When and How To Check Results

Dec 20

PREREQUISITE READING: SELECTION BIAS IN VARIANCE CALCULATIONS

In Phil Galfond's excellent article, Poker and Your Life, he writes about the skills that he thinks make a great poker player. I think most good poker blogs try to tackle this question at one point or another. Phil starts with a few hard skills: deductive logic, psychology, and math/statistics. I tend to agree with him on all these points. But then he goes on to list three additional soft skills:

There are also three minor categories, which are less about predicting poker aptitude and potential, and more about predicting how likely you are to reach and use that potential:

Competitive Drive (especially with oneself)
Humility and Self-Awareness
Self Control

Again, I agree that all of these qualities are very important, but I think he left the number one soft skill off the list. Maybe it just slipped his mind, or maybe it didn't occur to him because he's naturally such a beast at it. Whatever the case, here's my vote for the most important soft skill in poker: risk tolerance.

If you're going to play poker for a living, then you're going to swing like crazy—it's inevitable. If you want to become great at poker and sustain your level of skill, you have to have the stomach to deal with those swings without letting them drastically affect the quality of your play or your mental health. You have to be able to show up every day and play well, even when the shit hits the fan and you know that things can always get worse before they get better.

I believe risk tolerance is more or less an innate quality. It is probably genetic for the most part, but it also could be impacted by events in your childhood. I would rate myself pretty low on the risk-tolerance scale, which is actually the main reason why I write these articles. The only way I have been able to manage this weakness is by developing a better mathematical understanding of variance.

Variance is a gift and a curse. On one hand, if there was no variance in poker, then nobody would play it for fun and almost none of us would be able to make any money doing it [1]. On the other hand, variance makes it so that you have basically zero control over whats going to happen at the tables on any given day.

For example, even a player with a respectable win rate of 5 bb/100 still has a 44% chance of losing over a sample of 1,000 hands (at a standard deviation of 115 bb/100). And the probability of a loss goes down at a stubbornly slow rate even over much larger samples. Below, I've plotted the normal distribution (also known as a bell curve) of this variance calculation:

The y axis is the probability density. The x axis is the winnings in buy ins (100 bb). Without getting too technical, we can say that the higher up on the bell curve you are, the more likely it is that the result of the 1,000 hand sample will equal the value in buy ins at that point on the X axis.

The mean of the distribution (the highest point on the curve which is marked with the green line) is 0.5 buy ins. This is the expected value of the sample, which is just the product of the volume and the win rate. (5 bb/100 * 1,000 hands = 50 bb, or 0.5 buy ins). The red shaded area is the area under the curve to the left of zero on the x axis. This accounts for about 44% of the total area under the curve and represents the probability of a loss over the sample.

As you can see, the expected value of 0.5 buy ins is hardly noticeable in the context of the range of possible outcomes. In fact, you can actually expect a result of at least ±5 buy ins approximately 20% of the time.

And yet, despite the obvious contradictions, many players, including myself, are terribly results oriented. A winning day is a good day; a losing day is a bad day. On a big winning day, we congratulate ourselves for making the right decisions; on a big losing day, we blame ourselves for making mistakes. We're only human, and unfortunately this is how our monkey brains work.

I've been a full-time poker player for about a year now. Initially I thought that as I played more hands and gained experience, I would get better at managing my results orientation. Actually, I don't think I have gotten any better at all. In fact, I may have actually gotten worse.

To be completely honest, I thought I would have less fucks to give with a quarter million hands and a year of winning under my belt, but sometimes it feels like I have a shorter fuse than when I started. It's not so much the higher stakes the has made coping with downswings more challenging, but that my identity has gotten wrapped up in being a winning poker player. Of course losing money still bothers me, but at this point it's more of a hit to my ego than to my bank account [2].

A quarter million hands is barely anything in the grand scheme of things, but it's the trajectory that bothers me. I should be getting better at handling the swings, not worse, right? For that reason, I'm making an effort to change the way I look at my results. Rather than check results haphazardly whenever I feel like it, I want to take a smarter, more disciplined approach. So I've made it my goal for 2020 to follow the guidelines below.

Guide For Checking Results

To manage results orientation, it's extremely important to check your results after a predetermined number of hands. This is crucial to avoid selection bias in your interpretation of the results. The number of hands you choose is totally up to you, but it shouldn't be lower than 10k hands for an online player. I think most online players would probably agree it should be somewhere in the range of 10-50k hands.

