Poker bankroll management, without the guesswork
Start with buy-ins you can afford to lose, then set a move-down rule before you play. The table and calculator show how your estimated edge and swings change the bankroll you may need.
Buy-ins, not money
Your bankroll size in buy-ins, set against your win rate and standard deviation, sets the stakes your roll can support at the risk you choose. Thinner edges and bigger swings demand more buy-ins for the same low risk of ruin.
Moving up and down on rules
Move up only when both the buy-in count and a proven win rate clear the bar, not on a hot streak. Move down on a pre-set rule when the roll dips. The discipline is in deciding before emotion does.
Surviving variance
You cannot remove variance, only outlast it. Enough buy-ins, stakes you are rolled for, and a stop-loss to protect the A-game keep you in action through the downswings the maths says to expect.
A practical bankroll rule set
Good poker bankroll management is not a single magic buy-in number. It is a rule set you can follow when the latest session is trying to talk you out of discipline. Start by separating the poker bankroll from living money. Then size the stake in buy-ins, not in cash, because a GBP 1,000 bankroll means something very different at 1/2 than at 2/5. Finally, write the move-up, shot-taking and move-down rules before you need them.
For live cash, a conservative starting frame is simple. Keep the main stake deep enough that a normal downswing does not threaten the roll. Take shots only with a fixed budget and a clear stop point. Move down automatically when the buy-in count falls below the rule, even if the last session felt unlucky. The rule should be boring enough to follow while tilted. If it needs a fresh argument every time, it is not a bankroll rule, it is a hope.
The right buy-in count depends on win rate, standard deviation, game type and life pressure. A player with a thin edge, high-variance games and a roll that matters more to their finances needs a deeper roll than a recreational player with stable income and a small capped risk. Overshove does not pretend the same answer fits both. The free core keeps the session record, true hourly after costs and the bankroll graph together, so the bankroll decision starts from the results you actually logged. The free calculators below do the variance and risk of ruin maths.
Risk of ruin, and where the 5 percent rule comes from
Risk of ruin is the probability that you lose your whole bankroll before your edge plays out. It is the number the buy-in count is really trying to control, and it has a closed form for a fixed win rate and standard deviation:
risk of ruin = e^(-2 × W × B / S²)
W is your win rate in BB/100, S is your standard deviation in BB/100, and B is your bankroll in big blinds. Rearranged for the bankroll that hits a chosen risk, it becomes:
bankroll in big blinds = -S² × ln(risk) / (2 × W)
The commonly quoted 5 percent rule is just that formula with risk set to 0.05. Because the natural log of 0.05 is about -2.996, the whole thing collapses to roughly three times S squared, divided by twice your win rate.
Worked through: a 4 BB/100 winner with a 90 BB/100 standard deviation needs about 3,033 big blinds, near enough 30 buy-ins at 100 BB each, to hold risk of ruin at 5 percent. Drop to 20 buy-ins and the same player's risk of ruin rises to about 14 percent. Halve the edge to 2 BB/100 and raise the standard deviation to 100, and the 5 percent bankroll jumps to roughly 75 buy-ins. Push for 1 percent instead of 5 at the original numbers and it is about 47 buy-ins.
Two honest caveats. The formula assumes a constant edge and normal swings, which real poker only approximates, so treat the output as a sizing guide rather than a guarantee. And it says nothing about whether your measured win rate is real: a win rate from too small a sample makes the whole calculation confident nonsense, which is why sample size matters before bankroll maths does.
The move-up test
A move-up decision should clear three tests. First, the bankroll test: after buying into the next stake, the remaining roll still leaves enough buy-ins to survive a normal bad run. Second, the skill test: the lower stake sample shows a real edge, not just a short heater. Third, the behaviour test: the bigger pots do not change the decisions so much that the old win rate becomes irrelevant. Missing any one of those tests turns a move-up into a gamble.
Shot-taking is different from permanently moving up. A shot is a budgeted experiment. You decide how many buy-ins can be risked, what result ends the shot, and what evidence would justify another one. The cleanest rule is written before the first hand: if the shot loses two buy-ins, return to the main stake; if the game is excellent and the roll is still within the rule, continue; if the bigger game makes you passive or reckless, stop even if the result is positive.
Moving down is the part players avoid, but it is the move that keeps a bankroll alive. Dropping stakes after a rule is not failure. It is the system doing what it was built to do. The player who moves down on time gets to rebuild from a controlled spot. The player who waits until pride is satisfied often rebuilds from zero.
