How to interpret “bad beat” stories

Mike Caro   Exit

---

Note: Not at the old Poker1 site. A version of this entry was originally published (2002) in the revived Gambling Times, called Win magazine.

---

I seldom talk about roulette, yet my last two columns have been devoted to it. I presented Caro’s Roulette System #1 two columns ago. I promised that it would cut the house edge to “literally zero,” and it did.

Unfortunately, as I explained last column, when you carefully followed the complex instructions, you didn’t end up making any bets. My point was that there is no magic, mystical way of choosing numbers or manipulating the sizes of your bets that can overcome the odds against you. There is no scientific way, either, short of timing balls and wheels — which is a technique I think works better in theory than in practice under real-world conditions.

In order to win at any form of gambling, you must be able to make rational decisions that improve your chances. And those correct decisions must be powerful enough to overcome the odds against you. In some forms of gambling this is possible.

A game like poker is beatable, for instance, because it’s a war of decisions. Over the long term, if the quality of your poker decisions is substantially better than your opponents’, you’ll probably win. Now, back to roulette…

What Peter told me

In the whole history of the world, did the same number ever come up seven times in a row on an honest American-style roulette wheel? I’m speculating about this because roughly 20 years ago my friend Peter said it had happened.

He came to me broke and complained, “The same number hit seven times in a row. And I was betting the same number every time – just not the right one. Do you realize what would have happened if that were my number? I’d be richer than Howard Hughes!”

---

What Mike Caro teaches students about bad-beat stories…

If you tell me a bad beat story, I’ll pretend to listen. I’ll nod sympathetically.

But you need to know that I’ll actually be using this valuable time to ponder more profitable things.

That way, you’ll experience the illusion that I care, while I’ll be productive. It works for both of us.

---

“What number were you betting?” I quizzed, feigning interest.

“Nineteen.”

“What number came up seven times in a row?”

“Thirteen.”

“Well, you know, thirteen is unlucky, so you were right not to bet on it,” I blurted, trying to minimize my tone of sarcasm.

Meanwhile, three possibilities came to mind: (1) It did, indeed, happen honestly as Peter claimed; (2) It happened as Peter claimed, but there was something funny about the roulette wheel; (3) It never happened.

Some odds

On an American roulette wheel, with both zero and double zero, there are 38 numbers to choose from (36, plus 0 and 00). That means the odds are 37-to-1 against your number winning. Fine. What are the odds against your number winning seven times in a row? If I remember the statistical tables that I memorized in high school correctly, it’s  114,415,582,591-to-1 against. That’s more than 114 billion (with a “b”) to one against.

But, wait. That’s not a fair answer. In order to see seven wins in a row for the same number, you’ve got to begin with some number.

This means the first one is free and you only need to duplicate it six times, not seven. So, having the same number come up seven times in a row is really much easier – only a 3,010,936,383-to-1 shot, which is slightly more than three billion to one against. So, in the whole history of the world, has this ever happened? I’m not sure. Let’s think about it.

Estimates

I doubt that the typical roulette wheel in a casino averages more than 300 spins a day, and it sits idle for much of the time. Maybe it’s more; maybe it’s less. It’s certainly more for a wheel in a highly trafficked area of a mainstream casino. How many wheels are there?

I don’t know that, either, but let’s say that over the last 100 years there have been an average of 6,000 American roulette wheels operating in legal casinos and illegal gambling joints around the world. Let’s say each wheel gets 110,000 spins a year.

I’m only talking about wheels with some potential for everyday gambling use, for amusement, or for practice, not ones stored in closets, kept for display, or the miniature toy type. That’s 660,000,000 spins a year – about two-thirds of a billion – most not earning much money for the house, because only a small percentage of this happens in major casinos.

Assuming these wild estimates have some semblance to reality, there were about 66 billion spins in the last 100 years and what Peter claims to have witnessed has probably happened about 20 times. (And of course, the potential streak might have been split across several gambling sessions or might not have been completed when a wheel stopped operating. These, and others, are picky points and don’t greatly influence our calculations.)

Learn to divide

But, back to my original question: Did Peter actually witness it? I’m guessing not. I’m guessing that Peter just wanted to complain about his bad luck and was seeking sympathy. I’ve learned long ago not to question any gambler’s “bad beat” stories. These seldom hold up to scrutiny.

Besides, you have to understand what the purpose of the sad story is. Twenty-five years ago, when I wrote the draw poker section for twice world champion and Poker Hall of Fame member, Doyle “Texas Dolly” Brunson, I included a “Table of Sad Stories.”

These were actual poker tales of misery I’d heard over the years. I presented them exactly as they were told to me. Then I carefully calculated the odds against them actually having happened.

Favorite

My favorite is: “Can you believe that? She gets two full houses and now a straight flush! I’ve been playing in Gardena [where they used a 53-card deck, including the joker] 10 hours a day, every day for 16 years, and I never had a pat straight flush!” The odds against that wrapped for seven extra lines in the answer column.

It calculated it as: 203,909,594,800,000,000,000,000,000,000,000,000,- 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,- 000-to-1 against. In other words, if you play that long, you’ll get a pat straight flush.And if you tell me it never happened, I don’t believe you.

So, what’s my point? No point really. I’m just providing a little friendly advice about getting along with your gambling pals. When they tell you a sad story, they don’t think that it will generate sufficient sympathy unless they embellish it. They’re not telling you what really happened. They’re telling you how they feel about what really happened. If they say they lost on nine flushes, they probably lost on about three flushes.

And that’s the key. Each gambler has a number by which you should divide all bad-beat claims. For some, it’s quite high, and for a few it’s low or nonexistent. I believe the average is three. That’s what you need to divide by.

If you hear a sad gambling story, nod sympathetically and pretend to believe it. But, if you want to know the truth – divide, divide, divide. — MC