Now, I'm not saying you absolutely cannot check your results before that time comes. You and I both know we're going to do it, no matter what I say in this blog post. (In fact, it's actually essential to closely keep track of your losses if you're taking shots at higher stakes.) What I am saying is that if you check your results prematurely, you should do so with an understanding that you are merely indulging your curiosity.

There's a big difference between glancing at your results at the end of the day, and seriously evaluating those results, giving them a kind of legitimacy and causing yourself to worry about them. When you check your results after a few thousand hands, the data you are looking at is meaningless, and you should make an effort not to draw conclusions from it or let it influence your strategy or sense of self worth [3].

For example, let's say you choose to check your results every 30,000 hands. Your current volume goal is to play 7,500 hands per week, so you'll check results every four weeks. You can mark it on your calendar, "Results Day."

When Results Day comes, you'll be able to put your results into perspective with variance calculations. The variance calculations give you an estimate for your probability of a loss. They will also give you confidence intervals to establish some upper and lower thresholds for how large of a range of outcomes you can realistically expect to see over the sample.

Essentially, all you want to do is compare your results to the variance calculations and see if the outcome lies within a couple standard deviations of your expected value (that would be a 95% confidence interval). If it is—and it will be the vast majority of the time—that's great. Keep playing, keep working hard on your game, and come back to check again in another 30,000 hands.

If you actually are experiencing a two-standard deviation downswing or worse, then go ahead, freak out. Take some time off, talk to someone, go to therapy, maybe drink heavily. Whatever it takes to say, "Well, that was fucked up, but I'm ready to get back to playing."

Whatever you do, it's essential at the end of the review to reset the part of your brain that subjectively interprets the results and attempts to create a narrative about how you've been running. You have to let go, because the next 30,000-hand sample has nothing to do with the previous one, or the one before that.

Things can always get worse, no matter how bad they have gone; and things can always get better no matter how well they have gone. You're not due for anything in particular to happen. Your expected value is the mostly likely outcome, but nothing is deserved.

The key point I am trying to get across is this: whether your results are positive, break even, or negative, they probably mean much less than you think they do, even over relatively large samples.

Almost always, the correct course of action is simply to keep doing what you have been doing and play more hands. But an obvious follow up question that I need to address is, "How long do I have to lose or break even before I actually decide to change my game plan in some way?"

Unfortunately, I can't give you an answer to this question. It can always "just be variance," no matter how bad your results are. All you can say is, the more money you lose, or the longer you break even, the smaller the odds become that it's just variance relative to the odds that you have overestimated your win rate in the variance calculations.

In the end, it doesn't really matter, because as soon as you start to doubt whether you are truly a winner in your games, you're already dead in the water. Once you start to expect to lose, it becomes a self-fulfilling prophecy because you will actually play worse.

Dropping down in stakes or moving to a different site temporarily can help you refresh your mindset and rebuild confidence, and it also diversifies your game selection to protect your bankroll from ruin in the case that you are actually -EV in your games.

If you like this strategy and want to use it to check your results, I've included a summary of variance calculations over a variety of sample sizes below to help you visualize variance in the short and medium term. I used a win rate of 7.5 bb/100 and a standard deviation of 115 bb/100 for these calculations [4]. If your win rate and/or standard deviation is significantly different from the ones I have used, feel free to make your own versions.

Variance Calculation Inputs

Variance Calculation Results (Table)

Variance Calculation Results (Graphs)

Footnotes

By the way, if you think you're super sick poker player and you don't need fish at your table to make money, read this article. If fish didn't exist, there would probably be less than 100 people making any real money playing poker.
Jungleman discusses ego and tilt in his interview with Elliot Roe on the Mindset Advantage Podcast.
If you have a problem with checking your results way too much, as in multiple times per day, then you can make it more difficult to check results by hiding stats in your tracking software. I've even heard of some players using custom scripts to hide the cashier in the poker client. But unless you're really hardcore, you're probably going to take a peek from time to time. And that's not really a bad thing as long as you are able to manage your expectations.
An interesting side note: a win rate increase from 5 bb/100 to 7.5 bb/100 is a 50% increase in expected value. However, over a sample of 1,000 hands, the probability of booking a win for a 5 bb/100 winner is 56%, and for a 7.5 bb/100 winner it is just 58%. This is why you can work very hard and get a lot better at poker, but it's extremely difficult to actually see the edge that you have gained from a day-to-day perspective.

Resources

Variance Calculator: https://www.primedope.com/poker-variance-calculator/
Normal Distribution App: https://homepage.divms.uiowa.edu/~mbognar/applets/normal.htm

Patrick Howard