Variance in poker: how big the swings get and how to handle a downswing

Variance in poker is the part of your results that comes from the cards rather than from your decisions. You can play a session well and lose, or play it badly and win, and over a few thousand hands luck says more about your results than skill does. Knowing how big these swings normally get is what lets you tell a bad run from a bad habit, and keep playing through a downswing without wrecking your bankroll or your game.

What variance means in poker

Every decision has an expected value: what it would win or lose on average if you could repeat it thousands of times. Your actual result in one hand is a single draw from that range, and it can land far from the average. Variance is the size of that gap.

The cleanest example is an all-in before the flop. You hold A♠ A♥, your opponent K♣ K♦, and all the chips go in. Your aces win 81.3% of the time, so getting the money in is a clearly profitable decision. Then the flop comes:

You made the right play and lost the pot. Nothing about your decision changed; the cards simply landed in the 19%. Over a career you will be on both sides of this spot many times, and on average the aces collect what they are owed. In any one session, they may not.

Players measure the size of these swings with the standard deviation, usually in big blinds per 100 hands (bb/100). A standard deviation of 90 bb/100 means that in about two of every three 100-hand stretches, your result lands within 90 big blinds of your true average. With a win rate of 5 bb/100, that is anything from −85 to +95 bb. The win rate is small next to the noise, and that is the whole problem.

Variance doesn’t “even out” by the cards owing you a win. A bad run never makes the next hand more likely to go your way. Luck stops dominating your results only because, over a long enough sample, your edge adds up faster than the noise does.

How big the swings get: a simulation

To show what these numbers look like in practice, we simulated 10,000 players over 100,000 hands each. Every one of them is the same winning player: a true win rate of 5 bb/100 and a standard deviation of 90 bb/100, typical for a solid six-max no-limit Hold’em regular. The only difference between them is luck. The chart shows 20 of those players, picked at random.

All 20 players should end up around +5,000 bb, or 50 buy-ins of 100 bb. A few do; others end near +9,000 or barely above zero, and one finishes in the red. The full set of 10,000 players gives these results:

Read the last lines again with a real schedule in mind. 29,000 hands is several weeks of steady multi-tabling, or months of part-time play. A winning player can spend all of that time below their previous best and do nothing wrong.

These numbers depend on the assumptions. A lower win rate makes everything worse: the same player at 2.5 bb/100 has far longer flat stretches and a much higher chance of losing over 100,000 hands. A bigger standard deviation, as in pot-limit Omaha, makes the swings wider.

Swings at the highest stakes follow the same rules. In the 2019–2020 Galfond Challenge, Phil Galfond played €100/€200 pot-limit Omaha against an opponent known as VeniVidi1993 and was more than €900,000 down at one point. He won the match.

Standard deviation by format

Different games swing by different amounts. The ranges below are the ones tracking-software users commonly report and the ones Primedope’s variance calculator suggests as starting points. Your own number depends on your style: a loose, aggressive player sees bigger swings than a tight one at the same table.

Tournaments are measured differently, because one deep run can be worth hundreds of buy-ins. In our own model of a 500-player tournament, the standard deviation is about 6–7 buy-ins per event, far above what any single cash-game session produces. The bigger the field, the larger it gets.

If you track your hands, your software shows your own standard deviation. You can then enter your figures into a variance calculator and see your own range of outcomes instead of ours.

How many hands until your results mean something

Because the noise is so large, your measured win rate is only an estimate, and a rough one over small samples. The table shows how wide the range of possible true win rates still is after a given number of hands. We use 95% confidence: the true rate falls inside this range in 19 of 20 cases.

Say you have played 10,000 hands of six-max and won at 8 bb/100. Your true rate could be anywhere from about −10 to +26 bb/100. That is why you so often hear that results “settle down” after 10,000 hands, and why that idea is wrong. Even after 100,000 hands, a measured 5 bb/100 could still be a losing player who ran well. Our guide to calculating your win rate shows how to read your own numbers.

Why tournaments swing harder

In a cash game, every pot is a small part of your result. In a tournament, most of the money sits in a handful of finishing places, so a whole year can depend on a few deep runs. To put numbers on it, we modelled a 500-player tournament with 15% of the field paid and a winning player with a 20% return on investment (ROI). The model is simplified: skill raises the chance of every paid finish by the same amount.

