---
title: "Variance in Poker, Explained"
url: "https://georgelipoker.com/mental-game/variance-explained.md"
canonical_url: "https://georgelipoker.com/mental-game/variance-explained"
last_updated: "2026-10-22"
type: "guide"
summary: "Variance is how far short-run outcomes move around the long-run average, shown here with exact losing-run odds."
related: ["https://georgelipoker.com/mental-game.md", "https://georgelipoker.com/mental-game/downswings-and-decisions.md", "https://georgelipoker.com/mental-game/bankroll-stress.md", "https://georgelipoker.com/mental-game/tilt-after-a-bad-beat.md", "https://georgelipoker.com/tools/equity-calculator.md", "https://georgelipoker.com/tools/pot-odds-calculator.md"]
---

# Variance in Poker, Explained

Variance is how far short-run outcomes move around the long-run average, shown here with exact losing-run odds.

Variance is the spread of short-run outcomes around what the math expects. At a win chance of 50 percent per trial, a losing run of 8 in a row shows up somewhere in 100 trials 17.02% of the time, with no mistake involved.

## What are expected value and variance?

Expected value is the average outcome over many trials. Variance is how far a short run strays from that average. Standard deviation is the usual way to measure the stray. A decision with positive expected value can lose several times in a row without anything being wrong, because the average only appears over many trials.

## How likely is a losing run?

Take each trial as independent, with a fixed win chance. A losing run of k in a row is not rare once the number of trials is large. A trial can stand for a session, a tournament or an all-in. The tables are exact, computed by dynamic programming over the trial on which each run ends, with no simulation.

Chance of at least one losing run, win chance 40 percent per trial:

| Trials | Run of 5 | Run of 8 | Run of 12 |
| --- | --- | --- | --- |
| 100 | 97.58% | 48.97% | 7.65% |
| 500 | more than 99.9999% | 97.06% | 35.06% |
| 1000 | more than 99.9999% | 99.92% | 58.19% |

Chance of at least one losing run, win chance 50 percent per trial:

| Trials | Run of 5 | Run of 8 | Run of 12 |
| --- | --- | --- | --- |
| 100 | 81.01% | 17.02% | 1.09% |
| 500 | 99.98% | 62.51% | 5.81% |
| 1000 | more than 99.9999% | 86.11% | 11.40% |

Chance of at least one losing run, win chance 60 percent per trial:

| Trials | Run of 5 | Run of 8 | Run of 12 |
| --- | --- | --- | --- |
| 100 | 45.91% | 3.63% | 0.09% |
| 500 | 95.76% | 17.70% | 0.49% |
| 1000 | 99.82% | 32.43% | 0.99% |

## How do I read the table?

Pick a row and a column. At a 40 percent win chance, a run of 8 losses in 100 trials has a 48.97% chance of appearing. At a 60 percent win chance, the same run in 100 trials appears 3.63% of the time. Move to 1,000 trials at 60 percent and a run of 8 has a 32.43% chance of showing up at least once. Chances shown as more than 99.9999% are never exactly certain; they are the closest the table gets.

Each trial in the table is independent and has the same win chance, so you can read it as your own sessions, tournaments or all-ins by picking the win chance that fits them.

## What does the table say about my decisions?

A run of bad outcomes at a good win chance is ordinary arithmetic. It is not a sign that the plan is wrong. What it does tell you is to judge the decision by the numbers at the time you made it, and to keep the outcome out of that review.

Judge the decision by the equity and the price at the moment you made it. The run that followed belongs to the table above.

## How do I plan around variance?

Sample size, bankroll rules and session length are decisions you make in advance. Plan how many trials you will look at before drawing a conclusion, and write that number down. The related guides cover the bankroll rules and the decision review that go with it.

- [Downswings and decisions](https://georgelipoker.com/mental-game/downswings-and-decisions.md)
- [Bankroll stress](https://georgelipoker.com/mental-game/bankroll-stress.md)
- [Tilt after a bad beat](https://georgelipoker.com/mental-game/tilt-after-a-bad-beat.md)
- [Equity calculator](https://georgelipoker.com/tools/equity-calculator.md)

## What should I do with the table?

1. Pick a win chance and a number of trials from the table that match something you play.
2. Read the chance of a losing run of 8 and write it next to your plan.
3. Write a rule for how you will check your decisions during a long losing run.

## Questions

**What is variance in poker?**

The spread of short-run outcomes around the long-run average. A good decision can lose many times in a row, and the tables on this page give the exact chance of those runs.

**How long can a losing run last at a good win chance?**

The table gives the exact chance for runs of 5, 8 and 12 across 100, 500 and 1,000 trials. At a 60 percent win chance, a run of 12 in 1,000 trials has a 0.99% chance of appearing.

**Does a losing run mean I am playing badly?**

Not by itself. Check the decisions against the numbers at the time instead of reading the outcomes.

Want to put your own stretch of play against the table? Book a session and bring your notes.

[Book a session](https://georgelipoker.com/book.md)

## Related

- [Poker Mental Game Coaching](https://georgelipoker.com/mental-game.md)
- [Downswings and Decisions in Poker](https://georgelipoker.com/mental-game/downswings-and-decisions.md)
- [Bankroll Stress in Poker](https://georgelipoker.com/mental-game/bankroll-stress.md)
- [Tilt After a Bad Beat: What to Do Next](https://georgelipoker.com/mental-game/tilt-after-a-bad-beat.md)
- [Free Poker Equity Calculator](https://georgelipoker.com/tools/equity-calculator.md)
- [Pot Odds Calculator: Equity You Need to Call](https://georgelipoker.com/tools/pot-odds-calculator.md)