Variance: A Mathematical Explanation of 'Bad Luck' in Poker

Here, poker usually reveals its key characteristic: even the right decisions don't always turn into money in your account. We can have an excellent session by making the right decisions, yet still not profit, and we can make mistakes — and still be ahead over a short distance. In poker, this gap between expectations and reality is called 'variance'. 

In this article, we will discuss: 

• what variance is and why it is inevitable

• how variance is related to the term downswing

• what factors exacerbate or soften the swings of variance

• what to focus on to reduce the impact of variance

And most importantly: we will draw conclusions so variance is seen as an integral part of the game, not something that intimidates and demotivates.

What is poker variance in simple terms

Poker variance is the deviation of actual results from the mathematical expectation. To put it simply: it's the difference between how much we should earn on average given our level of play, and how much we actually earn over a specific stretch.

A simple example to illustrate the mechanics

Imagine the situation: we regularly go all-in* with a 60% advantage. According to EV*, this is a good scenario: over a large sample, we should win more than we lose. But over a short stretch — for example, 20 all-ins — we might:

• win 16 out of 20 — a result above EV

• win 12 out of 20 — approximately at EV

• win 8 out of 20 — a result below EV

All these scenarios are statistically possible; they just have different probabilities. 

* EV (Expected Value) — is the mathematical estimation of the expected profitability or loss of a specific action or decision in a particular game situation.

* All-in in poker — is when two or more players put all their chips in the pot and reveal their cards. 

It's important to immediately note a few key points.

Firstly, variance works both ways. It can manifest as negative deviations — prolonged losing streaks — or as positive ones — where results are temporarily better than we deserve. 

Secondly, variance tells us nothing about the quality of decisions in the short term. We can play correctly and lose, and we can play with errors and win. This is not a contradiction but a direct consequence of the game's probabilistic nature.

And thirdly, variance is a fundamental property of the game, without which poker could not exist and bring income to professional players. If you imagine poker without variance, the outcome of each decision would be predetermined — like in chess.  Stronger players would consistently and quickly take money from weaker ones with no variances. In such an environment, amateurs would have no chance of success, no hope of winning, and no motivation to return to the table. The poker economy would simply stop.

Therefore, a correct conclusion sounds like this: variance is not always pleasant, but it is necessary. It is what makes the existence of the game possible, attracts amateurs, and ensures the long-term profitability of strong players.

How variance can affect your expectations from the game

The main issue for beginners and even many experienced players is not variance itself, but the inability to accept this factor as part of the game and profession. 

We tend to think: “If I play correctly, then the results should be stable.” In practice, this is not the case — especially in tournament poker. Even with a positive ROI, long stretches can occur where the result is zero or negative. 

To make this clearer, it's helpful to look at probabilistic ranges of results over a distance, rather than individual sessions. 

In the poker world, there are variance calculators that help players take a more adequate view of potential career scenarios. 

Let's look at a situation with a concrete example. 

The first line is Number of players: here we enter the total number of participants who took part in the tournament. Usually, this is the average number of participants in tournaments across all formats in which we participate. Let’s specify in this cell the value — 1500 people. 

Just below — Places paid. This is the number of prizes paid out to players in the tournament. Normally, this value ranges from 16 to 20%. Let's pick 18% — somewhere in the middle. 

The payout structure can be found in the lobby by dividing the number of prize places by the total number of entries.

Next — Buy-in: the cost of entry into the tournament. Note that the buy-in is specified separately from the rake. The exact rake amount can be found in the tournament lobby — as well as the buy-in. Let’s assume, for tournaments with a buy-in of 5.50, we specify 5 in this line, and in the rake line — 0.5.

The next item is — ROI. This reflects the profitability of play: how much money you expect to receive from each dollar you invest in the game. On average, a good ROI for micro limits would be around 20%. Naturally, some will show better profitability, some worse, but let’s take 20% as an example.

Further below we specify the distance (Numbers) we want to calculate. Let's try to estimate what happens to us over a year's distance. We'll act based on the playtime of FunFarm players — an average of 400 tournaments per month. We enter 4800 tournaments in this line. 

Just below we specify the sample size, meaning the number of times the calculator should simulate these tournaments to give a final result. The more, the better. Let's do 20,000 simulations. 

Click Calculate — and see the result below.

Here is a distribution chart, showing results on the X-axis, and probabilities on the Y-axis. 

We see that most scenarios are above zero, but in one case we end the year in the negative, i.e., most likely we will earn about $5,000 on average for the year, in the best case — about $25,000, and in the worst case — about -$5,000. 

How to reduce the impact of variance practically

When we talk about variance, we usually describe a statistical phenomenon — the result deviates from the expectation. 

But in actual play, variance is felt not as a formula, but as a downswing — a period when the final results are consistently worse than we are used to seeing or than our EV suggests.

A downswing is a stretch during which we record a series of weak results: losing sessions, no deep runs, frequent knockouts, a prolonged plateau without noticeable profit.

It is important to understand the connection between terms: variance is the statistical spread of results around expectation, downswing is the practical manifestation of this spread negatively over a specific stretch.

At the same time, a downswing is not always pure variance. It can consist of two components: bad luck and normal fluctuations and/or a decline in the quality of play — fatigue, tilt, mistakes, poor tournament selection, misaligning limits with skill level. 