• Cashes: about one event in five. Ten events in a row without a cash happen to this player about 11% of the time.
• Final tables: about once every 42 events. There is a 9% chance of playing 100 events without reaching one.
• Wins: about once every 380 events. Over 500 events, 27% of players with this edge never win one.
• Where the profit comes from: the top three places produce 37% of the expected winnings, and the final table 58%.

The same thing makes tournament results slow to read. With a true 20% ROI, the range of possible results is still about ±37 percentage points after 1,000 tournaments and about ±21 points after 3,000. A few hundred events say almost nothing about whether someone wins, which is why tournament players need the far larger bankrolls in the next table. Strategy for these fields is covered in our guide to multi-table tournaments.

What makes your swings bigger or smaller

You can’t remove variance, but several choices change how much of it you face.

• Playing style. Playing more hands and putting more chips in with draws and bluffs raises your standard deviation. A tighter style swings less, though it may also win less.
• Game and format. Full-ring cash swings less than six-max, six-max less than PLO, and any cash game less than large-field tournaments.
• Field size. In tournaments and sit-and-gos, a smaller field means more frequent cashes and smaller swings.
• Running it twice. Where the site or the table allows it, dealing the remaining board twice after an all-in splits the pot more often. Your expected value stays the same; the swing per all-in shrinks.
• Volume. Playing more tables doesn’t change variance per hand, but it gets you through a given number of hands faster, so the long run arrives sooner in calendar time.

How variance sets your bankroll

A bankroll is the money you set aside for poker only, and its job is to survive the downswings above. The usual way to size it is risk of ruin: the chance that a run of bad luck takes the whole bankroll before your edge pulls you back up. The table shows roughly how many buy-ins keep that risk near 5%.

The cash-game figures use the standard risk-of-ruin formula. The tournament figures come from our simulation over 3,000 events, with 15% of the field paid and a top-heavy payout structure. Treat all of them as a minimum for a player who really has that edge, not as a target. Three things push the number up:

• A smaller edge. Halving the win rate roughly doubles the bankroll you need. A breakeven player has no safe bankroll at all.
• Uncertainty about your edge. If you only have 20,000 hands, you don’t know your win rate yet. Plan for the lower end of the range.
• Money you can’t afford to lose. A bankroll only works if it is separate from rent and savings.

To see how a bankroll can be built without a large deposit, see building a bankroll with freerolls.

Downswing or leak: how to tell

The hardest part of a downswing is not knowing whether it is one. A losing stretch can be pure variance, or a problem in your game that variance is hiding. These signs point one way or the other:

The all-in EV line is the most useful single check. Tracking software can show what you would have won if every all-in had paid out its expected share. If that line is going up while your real results go down, the cards are behind most of the gap. If both lines are falling, look at your play.

Tilt belongs on the leak side even when the downswing started with bad luck. Calling down too light or forcing bluffs after a beat turns a normal swing into a real loss. Our article on tilt in poker covers how to spot it.

What to do during a downswing

Once you are confident the losses are mostly variance, the job is to keep playing your normal game. A downswing your bankroll was built for doesn’t require anything special.

• Keep your stakes if the bankroll allows it. There is no need to move down just because you are losing. Move down when the bankroll drops below the limit you set for those stakes, or when you have found a leak or tilt you need to fix first.
• Never move up to win it back. Raising the stakes to recover losses is the fastest way to turn a downswing into a lost bankroll.
• Review hands, not results. Pick the biggest pots of the week and check the decisions. If they were right, the money will follow over time.
• Set session rules in advance. A stop-loss or a fixed session length decided before you sit down protects you from the decisions you make when tilted.
• Take breaks. A few days away costs you nothing if your play is good, and helps if it isn’t.

Keep a downswing journal

A short note after each session makes the variance-or-leak question much easier to answer a month later. Five lines are enough:

1. Date, game, stakes and hands played
2. Result and all-in EV result
3. The two or three biggest pots, and whether you were ahead when the money went in
4. Your mood and focus, on a scale of 1 to 5
5. One hand to review before the next session

After a few weeks, the journal shows patterns you won’t see from inside a downswing: losses that only happen late in long sessions, or a mood score that drops before the results do.

When it stops being about poker

Everything above assumes poker is a game you can afford. Variance can also hide a different problem: playing to win back losses, with money meant for something else, or for longer than you meant to. If you notice that, or the people around you do, treat it as more important than any downswing. Our responsible gambling page lists warning signs, tools such as deposit limits and self-exclusion, and organisations that offer free, confidential help, including GamCare in the UK and 1-800-MY-RESET in the US.

Variance in poker FAQ