Variance: Beyond the Surface
Variance is one of those words people throw around as if they fully understand it and its implications.
In actuality, it’s a confusing and abstract concept.
Today, I want to share the three most common misunderstandings relating to variance among poker players (who understand it much better than the rest of the world!).
Unintuitive Results
The human mind isn’t built to handle variance well.
We evolved to learn from our actions.
A caveman only needs to put his hand in a fire one time to learn never to do it again. That’s a fast education!
We take an action, we get a result, and we calibrate our actions based on that.
Imagine if that caveman had two options:
Put his hand in a fire.
Put his hand in cool water.
But instead of things working the way they would in the real world, the fire burns him 70% of the time, and the cool water burns him 30% of the time.
It’s going to be a lot harder to learn which the better option is.
Definition
In poker, people tend to equate variance with bad luck and downswings:
“I’ve been dealing with some variance lately.”
That’s not what it really means.
Variance is a statistical measure that represents the degree of spread in a set of data points.
It quantifies how much the numbers in a dataset vary or differ from the average (mean) value of the dataset.
In simpler terms, it addresses the question:
How much might my results differ from the average result?
You don’t need to understand how to calculate variance, or that the standard deviation in a data set is the square root of the variance.
But you do need to understand its impact on results.
In poker, you have your expected result (expected value, expected winrate), and variance.
The higher the variance, the more likely it is that your actual results will differ from your expected results.
Let’s get into the misunderstandings, starting with the least misunderstood.
#3: It Can Really Get That Bad (and Worse!)
Most everyone underestimates variance.
When I was just starting in poker, I remember reading the words of a successful player that really stuck with me:
“If you play poker long enough, you’ll eventually run worse than you ever thought possible.”
I’ve seen it happen to myself, and to countless other players. The losses somehow keep piling up in spite of it seeming astronomically unlikely.
In your local $1/$3 NL cash game, with a winrate of 5 big blinds per 100 hands, what do you think the odds are that you’d win over one year of playing?
Well, at 30 hands/hr, and 16 hours of play per week, you’d play about 25,000 hands in a year.
The chances of losing over that year are something in the neighborhood of 13%*.
*These calculations were done with Primedope's free variance calculator.
Play better than your opponents for an entire year, and you still have a thirteen percent chance of losing!
What if you play for three years? Surely by that time, the long run will have hit, right?
Well, sort of.
Now it’s only 2.5% likely that you’ll be losing after that three-year stretch.
That’s still one out of forty players!
And what’s worse is that in a sense, every time you play, you’re starting the clock over.
Over the course of 10 years, there are countless opportunities to start a 3-year downswing. You might fade the first 2.5% by winning a lot in year one, only to lose over years two through four.
I know what some of you are thinking:
“OMG. That’s what happened to me!”
This brings me to the next misunderstanding…
#2: Variance Works in Both Directions
If bad runs can go on longer than we think… Guess what?
Good runs can too.
How many of you thought, “OMG. I’ve been winning for three years without studying. I must be running hot!”?
How often have you felt like you were running above expectation for a long time?
Many people don’t ever feel this, because they think they deserve to win. It’s easy for your mind and ego to construct a story around you winning:
“I’m playing great.”
“I knew I was a genius.”
“I studied preflop charts for 30 minutes.”
And it’s just as easy to construct a story around losing:
“I’ve been so unlucky.”
“My opponents always hit their stupid draws when I have a big hand.”
“If I didn’t get my aces cracked three times, I’d be winning this month.”
Even for more advanced players who know otherwise, it’s easy to think that variance only happens in one direction.
This leads players of all skill levels to overestimate their winrates and abilities. It makes them play in games they shouldn’t and experience even more “variance”.
So, what can you do about it?
How can you reduce variance?
This brings me to the most common misconception of all:
#1: Variance Reduction
“I know I should 3-bet 10% of hands here, but I feel better 3-betting just my premiums to reduce variance.”
“I could bluff here, but I don’t know if it’ll work. Giving up is lower variance.”
“I’m probably ahead, but many rivers will be tough to play, so I’ll just fold to reduce variance.”
Let’s go back to our example – a 5bb/100 winrate over one year of play – and see what impact reducing our variance would have.
If we play a variance reduction style, we might take the standard deviation from 70bb to 50bb/100.
Now, instead of losing 13% of the time, we lose only 5.7% of the time. Cut it in half!
Not bad, right?
Here’s the problem:
When you take alternate betting lines instead of the “right” ones in order to reduce variance, you are, by definition, playing worse.
You’re passing up on spots where you could win money on average because they are riskier.
You become much easier to play against, which, if players notice, is going to hurt your winrate even more.
What happens in practice is that your 5bb winrate may get reduced to 2bb/100.
And now, with a 2bb/100 winrate and the “lower variance” of 50bb/100 standard deviation, you’ll lose after one year 26.4% of the time.
You doubled the chances of losing!
What Does This Mean?
Does playing a tighter, more passive, nitty style reduce variance?
Yes.
But reducing variance doesn’t mean reducing the chance of downswings.
Usually, it means increasing it!
You see, if you play around with a variance calculator for thirty minutes, you’ll figure out that “swings” depend on exactly one thing:
The ratio of your winrate to your standard deviation.
Let’s say instead, we keep the standard deviation at 70bb and we double our winrate to 10bb/100.
Now, after one year, we lose only 1.2% of the time.
From 13% to 1.2%!
If your goal is to reduce your swings, you don’t need to reduce your variance. You need to get better at poker.
And your winrate has importance that goes far beyond your swings…
Even if we took the standard deviation down far enough to make you only lose 1.2% of the time with a 2bb/100 winrate (which isn’t realistically possible), your average outcome on the year would be +$3,000.
With the 10bb/100 winrate, your average outcome would be +$15,000.
The Bottom Line
Are there scenarios where changing your strategy to reduce variance makes sense?
In theory, probably some.
Should you ever do it?
I’d argue, no.
Your winrate is everything.
A sacrifice of your winrate to the gods of variance is unlikely to be worth the cost.
If this post scared you, good.
Take that fear and do something positive with it.
Don’t leave your fate up to luck.
Study, hire a coach, run variance simulations, work on your game.
Don’t be one of the many people reading this right now who give in to their delusions.
Delusions that they’re unlucky.
That they know “enough” about the game.
That they’ve won for a few months because they’ve figured it out.
Not one great poker player has ever learned enough that they couldn’t still improve.
Variance is scary.
And fear is a terrible thing to waste.