- →Bankroll is measured in buy-ins, sized to your edge and swings.
- →Move up on a proven win rate, not an upswing.
- →Move down on a rule, before tilt decides.
- →Keep risk of ruin low so a normal downswing never busts you.
Poker bankroll management for live cash: set the rules before the swing
The formula box above shows the risk of ruin model at 4 BB/100. This lesson applies the same model to a live player who keeps records in hours. It covers which money belongs in a bankroll, what a buy-in rule quietly assumes, a worked £1/£2 example, written move-up and move-down lines, shot budgets, and what to do after a downswing without chasing it.
What a bankroll is, and what it is not
A poker bankroll is money set aside only for poker that you could lose in full without affecting rent, bills, debt repayments, savings or anyone who relies on you. If losing it would mean cutting back elsewhere, borrowing, or feeling that you have to win it back, it is not bankroll.
Three quick tests:
- Would you have to replace it? Then it is living money.
- Is it on a credit card, an overdraft or a loan? Then it is not yours to risk.
- Are you topping it up from wages to keep playing your usual stake? Then the rule has already failed. The answer is a lower stake or a break, not a bigger top-up.
Keep the bankroll in a separate account, or at least a separate record, and log every top-up and withdrawal. The risk of ruin model assumes neither happens. Spending from the roll makes the real risk higher than the model says, and adding to it hides how the poker is actually going. If poker money is starting to cause worry, the responsible play page lists where to get help.
Buy-in counts by stake: a starting point, and what it assumes
The bankroll by stake guide gives illustrative ranges of 25 to 40 buy-ins at 1/2 and 2/5, and 40 or more at 5/10. Run the calculator’s formula backwards and you can see the edge each count assumes. At the calculator’s default standard deviation of 90 BB/100:
| Buy-ins of 100 BB | Win rate for 5% model risk | Win rate for 1% model risk | Money at 1/2 (£200) | Money at 2/5 (£500) |
|---|---|---|---|---|
| 25 | 4.9 BB/100 | 7.5 BB/100 | £5,000 | £12,500 |
| 30 | 4.0 BB/100 | 6.2 BB/100 | £6,000 | £15,000 |
| 40 | 3.0 BB/100 | 4.7 BB/100 | £8,000 | £20,000 |
| 50 | 2.4 BB/100 | 3.7 BB/100 | £10,000 | £25,000 |
Read the first row this way: 25 buy-ins holds the modelled risk at 5% only if your true edge is about 4.9 BB/100 after rake and tips. At 25 hands an hour that is roughly 1.2 BB an hour. If your own records cannot support that, sit higher in the range.
Every row rests on the same assumptions:
- A buy-in is 100 big blinds. If you usually sit with more, count buy-ins at what you actually bring. £9,000 is 45 buy-ins at a £200 buy-in but only 30 at £300.
- One fixed stake, with no withdrawals and no top-ups.
- A steady win rate, measured after rake and tips, and swings that follow a normal curve.
- A standard deviation of 90 BB/100. Bigger swings need more buy-ins for the same risk.
Risk of ruin in plain terms, with a live example
The site’s bankroll and risk of ruin calculators use this formula:
Bankroll in big blinds = −SD² × ln(risk) ÷ (2 × win rate)
The other way round, risk of ruin = e^(−2 × win rate × bankroll ÷ SD²). In plain terms, the risk depends on one thing: your bankroll multiplied by your edge, compared with the square of your swings. The win rate and SD must use the same unit, both per 100 hands or both per hour.
Worked example. A £1/£2 player buys in for £200, which is 100 big blinds. Their records, after rake and tips, show 2 BB an hour (£4) with an SD of 60 BB an hour (£120). They want a 5% model risk.
- Square the SD: 60 × 60 = 3,600.
- Multiply by −ln(0.05), which is about 2.996: 3,600 × 2.996 ≈ 10,785.
- Divide by twice the win rate: 10,785 ÷ 4 ≈ 2,696 big blinds.
- Divide by 100: about 27 buy-ins, or about £5,392 at £2 a big blind.
For a 1% model risk, use ln(0.01), about −4.605: 3,600 × 4.605 ÷ 4 ≈ 4,145 big blinds, about 41 buy-ins or £8,289.
