Poker Variance: Understanding the Swings

Professional US poker players call the game “a hard way to make an easy living” for a reason: income rarely runs in a straight line. Even with elite skill and years of experience, pros can leave the table down money after a well-played session.

The gap between good decisions and short-term outcomes creates the sharp rises and sudden drops that define poker’s financial reality. Those inevitable swings, wins, and losses that don’t reflect true ability are what players mean by variance over time.

What is Poker Variance?

In poker, variance is the statistical lens that shows how far your short-term results drift from your long-run average — the math behind every upswing, downswing, and brutal in-between stretch. Statistically, it measures how widely individual outcomes spread around the mean.

Here’s a quick calculation using a small sample. Imagine you log seven sessions in a $1/$2 no-limit hold ’em game:
–11, +85, –30, +144, +9, +30, –87.

Add them up, and you’re ahead +140 overall. Divide by seven sessions, and your average result is +20.

Variance starts by measuring each session’s distance from that average. The first result, –11, sits 31 below the mean (20 – (–11) = 31). Squared, that becomes 961. Do the same for the rest, and you get:
961, 4225, 2500, 15376, 121, 100, 11449.

Sum those squared gaps:
961 + 4225 + 2500 + 15376 + 121 + 100 + 11449 = 34,732.

Divide by seven to find variance:
34,732 / 7 = 4,961.71.

The standard deviation — another key volatility marker — is the square root of variance:
√4,961.71 ≈ 70.43.

In plain terms, most sessions should land within about $70 of your average. With a mean of +20, the “typical” range here runs roughly from 50 to +90. Some results will sit well outside that band. Those big wins or gut-punch losses are outliers, and they’re normal in small samples. Over a much larger set of sessions, the luck component fades, the spread stabilizes, and your real win rate comes into focus.

Variance and the Central Limit Theorem

Another important mathematical concept that comes with sample size is the “Central Limit Theorem”. This concept states that, as the number of data points in a set grows, a plot of those points on a graph will resemble a normal statistical distribution, as seen in the classic “Bell Curve”.

The guiding principle is that, the larger the sample size, the more data points that will fall at or near the average. This measure of variance gives the player a more accurate idea as to what to expect from his results.

Variance and Luck

Even in the most distinguished poker careers, a player will have sessions where he has wins (or losses) that go two or more standard deviations away from the average. Many inexperienced players attribute these results to luck, but they are within the realm of possibility shown in the Bell Curve.

These data points are known as “outliers” and, individually, have little effect on the variance seen over a career. If these “outlying” results continue to appear, however, they may signal the start of a new trend.

Variance and Bankrolls

A sufficient poker bankroll is necessary to act as a cushion against variance. Some players may believe that, with just a few positive results at a $1/$2 no-limit hold’em game, they are ready to jump into a $2/$5 or $5/$10 game, regardless of their bankroll size. When the variance swings in the negative direction, as it inevitably will, a depleted bankroll could send the player to either a lower-stakes game or out of the game entirely.

Variance and Structure

Some poker variants naturally produce bigger ups and downs than others. A fixed-limit Razz game, for example, tends to have far less variance than a $1/$2 no-limit hold ’em game, mainly because of how the betting structures work. In Razz, wager sizes are capped on every street, so pots can’t balloon out of control, and the swings stay relatively small. In no-limit hold ’em, players can shove their whole stack whenever they want, which creates much larger pots and, as a result, much wider fluctuations in outcomes.

Variance in Poker Tournaments

Even with all the hype and spotlight that televised no-limit hold’em tournaments bring, they’re still a clear reminder of how harsh variance can be. In MTTs, even the best players on earth can hit downswings that last for months. How wild those swings get depends a lot on the size of the field, how big your edge is, and whether you’re choosing games where that edge actually shows up.

Tournament structure is a big part of the chaos. As blinds and antes rise, you’re forced to open up your range, take thinner spots, and risk your stack more often just to stay alive. You also end up bluffing at higher frequencies.

All of that pushes variance way higher than in cash games, where stacks are deeper, situations are less urgent, and you’re rarely putting your whole session on the line in one hand.

However, volatility hasn’t chased pros away. These days, plenty of professionals focus primarily on tournaments, leaning on staking deals, solver work, and data-heavy study to stay afloat and let their skill shine across large samples, even when the short-term results get rough.

Variance and Playing Styles

In a previous piece, we examined the four primary playing styles (loose-passive, loose-aggressive, tight-passive and tight-aggressive). Just as the tight-aggressive style has been shown to be the most profitable, it also often results in the lowest variance.

Both the loose-passive and the tight-passive players depend on catching cards to win hands (a high-variance strategy) while the loose-aggressive style relies on big bets to push players off hands.

The tight-aggressive method relies on strong starting hand selection, infrequent bluffs, and a well-founded understanding of probabilities, all of which contribute to reducing variance.

Variance and Emotion

The effects of big wins and staggering losses are not strictly limited to a player’s bankroll. The emotional roller coaster that comes with big swings in variance can also affect how a player approaches the game.

Players who have become accustomed to big wins may lose their cool when confronted with a crushing loss. One bad session can set a player “on tilt,” wrecking both his skills and his confidence.

How to Deal with Variance

Shifts in variance can be as unpredictable and dangerous as shifts in the weather: everybody complains about them, but no one can do anything to prevent it. The most important aspect of success in poker lies in treating each session or tournament as a continuation of one long game.

Experienced players understand that their success or failure as a player does not lie in the results of a single tournament or a handful of cash-game sessions. Each session represents only a single data point: a consistent approach will often reduce (but never eliminate) variance.

Conclusion

Former World Series of Poker Main Event Champion Chris “Jesus” Ferguson once said that poker is “100 percent luck and 100 percent skill”. The turn of each card is the result of luck, but how a player responds to that unpredictable event is the product of skill, practice, and experience.

The ability to manage the game’s inherent variance is a skill on par with calculating odds and outs in terms of how successful a player can eventually become.