Are You Really Unlucky?

My last column, “Bad Beats and Murphy’s Law,” stated that many people grossly overestimate their bad luck, and feeling like an unlucky victim makes them become one. They hurt their bottom line by playing scared, passive poker.

When I made that point to a friend (we’ll call him Bill), he was offended and insisted that he was not exaggerating his bad luck. He told me of many hands in which he had a huge edge, but lost. He got beat by a two-outer here and by a runner-runner flush there. I said, “Your sample size is too small to matter.”

He then showed me an e-mail from one of his friends, who insists that poker can’t be beat with skill. To prove it, his e-mail contained page after page of hand histories, with one bad beat after another.

I said, “His hand histories mean nothing at all.”

“What? How can you say that? I told you about only a few hands, but he listed more than a hundred of them.”

“So what? He has played tens of thousands of hands. The sheer size of the sample is irrelevant if it is not taken properly. If you select the hands on anything other than a random basis, you bias the results. In fact, if you let me cherry-pick the hands, I can prove anything I want — even that 7-2 offsuit is better than pocket aces.”

“Nonsense! If you picked just the times that 7-2 cracked aces, I would know you were cheating.”

“How do you know that you’re not cheating?”

“I wouldn’t do that. I’m an engineer and respect data.”

“I know that you wouldn’t deliberately cheat, but you, I, and nearly every other poker player base our conclusions about our luck on terrible data.”

I then explained to Bill why we believe that we get more than our share of bad beats:
1. We never learn about most of the times that we were lucky. Our opponents were ahead or missed their great draw, then quietly folded.
2. If someone draws out on us, it’s not necessarily a bad beat. It’s a mathematical certainty that players will hit some of their draws. When they miss, we don’t even think about it.
3. Even if we realize that we have been lucky, we are much less likely to remember it. Our selective memories retain the hands that support our beliefs and desires, and we forget the ones that conflict with them. Since we want to believe that we are good but unlucky, we are much more likely to remember bad luck than good luck. As I’ve said many times, for every bad beat, there is a good beat. If it’s a bad beat for you, it’s a good beat for the other guy, but you almost never hear good-beat stories.

Let me digress. The Literary Digest conducted a political poll with the largest sample size in history that predicted that Alf Landon would win the 1936 presidential election, but he was buried in a landslide.

As I said in Your Best Poker Friend, “The huge sample was worthless because of a systematic sampling error: It used lists of telephone owners, magazine subscribers, and car owners. These people liked Landon. But it was the middle of the Depression, and most people could not afford telephones, magazines, and cars. The poorer people greatly preferred FDR.” (Page 317) The Literary Digest’s owners certainly didn’t mean to “cheat,” but they did, and it made them look foolish.

Bias — whether deliberate or unconscious — caused that online player to select hands that supported his belief that he is good but unlucky. I’m certain that he did not include all of the times that his pocket aces or top pair/top kicker held up, or all of the flush draws that he made, or all of the times that he was the lucky guy who won a monster pot by spiking a two-outer.

When people tell me about their bad luck, I tell them to stop whining unless they can prove that they are unlucky. Then I provide a simple but laborious procedure for assessing their luck. It works best for online players, because they can get hand histories.

1. Get a random or complete sample of your hand histories. If you have played many thousands of hands, start the randomization process by selecting hands played on certain days, such as every second Wednesday. Purists will correctly object that this procedure is not random, but it’s close enough.

2. Take a random sample of these hand histories by selecting every fifth, or 10th, or 100th hand that was played to showdown. Pick a fraction that yields at least 100 hands.

3. For the selected hands, use the odds calculator at CardPlayer.com to compute your equity.

4. Add up your equity.

5. Add up your real results.

6. Compare your results to your equity.

To the best of my knowledge, not one online player has even tried to use this procedure. They say it’s too much work, or they don’t have the time, or it’s not necessary because they know how unlucky they are. In other words, they don’t value the truth about their luck enough to measure it accurately. I can’t do anything else for them, and I won’t even try.

Fortunately, Bill really did want to know the truth. Since he doesn’t play online, we could not get all of his hand histories, but he did have good notes about a number of pots in which he had gone all in. For all of these hands, he took the last four of my recommended steps.

He was astonished to find that he had won slightly more than his equity. Despite his questionable sample, his results directly contradicted his feelings. Even though he had good notes about these hands, he had drawn a conclusion that contradicted his own data.

He then realized how easy it is to believe something that he wanted to believe. More importantly, he stopped feeling so sorry for himself and started playing more confidently and decisively.

If you follow Bill’s example and do the work needed to assess your luck accurately, you almost certainly will find that you are not that unlucky. You may have won a little more or a little less than your EV [expected value], but if your sample is random and large enough, your EV and results will be quite close. The law of averages (aka probability theory) has not been repealed.

If you keep whining about your bad luck, you will play like a weak, scared, passive victim. You will lose, and deserve to lose. If you realize that you’re about as lucky as everyone else, you can play like a confident, decisive winner.

To learn more about yourself and other players, you can buy Dr. Schoonmaker’s books, Your Worst Poker Enemy and Your Best Poker Friend, at CardPlayer.com.