To check it in the bankroll calculator, enter 2 as the win rate, 60 as the standard deviation and 5 as the acceptable risk of ruin. It shows 27.0 buy-ins and 2,696.2 big blinds. The fields are labelled BB/100, but the answer does not change as long as both numbers use the same unit: converted at 25 hands an hour, 8 BB/100 and 120 BB/100 give the same 2,696 big blinds.
Three rules of thumb follow from the formula. Each is exact under the model:
| Change | What happens to a 5% risk |
|---|---|
| Double the bankroll | Falls to 0.25%, because the risk is squared |
| Your true edge is half what you assumed | Rises to about 22.4%, the square root of 5% |
| Your swings are 20% bigger than you assumed | Rises to about 12.5% |
The middle row matters most for live players, because a live win rate is never known precisely. After 400 hours with an SD of 60 BB an hour, a measured 2 BB an hour has a 95% band of about −3.9 to +7.9 BB an hour. If the example player’s true rate were 1 BB an hour, the 27-buy-in roll would carry about a 22% model risk, and holding 5% would need about 54 buy-ins (£10,785). Run the calculator at half your measured win rate as well as at the full rate, and size the roll for an answer you could accept either way.
The model treats ruin as reaching zero at one fixed stake. Moving down on a rule lowers your chance of losing everything, but it means playing smaller for a while. The model also knows nothing about withdrawals, top-ups, changing games or tilt. The risk of ruin calculator runs the same model forwards from your buy-in count.
Moving up and moving down: write the lines down
The move-up test above sets the conditions. Turn them into numbers before you need them, and leave a gap between the line where you move up and the line where you move down, so that one bad night does not bounce you between stakes.
Here is an example rule card for a player at 1/2 thinking about 2/5, where a buy-in is £500:
| Rule | Line | Why |
|---|---|---|
| Move up to 2/5 | Roll reaches £15,000 (30 buy-ins at 2/5) and the 1/2 win rate’s 95% band sits above zero | Both the money and the sample have to pass |
| Move back down to 1/2 | Roll falls below £12,500 (25 buy-ins at 2/5) | Decided in advance, not after a session |
| Gap between the two | £2,500, or five 2/5 buy-ins | One losing night cannot force a move |
The win-rate confidence calculator shows whether your 95% band clears zero. Back at 1/2, £12,500 is 62.5 buy-ins, which is a comfortable place to rebuild. If the player’s edge at 2/5 were 4 BB/100 with an SD of 90 BB/100, 30 buy-ins would carry about a 5.2% model risk and 25 buy-ins about 8.5%. A smaller edge at the new stake pushes both figures higher.
Write the card on a day you have not played, and keep it where you log your sessions.
Shot-taking: a budget, not a mood
A shot is a fixed amount set aside to try a bigger game. The “two buy-ins and back” rule above works best when the budget also protects your usual stake. Size the shot so that losing all of it still leaves you above the move-down line where you normally play.
For example, a 1/2 player has £9,000, which is 45 buy-ins at £200. Their floor at 1/2 is 30 buy-ins, or £6,000. The most a shot could cost without breaking that floor is £3,000. They choose two 2/5 buy-ins, £1,000. If both go, the roll is £8,000, still 40 buy-ins at 1/2, and nothing about their normal game has to change.
Two more rules:
- A winning shot is not a move up. The move-up line and the sample test still apply.
- Decide in advance what ends a shot early: the budget is gone, you notice you are playing scared or loose, or you reach the time limit you set for the night.
After a downswing: what to do, and what to avoid
Chasing means playing longer, at a higher stake, or with money from outside the roll to recover a loss. It increases your exposure at exactly the point where your judgement is under the most pressure.
A calmer order of work:
- Stop when your session limit says stop. The stop-loss calculator can help you set one before you play.
- Count the roll in buy-ins at your current stake. If it is below your move-down line, move down. No renegotiating.
- Check the loss against your own numbers. For the example player (2 BB an hour, SD 60 BB an hour), the 95% range over 100 hours runs from about −976 to +1,376 big blinds, and a loss of 1,000 big blinds or more in 100 hours would happen about 2.3% of the time. A loss well outside your range is a reason to question your inputs, not just the cards. The variance calculator shows the range for your own figures.
- Review decisions, not results. Pick two or three hands from the stretch and review them away from the table.
- Leave the roll alone. Do not top it up from wages to stay at your stake, and do not move up to win it back.
- Take a break if you want one. Time away from the table never adds to your risk of ruin.