If we want to reduce the impact of variance, our goal is to build a system that helps us withstand any normal fluctuations, prevents game deterioration from exacerbating the downswing, and maintains EV and bankroll. Below are practical measures that address this.

1. Improve the quality of play

The higher our actual ROI, the narrower the range of possible negative deviations. Even a small improvement in expectation significantly reduces the likelihood of deep and prolonged negative periods.

Let’s take the scenarios from the previous block, but instead of a 20 ROI, put a 30 ROI.

As we can see, the average expectation has risen above $5,000, more scenarios are in the range between $5,000 and $25,000, and the worst of them is closer to $0.

The takeaway: what matters most is not what result your actions lead to, but how correct they are. 

2. Adjust expectations

The first step is not motivational but managerial: we acknowledge in advance that long negative stretches are possible even with a positive ROI in tournament poker.

Why is this critical? 

• if we expect stable and 'fair' growth, any loss is perceived as a signal for alarm

• if we anticipate the possibility of a downswing, negative periods become a reason to check game processes rather than react emotionally

The practical sense of acceptance is not to resign but to avoid making decisions emotionally — not to change strategy chaotically, not to jump limits, not to increase volume in an attempt to beat variance.  

3. Differentiate between variance and poor play

This is the central diagnostic block. A downswing is dangerous not in itself, but in how we often begin to play more cautiously and lose EV, attempt to recover, change tournament grids to more risky ones and thereby fall in our quality of play and emotional resilience. 

We need a sober assessment. What do we check first?

Signs that it's variance: 

• it feels like we are playing as usual, without declining discipline

• decisions on standard spots remain the same

• the problems are mainly in execution: all-ins, coolers, lack of hits.

Signs that it's a drop in play: 

• we're more often playing tired, extending sessions

• the number of impulsive decisions has increased

• there's a desire to recover or not to lose

The best format at this stage is to review the database alone or with a coach. It’s crucial to see where we lost EV in typical lines, whether ranges have changed, if post-flop quality has fallen and late stages have degraded, or if our tournament selection has worsened.

4. Reorganise the tournament grid

The same strategy can yield very different ROIs in different pools and structures. Therefore, a downswing sometimes intensifies not due to hands, but because we are playing too many hypers/turbos, load big fields without balancing them with stable tournaments, and play what's in the lobby rather than what offers EV.

If the goal is to reduce variance impact, we make the grid more manageable: more tournaments with adequate structure and more attention to compositions and field quality.

This does not mean avoiding variance at all costs. It means controlling its level so it matches bankroll and psychology.

5. Establish a financial cushion and maintain responsible bankroll management 

Without financial control, in a downswing, one of two states almost inevitably emerges: too high risk (playing more expensive than necessary) or too low quality (tilt, panic, forced play). 

Thus, the system looks like this:

• we determine conservative bankroll boundaries in advance

• we separate playing money from living money

• we regularly lock in part of large results, so we don’t plan on the next big hit

If we professionally play MTTs, a financial cushion outside the bankroll — living expenses for several months — is not a luxury, but a risk reduction for errors in the most vulnerable period.

6. Reduce ABI, not increase it

This is one of the most practical ways to ease the impact of variance. The logic is simple: reducing ABI increases our expectation relative to the field, ROI rises, variance becomes more bearable, and returning to expectation is easier.

The typical mistake is trying to play more expensively to earn more. In practice, this often worsens the situation: the field is stronger, our ROI lower, variance higher, and the cost of errors more expensive.

If we want a stable exit from a downswing, we choose the path that increases the likelihood of EV recovery, not the path that increases bets on randomness.

7. Work with mental state 

A downswing almost always pressures decision quality. Even if we don’t notice tilt, it can manifest through:

• reduced courage in challenging spots

• relinquishing profitable aggression

• using strategies on autopilot

• desire to end the session quickly 

If we feel emotions starting to alter play style, working with a mental coach or a systematic mental routine is a necessity. 

For advice on dealing psychologically with a downswing, we wrote this article. 

8. Balance between play and study 

In a downswing, two common extremes are equally harmful. 

The first extreme is “outplay the stretch”. We dramatically increase volume, play without days off, tire, and quality declines. ROI decreases — variance becomes even tougher.

The second extreme is “stop playing until figured out”. We learn but don’t cover distance. In tournament poker, distance is part of the work: without it, we don’t return to expected result distribution.

The working strategy is to maintain a routine that simultaneously allows for covering distance, preserving quality and giving time for review and correction of errors.

9. Ensure resilience through additional income

This practical point is often overlooked, but it directly affects play quality. If we lack financial resources, stress begins to control decisions. 

In such a situation, it’s rational to reduce workload, temporarily strengthen stable income sources and remove the feeling that “we must win right now.” 

For players with the right level, coaching is often a viable option: it reduces financial pressure and simultaneously strengthens strategy by repetition and structuring of material.

Conclusion

If we want stable development in poker, we must separate results from the quality of decisions and understand that in tournament poker rare large results create long stretches without visible successes — even with a good ROI. 

Join our team to conquer variance, accept it as part of the game and learn to track your strengths and weaknesses as a player.