Variance is a bitch

I'm just about to start the analysis of my 2nd 10k hands at 10NL Rush but before I get to that I wanted to talk a bit about variance. This will be of particular interest to beginner players who are struggling with the ups-and-downs of poker, especially if you're a low volume player like myself.

What is variance?
If you're not familiar with the concept, variance is actually a fairly complex mathematical concept that, in layperson's terms, essentially refers to divergence from the statistical average. The simplest way to explain it is to use coin-flipping as an example. We know that each flip of a coin has a 50% chance of coming up heads but we also know that if we flip a coin 10 times, we will get a range of results. Each group of 10 flips won't result in a 50/50 heads/tails split. That range of results is the variance that occurs in a small sample. Over a large enough sample, however, the range of results would narrow towards 50%.

Since poker is a game of probability, just like coin-flipping, variance is a natural part of the game. We know that pocket Aces have an 80% chance of winning against any random hand, but we also know that we will sometimes go through bad runs where we get it all in with AA and lose more often than we should. For the developing poker player there are two aspects of variance in poker that are very important to understand: (1) the simple fact that variance is a part of the game; and (2) you actually need a very large sample of hands to reduce the impact of variance and actually get a clear picture of your ability as a poker player. Understanding this can help you stay calm and avoid frustration and tilt on your poker journey.

An Illustration
To illustrate the phenomenon of variance, I'm going to show you a series of graphs from my 20k hands at 10NL Rush.

The first graph is from my first ~5000 hands:

Not surprisingly, I was getting a bit frustrated and discouraged over my first 5000 hands. I thought to myself, 5000 hands seems like a lot and I'm barely a winning player. Maybe I suck at poker. But I kept at it.

Another 5000 hands later:

Not much better overall. I went on a bit of a nice run but then dropped back and ended up only slightly ahead of where I was at 5000 hands. Am I destined to be a mediocre poker player?

Another 5000 hands:

Okay, making a bit of progress but still...not a whole lot of return on my time investment. I've played 15,000 hands and I'm still only marginally profitable, running at just over 1BB/100 hands. Maybe I should quit.

But then look what happens: