Bankroll, win rate and variance in cash games: how many buy-ins you need and how to read your results

What a bankroll is and how many buy-ins to have

Your bankroll is money dedicated only to poker, kept separate from your living expenses. It has to be money you can lose without it affecting your life: never rent money and never borrowed money.

In cash games it is measured in 100 bb buy-ins:

Why 30 to 50 and not 10? Because cash games have long losing stretches even for winning players. With few buy-ins, one bad week forces you to stop playing or, worse, to play scared. The less sure you are of your win rate, the more you should aim for 50.

Win rate: what bb/100 measures

Your win rate is what you win on average, measured in big blinds per 100 hands (bb/100). Using big blinds instead of money lets you compare different stakes.

Example: you played 5,000 hands and won 150 bb. Your result is 150 / 50 = 3 bb/100.

Two important points:

• Win rate is measured after rake. At micro stakes, rake is large relative to pot sizes.
• What you see in your results is a sample, not your true win rate. With few hands the sample says very little, as the next section shows.

Standard deviation and the win rate interval

Standard deviation measures how much your results swing every 100 hands. It is your own number and comes from your hands; for the math in this guide we use 100 bb/100 as an example assumption.

The standard error of the sample is standard deviation / √(hands / 100), and the 95% confidence interval is win rate ± 1.96 × that error. Take a player with a true win rate of 5 bb/100 (an assumption for the math, not a target or a promise):

Read it like this: after 10,000 hands, a player who wins 5 bb/100 is down almost one time in three. And separating that win rate from zero with 95% confidence takes 153,664 hands: (1.96 × 100 / 5)² × 100. That is why you should not draw conclusions from a single week, good or bad.

Risk of ruin

Risk of ruin is the probability of losing your whole bankroll before your win rate takes over. With win rate μ and standard deviation σ per hand and a bankroll BR, all in bb, the formula is exp(−2 × μ × BR / σ²). With 5 bb/100 (μ = 0.05 bb per hand) and 100 bb/100 (σ = 10 bb per hand):

Three takeaways:

1. More buy-ins cut the risk very fast: from 20 to 50 buy-ins, risk drops from 13.53% to 0.67%.
2. If your win rate is half what you think, risk explodes. With 30 buy-ins it goes from 4.98% to 22.31%.
3. With a negative win rate the risk is total in the long run, whatever your bankroll. A bankroll protects a winning player; it does not turn a losing player into a winner.

When to move up and down: clear rules

Rules work if you set them before you sit down, not after a bad session. A simple, prudent scheme:

• Play the stake where you have at least 30 buy-ins, and 50 if your sample is short.
• Move up when you have 40 buy-ins for the next stake. From NL10 to NL25, at 1,000 USD (40 × 25).
• Move down if you drop below 30 buy-ins for your current stake. At NL25, if your bankroll falls under 750 USD, go back to NL10.

The gap between 750 and 1,000 USD stops you from bouncing up and down every week. Also:

• Do not move up to win back losses: it is the fastest way to turn a downswing into a real problem.
• When you move up, check that your game is ready too: NL50 opponents make fewer mistakes than NL10 opponents.
• If losses create financial pressure or you find it hard to stop, stop and ask for help.

Living with variance

Variance cannot be removed: it can be managed. What you do control is how you react.

• Judge decisions, not results. Review big hands by the decision you made with the information you had, not by whether you won.
• Watch out for tilt. Calling or raising hands you normally fold after losing a big pot is the clearest sign. End the session.
• Look at big samples. A bad 10,000-hand month does not prove you play badly; a good one does not prove you play well.
• Do not abandon a sound strategy over a few bad days. Change it when you find a specific mistake in your hands.

How to practice it

Write down your bankroll, your stake and your two rules (when you move up and when you move down) today. Track hands and results in big blinds, not money. At POKER AULA, variance and the mental game appear in the Intermediate level, and the Professional level has a module on study, variance and bankroll with win rate, samples and risk of ruin worked out step by step. The Professional Calculator runs these numbers with your own win rate and standard deviation, and the 48-hour free trial lets you try it with no card.