Stop Comparing Your Results to Others’
One of the most surprising things about my experience as a poker coach is how poorly understood the power of variance is by the average poker player.
As I’ve progressed in my career, I have transitioned from coaching mostly low-stakes players to coaching almost exclusively high-stakes and nosebleed players. And yet, shockingly, most of the elite poker players I coach now do not seem to have a much better understanding of variance than my former students did.
On a weekly basis, I still get questions from students like these…
“I’ve been breakeven over my last 100,000 hands. Can you check to see if I’m doing something wrong?”
“My win rate was 7 bb/100 last year, but it’s only 2 bb/100 this year. Can you tell me what changed?”
“I’m only winning at 5 bb/100, but I’ve noticed a few of your students are winning at 8 bb/100. Can you say what they are doing that I’m not doing?”
We all know that comparing yourself to others is usually misguided in a philosophical sense, but poker is rather unique in that comparing yourself to others is generally just mathematically wrong. Furthermore, it is wrong to compare your current results to your past results. The reason, of course, is variance.
Imagine you are in a study group of five players. You are all equally skilled and play on the same sites, and you each have an identical expected value of 3 bb/100 in your games. You each play 300,000 hands per year, so the group as a whole plays 1.5 million hands annually.
In reality, it is unlikely that all five players will end up with a win rate of 3 bb/100 at the year’s end. Some players will have higher win rates, and some will have lower win rates. This is to be expected, and yet when it actually happens, most study groups attribute this disparity to differences in skill, not luck.
Study groups tend to overvalue the opinion of the player in the group with the highest win rate, and ignore the player with the lowest win rate. To show how misguided this is, let’s do a quick variance calculation using the Primedope Variance Calculator:
Variance calculation for a 3 bb/100 winner over a sample of 300k hands.
As you can see, the probability of a loss for a 3 bb/100 winner over a sample size of 300k hands is approximately 7.65%. And the probability of this player’s win rate being less than 0 bb/100 or greater than 6 bb/100 is double that value, or approximately 15.3%.
Therefore, the probability that one of the five players in the study group has that result is…
1 - (1-0.153)^5 = 0.564
In other words, there is a 56.4% chance that one of the players in this group will either lose money on the year or perform at more than double his expected value!
But try to imagine how you’d respond if you had been in a study group for a year, played 1.5 million hands collectively, and, during a hand review, the player with the worst win rate in the group starts arguing with the player with the best win rate in the group.
When the winningest player speaks, you’ll probably be hanging on his every word, trying to glean whatever special information endowed him with such spectacular results. On the other hand, when the player with the worst win rate speaks, you won’t say it to his face, but what you’re probably thinking is, “Why is this guy even talking?”
Keep in mind, the example I gave was only for five players. Expand that to a group of one hundred players, and the variance calculations become even more shocking.
In my time as head coach of Poker Detox CFP, I was coaching up to 100 students simultaneously. I did extensive database reviews for many of these students to help them find their leaks*. Let me tell you, when you review dozens or even hundreds of players’ databases, you start to see some really weird shit, even over huge samples.
Most database reviews went as expected. The players with the highest win rates generally made very few mistakes. The players with the lowest win rates made a lot of mistakes. But sometimes I’d come across a player whose results were great, despite him playing rather poorly. And I’d also find players who were losing, despite playing very solid.
When I told these players the truth, that they were just very running well, or running very poorly, they didn’t want to hear it. When faced with extreme variance, people will usually try to explain the results with something they did. People have an incredibly hard time just accepting that they got extremely lucky or unlucky, especially over long periods of time.
The strangest thing I ever saw was when one of my students won at a high-single-digit win rate over several hundred thousand hands in a very tough pool. It wasn’t just how much he won that was strange, it was how he did it. The student never incurred a downswing of larger than about ten buy-ins over his entire sample. His graph was essentially a straight line up and to the right.
If you want to fully appreciate how weird this is, check out this article to learn about expected downswings. Even if this student’s win rate was actually that high, we would expect his average maximum downswing to be 30-40 buy ins over a sample of this size. And we would also expect him to have tons of downswings smaller than this, but still greater than ten buy ins. He never had one.
When I reviewed his database, I found he was playing well, but far from perfectly. Unfortunately, this student eventually went on a fairly large downswing, and needless to say it wasn’t easy for him to accept it after the sun-running for so long.
It’s difficult for the average person to fully appreciate the concept of variance because the average person, by definition, has never experienced extreme variance. The people who’ve experienced top 1% good or bad luck really are living in a different universe from everyone else.
And it gets worse. Remember, the examples I gave in this article were for cash games. In tournaments, variance is even more powerful.
The purpose of this article is not to say that poker is “all luck.” It is just to say that luck plays a larger role than most professional poker players expect, especially over large sample sizes.
Consider this next time you compare your results to others’, or to your own past results. It is usually better to not pay much attention to your results. Instead, focus on the quality of your decision-making process, and to simply try to improve it a little bit each day.