Check yourself
A player's records show 1.5 BB an hour with an SD of 45 BB an hour. What bankroll gives a 5% model risk?
45 × 45 = 2,025. 2,025 × 2.996 ≈ 6,067, and 6,067 ÷ 3 ≈ 2,022 big blinds, about 20 buy-ins or £4,044 at a £2 big blind. It matches the 6 BB/100 row of the table above, because at 25 hands an hour 1.5 BB and 45 BB an hour are the same as 6 BB/100 and 90 BB/100.
Your roll gives a 5% model risk. You double it and stay at the same stake. What is the new risk?
About 0.25%. Doubling the bankroll doubles the exponent in e^(−2 × win rate × bankroll ÷ SD²), which squares the risk: 0.05 × 0.05 = 0.0025.
You have £9,000 at 1/2 and a floor of 30 buy-ins. What is the most a shot can cost without breaking the floor?
£3,000. The floor is 30 × £200 = £6,000, and £9,000 − £6,000 = £3,000. A smaller budget leaves a margin for the sessions after the shot.
Sources and method
Original Overshove writing and arithmetic. Every bankroll figure uses the formula in the site's bankroll and risk of ruin calculators, bankroll in big blinds = −SD² × ln(risk) ÷ (2 × win rate), with ln(0.05) ≈ −2.996, ln(0.01) ≈ −4.605 and buy-ins of 100 big blinds. The model assumes one fixed stake, a steady edge, normally distributed results and no deposits or withdrawals. Hourly conversions assume 25 hands an hour, and the downswing range uses the same normal model as the variance calculator. The player, records and rule card are hypothetical examples, not recommended stakes or financial advice.
Questions
What is a good bankroll for poker?
One you could lose in full without affecting rent, bills, debts, savings or anyone who depends on you, and big enough in buy-ins for the swings at your stake. The bankroll by stake guide uses illustrative ranges of 25 to 40 buy-ins at 1/2 and 2/5, and 40 or more at 5/10. No count makes poker safe: the right number depends on your real edge after rake, your swings and the risk you accept.
When should I move down in stakes?
When your bankroll falls below a line you wrote down in advance, measured in buy-ins at your current stake. For example, a player who moves up to 2/5 at 30 buy-ins, £15,000, might move back down below 25 buy-ins, £12,500. The gap stops a single losing night forcing a move, and the line only works if you follow it without renegotiating.
Is 20 buy-ins enough?
Only if your edge is large compared with your swings. At the calculator's default standard deviation of 90 BB/100, 20 buy-ins of 100 big blinds hold the model's risk of ruin at 5% only with a true win rate of about 6 BB/100 after rake and tips. At 4 BB/100 the same roll carries about a 14% risk, and at 2 BB/100 about 37%. If your records cannot show an edge that size, use more buy-ins or a lower stake.
What should I do after a big downswing?
Stop playing for the day, count your bankroll in buy-ins and move down if it has crossed your line. Then compare the loss with the range your own win rate and standard deviation allow, and review a few hands away from the table. Do not top up from living money, play longer or move up to win it back.
Does a 5% risk of ruin mean I will go broke one time in 20?
Only inside the model, which assumes one fixed stake, a known and steady win rate, normal swings and no withdrawals. Moving down on a rule lowers the chance of losing everything. An edge smaller than you assumed raises it sharply: at half the assumed edge, a 5% risk becomes about 22%.
How many buy-ins do I need?
It depends on your win rate and standard deviation. The bankroll calculator sizes it for an acceptable risk of ruin.
What is the risk of ruin formula?
Risk of ruin is e^(-2 x W x B / S squared), where W is your win rate in BB/100, S is your standard deviation in BB/100 and B is your bankroll in big blinds. Rearranged for a target risk it gives the bankroll you need: -S squared x ln(risk) / (2 x W).
How many buy-ins for a 5 percent risk of ruin?
Set risk to 0.05 in the formula above. A 4 BB/100 winner with a 90 BB/100 standard deviation needs about 3,033 big blinds, roughly 30 buy-ins. At 20 buy-ins the same player faces about a 14 percent risk of ruin.
Can I use BB per hour instead of BB/100?
Yes, as long as the win rate and the standard deviation use the same unit. Live players often track BB per hour, so enter the hourly win rate with the hourly standard deviation. Mixing an hourly win rate with a per-100-hands deviation gives a wrong answer.
Live vs online, same rules?
No. Variance and stakes differ; keep the rolls separate and set rules per discipline.