Odds and Ends

The place is Vegas. The scene: the lobby of any big hotel. You are walking down a row of slots, past the backs of the acolytes. Hands reach up and down like earthmoving equipment. Large asses envelop the stools they perch on. There is a din of bells and clicking gears, but no one speaks.

Then, up ahead, you hear the gush of coins. A small, mousy woman wearing a red tracksuit and trainers is shoveling a big payout into a plastic bucket. You walk past, then moments later you hear another, smaller delivery. It is the same machine. Registering no emotion, the woman sweeps up her winnings and continues. Entranced, you watch. Nothing happens, for several minutes. The coins are absorbed like lozenges into the belly of a hungry beast. Then her machine once more starts burping coins into its tray. Do you (a) arm-wrestle her out of her place and work that same slot, (b) go tell the management that the machine is fixed, or (c) walk on?

A little later you are standing by the roulette table. Hands with chunky rings push squat piles of chips forward as an offering to the gods of chance. There is a blur of chrome and numbers, and after skittering like a water drop on a griddle, the little ball dives into a slice of the wheel: 17. The next spins ends with a 9. Then a 15, and a 23. With growing amazement, you stare at the wheel. The next spin seems interminable, but after dancing around the edge for nearly thirty seconds, the ball drops. 3! Do you (a) bet the farm that the next number will be even, (b) go tell the management that the croupier is crooked, or (c) walk on?

Finally, you head for the door. A man in shades and a midnight blue suit walks up to you and presses a backpack toward you. Through the half-open zipper you can see wads of bills. By its heft, the backpack must contain a very large sum of money. Do you (a) thank him and leave with the backpack firmly in your grip, (b) engage him in conversation and only accept the gift if his name is not Vinnie or Guido, or do you ignore him and (c) walk on.

The correct answer in each case is (c). Vegas turns many billions of dollars of profit each year thanks to the fact that few people understand probability. Addiction plus ignorance is a potent combination. You can leak it out slowly or void yourself in a series of diarrhetic spasms, but the end result is the same. Unless you can memorize a five-deck shoe or are willing to use radio-controlled devices (and risk the smashed joints that discovery would entail), your fate is sealed. It’s quicker to just go to the cashier as soon as you arrive and hand them a check for all you’ve got.

Independent events have independent odds. What happens next does not depend on what came before. Each roll of the dice, each pull of the lever, each spin of the wheel, is a freshly smelt bouquet of chance.

Here in a nutshell are the rules of probability. Keep them in a safe place, next to your PIN numbers and your spare house key. You never know when you might need them. These rules could (probably) save your life.

Probability ranges from 0 to 1. Zero is something that never happens, and 1 is something that always happens. But things that always happen (night following day) and things that almost never happen (free lunches) are not very interesting. Life occupies the zone between 0 and 1, the realm of the uncertain. You can think of probability as a fraction, as odds, or as a percentage, so ¼, 1 in 4, and 25% are all the same.

Different outcomes of the same event are probabilities that must add up to 1. So if we say that shit happens 3 times out of 10, then, lucky us, shit fails to happen 7 times out of ten. The probability of your next child being a girl is 0.52, and so the probability of it being a boy must be 0.48. Every day when you go into work, there is a 94% chance that nothing will happen, a 5% chance you will get a fat raise, and a 1% chance you will get fired. The sum of these must equal 1, or 100%, unless you subvert nature by lying in bed all day reading trash novels and eating bonbons.

You combine the probability of unrelated events my multiplying them. The odds of rain may be 1 in 2. Perhaps the odds of you breaking your leg on any day are 1 in 500. If you have a teenage daughter, the odds of her coming home with her tongue pierced are 1 in 15. So, on any particular day, the odds of you coming home on a rainy day with a freshly broken leg, having just been fired, to find your daughter with a rod in her mouth, are (1/2) x (1/500) x (1/100) x (1/15) = 1/1,500,000. Less than one in a million. That’s nothing to lose sleep over (which wouldn’t stop me…).

Back to the casino. When the old girl in the tracksuit hits paydirt three times, it’s just the random bunching up of somewhat unlikely events. Imagine rolling a die and getting three consecutive sixes. The odds of it happening are (1/6) x (1/6) x (1/6) or a bit less than 1 in 200. That’s pretty unlikely. But if you roll a die long enough, or pull that lever long enough, eventually it will happen. Meanwhile the casual gambler will have frittered away everything they own.

Also, if the odds of even a modest win are 1 in 200, then in a lobby filled with more than 200 slots, some machine is always paying out. We tend to concentrate on the lucky winner and ignore the sea of losers. So leave the old lady alone. Her machine is not special. If you grabbed it, the chance of it immediately rewarding you with a fistful of dollars are as slim as they are on any slot and at any time.

Same with the roulette wheel — walk on. Five odd numbers in a row sounds like a lot. Actually, the odds are ½ x ½ x ½ x ½ x ½ or 1 in 32. We think that a run of odd numbers makes an even number more likely, but that’s where they have us by the short and curlies. The probability of an even number on that next spin of the wheel is, yessireebob, ½. Try it. Take a coin and flip it repeatedly. You won’t see neatly alternating heads and tails, you will see groups and clusters of heads or tails a lot of the time.

As for the man in the nice suit (who may or may not be a made guy) shoving a bag of money at you; he has nothing to do with probability. Common sense says you should pass. Or ethics, if you want to get all lofty about it.

It’s natural that our critical thinking skills should be compromised in a place like Las Vegas. They are using classic techniques of psychological warfare. Raucous noise, harsh light, cheap drinks and steak dinners at any time of day and night are designed for sensory disorientation. The effect on the human brain is similar to time spent floating in a darkened tank of blood-temperature water. Sensory overload and sensory deprivation — both will leave you yelling for the happy jacket.

Our response to probability is not wholly rational. When people are offered the choice between betting $10 with a 1 in 2 chance of doubling their money or betting $50 with a 1 in 1000 chance of winning $10,000, they will almost always opt for the latter. Yet the second bet is 500 times less likely to pay off. Even if you made both bets over and over, and occasionally won, you would lose money 10 times faster with the second bet.

The lure of the big payoff always overcomes the small prospect of success. A lottery or sweepstakes is an extreme version of this attraction. (Ed McMahon, even as you read this, may be clambering into a minivan with an oversized check made out to YOU!) In a lottery, $1 buys you a shot at $10 million or more. Never mind that you could buy 10 tickets a week for the rest of your life and have no more chance of winning the big prize than of being hit by lightning.

Maybe a lottery is harmless entertainment. A buck is not much money. To inject a bit of logic into the process, you might never buy more than two tickets. Buying that first ticket increases your chances of winning from zero to a miniscule number. Buying the second ticket doubles the chances. But every ticket after that increases the chances by a smaller percentage, with the same amount of money spent.

I, for example, am supposed to be a smarty-pants, logical scientist. Much to my wife’s amusement, every few months I spend some time filling in forms and moving little stickers for on one of the big sweepstakes drawings. Yet I know deep down that I am as likely to win as I am to discover a process for turning plastic into gold. Which does not ease my compulsion to play these tiny odds.

Gambling is a distraction and a sideshow to the main event: the big lottery of life. As hunter-gatherers, we used to roll the dice every day. No calling out for pizza — gathering each meal risked a tussle with a predator. No handy pills or inoculations — each new food was a potential toxin, and each microbe was looking for new hosts. Life is comparably much safer now. Perhaps we need to take risks to feel alive. Las Vegas bets this is the case 365 days a year, and wins. Odds are you won’t be so lucky.

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