 1 means that the outcome is certain.
All of the probabilities for all possible outcomes must add up to 1. That means the probability that an outcome does
not
happen equals 1 minus the probability that the outcome
does
happen.The probability of an event (a combination of outcomes) is equal to the sum of the probabilities of the individual outcomes that make up the event.
With the coin flip, two outcomes are possible, head or tail. The number of ways a head can occur is 1, and the number of ways a tail can occur is 1. The total number of possible outcomes is 2: head or tail. So, in that case, the chance of a head coming up is ½ or 50%; the same is true for a tail. This is a 50-50 situation.
However, if you look carefully at the first rule, this explains why not everything with two outcomes has a 50-50 chance of happening. You have to look at the number of ways that each of the outcomes can happen. With your motorcycle raffle ticket, you can either win or lose. The number of ways you can win is 1, because the raffle organizers will draw only 1 winning ticket. The number of ways you can lose is 999 because all of the remaining tickets are losers. The total number of outcomes is 1,000. That means your chance of winning is 1 ÷ 1,000 = 0.001, and your chance of losing is 999 ÷ 1,000 = 0.999. Certainly, you have only two possible outcomes regarding your raffle ticket (win or lose), but each of these outcomes does
not
have an equal chance of happening, so this is definitely not a 50-50 situation.
| HEADS UP | Very few probabilities in life are actually 50-50. To be in a 50-50 situation, you must have only two possible outcomes |
So, you're ready to play the Powerball lottery. You've heard that the jackpot is now up to $200 million — you may buy more tickets than usual this time to increase your chances of winning. And you're ready to pick those numbers. (You have to pick five different numbers between 1 and 53, and then you pick a separate Powerball number between 1 and 42, and this one can be the same as one of the other five that you already chose.) To win the big jackpot, you need to correctly pick (in any order) all of the first five numbers, plus the correct Powerball number. What combination should you pick? Your brother's football number, your mom's birthday, four digits from your Social Security number, your dog's age in months, and the number you saw in your dream last night? These options sound as good as anything else, because any combination that you choose is just as likely to win as any other combination.
This makes good sense until you start thinking about the combination 1-2-3-4-5 with a Powerball number of 6. It seems like this combination should never happen because these numbers don't seem random enough. Well, this is a case in which your intuition can get the best of you. Indeed, this combination has the same chance of being chosen as any other combination that can occur. Take a small example in which the possible numbers to choose from are 1, 2, 3, 4, and you have to pick 2 numbers. The six possible outcomes are 1-2; 1-3; 1-4; 2-3; 2-4; 3-4. Your chance of winning is 1 out of 6. Notice that the combination 1-2 has the same chance of being chosen as any other combination. The same is true for the combination 1-2-3-4-5 with a Powerball of 6. Combinations like 23-16-05-24-18 with a Powerball of 12 may look easier to get, but remember that you have to get every single number exactly right in order to win the big jackpot.
| HEADS UP | A combination like 1-2-3-4-5 with a Powerball of 6 looks hard to get, but it actually has the same chance of winning as any other combination. What this combination should make you realize is how |
| TECHNICAL STUFF | Lotteries typically call the probability of winning the |
A Powerball lottery ticket only costs a dollar, and it gives you a chance to win a multi-million dollar jackpot. You figure that someone has to eventually win that
jackpot, so you decide you're going to take your shot at it. After all, if you don't play, you can't win. As long as you truly understand your chances of winning
and
losing, buying a few lottery tickets now and then can be cheap fun.
The problem, however, comes when people buy lots of tickets, thinking that their odds are greatly increased by buying more tickets. While holding a hundred tickets (versus only one ticket) does increase your chance of winning a hundred times, you have to realize that the chances of winning big are very small — almost zero. And a hundred times a number that's close to zero is still very close to zero. If you can't afford to lose that hundred dollars (and the odds are overwhelming that you will lose it), don't bet it all on the lottery.
To put the probability of winning the Powerball jackpot into perspective, look at
Figure 7-1
. This shows the prizes and the chances of winning each prize in a given Powerball lottery. (Most Powerball lotteries offer the same payouts with the same odds.) The gray circles indicate the five balls chosen from 1 to 53 and the black circle indicates the Powerball number. The odds of winning the $3 prize are 1 in 70, or 0.0142 (about 1.5%). Note that this is more like a probability than real odds, but I'll let it slide. As you go up the scale, the winnings increase, but your odds of winning decrease, and they do so exponentially. Matching 4 of the 5 numbers, for example, has odds of 1 in about 12,000; matching 5 of the 5 numbers has odds of 1 in about 3 million; and finally, matching all 5 numbers plus the Powerball number, decreases your odds to one in over 120 million.
Figure 7-1:Payouts and chances of winning for a Powerball lottery.
| TECHNICAL STUFF | Why do the odds decrease so quickly just by having to match one more number each time? A small example may help illustrate this. Suppose you have to pick 2 numbers between 0 and 9. If you have to match only one number, your chances are 1 in 10. If you have to match both numbers, your chances drop to 1 in 45. This is because you have 10 possibilities for the first number, times 9 possibilities for the second number (because no repeats are allowed), for a total of 90 possibilities. But now you have to divide those 90 possibilities by 2, because you can have the numbers in either order and still win. (You don't want to count 1-0 and 0-1 as separate combinations, for example.) The odds change dramatically because of this multiplier effect. Having to match the Powerball number in addition to having to match the first five numbers multiplies the odds by an additional 42 times (because you have 42 possible numbers for the Powerball). |
The overall chance of winning
any
prize (not just the big prize) is reported by the lottery to be 1 in 36. Because the overall chance of winning is the same as the chance of winning any prize, add up all the probabilities of the prizes, and you get 1 in 36. You're using the fourth rule of probability here (see the "
Having a 50-50 chance
" section earlier in this chapter).
| REMEMBER | Before you play any game of chance, always look at the odds or probability of winning. And don't spend more money than you can easily afford to lose. With games that have big payoffs, the chances of winning are always extremely small, and buying many more tickets, or playing many more times, won't increase those chances by enough to justify the added cost. Like the saying goes, the best way to double your money in gambling is to fold it in half and put it in your pocket! |
Joe and Sue have already had three girls, and they're expecting their fourth baby soon. They really want to have a boy this time. Friends and family think that their chances of having a boy are higher this time, because they've had three girls in a row. Are they right? This is similar to the people around a craps table who are cheering on the shooter (the person with the dice) because he's on a "hot streak" and can do no wrong. Do winning or losing streaks really exist, and after a certain string of events has happened, does that increase or decrease the chances that the same thing will happen again?
In many situations, especially in gambling, winning or losing streaks don't exist, because each time you play a game of chance, everything resets itself, and the outcome from last time has no effect on the outcome this time or on the outcome next time. In other words, when events are independent of each other, the probability of an event remains exactly the same each time the game is played.
For Joe and Sue, this may be bad news, but the probability of having a boy is still 50-50, the same as it's always been, regardless of whether they have already had three girls. Similarly, if you flip a fair coin three times and get heads each time, you shouldn't expect a tail to have a higher chance of appearing on the fourth toss. The chance is still 50-50.
| HEADS UP | Probabilities work only in predicting long-term behavior, not short-term behavior. If you know that the chance of heads is 50%, that means if you flip the coin many times, you should expect about half of the outcomes to be heads and half to be tails. However, you can't predict |
