A-Minus Math Students Shouldn't Gamble

Good at Math?

ALBERT EINSTEIN
ALBERT EINSTEIN

The Know-it-All Knows When to Quit

The famous Princeton professor named Einstein never had a problem with gambling although he knew the rules of probability backward and forward. This may have been because he was very down-to-earth in many ways despite an unfathomable grasp of relativity and concepts that elude most everyone. He had common sense.

The rules of chance certainly do have a direct connection to gambling. Some rules we take for granted, but others are less obvious. A sure bet won't be found in a casino. If only numbers from one to eighty are possible, and twenty numbers are chosen at random, it's a sure bet they'll all be somewhere from one to eighty, but it's most likely the numbers you choose won't earn you any money because certain people, with the brains 99% of us lack, planned it that way. Unfortunately, games of chance aren't easy.

We're expected to know that if something really is impossible, then there's literally no chance at all of winning. Kindly, the casinos spare us from that pothole and, in the one-to-eighty game, won't let us bet on ninety-two when we've had one too many.

The necessity for logical thinking starts when logical answers get less obvious, which unfortunately is when we need logic the most. What if you threw your dice and had to get them to total 7? A 5 and 2 would do the trick, as would 6 and 1 or 3 and 4. Switching the dice around so these combinations still come up, but the 2 is on the other die, and the 5 on the opposite one, and so on would be like finding the same lucky numbers together, but possibly on different dice. Should that chance be worked into the probability formula? Any possibilities that add up to 7 have the same level of probability as each other don't they, or do they? Should the dice be calculated separately to determine an overall probability for both dice? Now it's confusing. At such times a gambler may want to go to the bar for a while and relax, to collect his thoughts.

But how does the possibility of a combination of numbers coming up on different dice affect the chance of rolling a 7? It shouldn't affect them at all it seems, but the average gambler probably doesn't know for sure. Unfortunately we probably didn't know what the chances were exactly in the first place. A math teacher would know, but what's the chance of one sitting next to me at the bar? Here we are back to the law of probabilities again. Why don't more math teachers gamble? Now we're getting somewhere, because the answer to that question might make the difference between having and keeping a house, marriage, or job, or not having and keeping those things, if addiction sets in.

Back to the casino. It's time to get up on that horse and ride it again. We are faced this time with the certainty that one thing or another will happen while the game makes it impossible for both things to happen. Now gambling seems more like real life. If either an even or odd number will come up, and if we know no number that's both odd and even is a possibility, we sense instinctively a 50% chance of odd, and the same chance of even. We are on solid ground. But suddenly an uneasy feeling arises when complications of the game are explained. It's a one-to-eighty game in which we have to figure out the chance that a single number picked will be in the 70's or 30's. Should I add the chance of it being in the 70's to the chance of it being in the 30's? It seems only logical. But a poet once wrote, "A little learning is a dangerous thing." Thank you, Alexander Pope, for not letting me feel too cocky.

Some games involve the opposite of something happening, which shouldn't be much trouble to figure out. It just means we're betting it won't happen. The opposite of an odd number would be an even number. That's simple. If three odd numbers in a row have been picked at random, the chance of an even number next time must be getting pretty good, but exactly how good? The next pick might be yet another odd--must be a slim chance (same as a fat chance). But what if you were able to know exactly what the chance is? Math teachers know, most likely. But strangely there aren't many of them at the casino.

It shouldn't get more complicated, but unfortunately it does. What if the numbers one through eighty each had one of two different colors? The colors are there for a reason, not to make the numbers pretty, but to offer a more complicated situation. If the colors are assigned randomly as to whether they are on odd or even numbers, and if there are a total of 15 red numbers and 65 blacks, but you don't know which numbers are red or black, then you start to feel hopeless. There's a certain chance, if two numbers are picked consecutively, that both of them will be odd and red. There's another probability that of the two, at least one will be odd and red. The probability that only one, not two, will be odd and red should be determined from adding the chance of first number's being odd and red to the probability of the second one also being odd and red, and then subtracting the probability that both of them will be odd and red. You know this because you worked it out with your pen on a napkin with the help of the bartender. It looked good at the time and it still looks good. It's air-tight logic. You're going to go with it. But suddenly you realize that even if you're right, you still might lose.

After losing sufficiently, dark thoughts enter your mind. What good does it do for a gambler to be puffing on a cigar and feeling confident? There's something called luck involved in winning, regardless of the odds. In the midst of these dark thoughts we realize that one more factor, directly connected with luck, has to be plugged into the probability formula to make it work for gamblers. It's knowing when to quit.

Only a good night's sleep can prepare me for tomorrow, I tell myself. Then I can handle more complicated games of chance, such as those incorporating "conditional probability." That's when the fact that one thing has just happened has an effect on the chance that another event will occur. The probability that the second event will occur has to take into account the chance of the first occurring in the first place. In this game, the chance that the second event will occur, if the first happens, is determined by figuring the probability that both events will occur, and then dividing that probability by the chance of the first event's really happening. Stimulated by this revelation, I get up from the breakfast table and head for the casino floor.

I have to know beforehand what the chances are, if after the first of two numbers picked is red, that a second number will be colored black instead of red. I decide to figure the probability of a red number followed directly by a black number, then divide that probability by the chance the first number really will be red. The trouble is I can't think clearly enough to do this when, lurking in the back of my mind is the realization that people who can run circles around me already worked out the game and all the other limiting factors are slanted against me.

The famous gambler Minnesota Fats, a New Yorker who once made a trip to Minnesota, said that he knew better than to gamble at a slot machine because the chance of winning was only luck, whereas his best bet was to gamble on something requiring skill because winning there has to do with motivation. Fast Eddie Folsom of Los Angeles and Nate Raymond of Cleveland have agreed likewise, as has Nick The Greek Dandalos, who, after proclaiming, "There is no greater thrill in life than suddenly winning a large sum of money," died penniless.

Surely there's a connection between math and gambling. But the deviousness of the games in casinos suggests a hint as to why drinks are free to steady gamblers, and also why Einstein didn't get involved. The stage shows in Las Vegas are very uplifting and entertaining. They are a better investment than a bet at a roulette wheel. Many a gambler appears to have gotten religion when seen storming off a casino floor taking the Lord's name in vain. In the long run the casino will come out on top. They planned it that way. Those who can count and memorize cards have an advantage but may be asked politely to leave, after it's discovered. But there is always a "deviation" from the expected, probable result. This is called "luck" and can happen to anyone at anytime. However, the more we play, the better the chance is that overall we will lose. In moderation, gambling can be fun if only a negligible amount is wagered. The key is to realize that despite the correct calculation of probabilities, the limitations and requirements for winning favor the casino.

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