Risk of ruin calculator
Risk of ruin is the probability that a winning player still goes broke because of variance. Enter your bankroll, average buy-in, expected ROI and how widely your results swing.
Per tournament, after fees.
In buy-ins per tournament. Roughly 1.5-2 for 9-player sit & gos, 3.5-4.5 for 100-200 players, 5.5-7.5 for 500-1,000.
- Risk of ruin
- 43.5%
- Bankroll in buy-ins
- 100
- Buy-ins for 5% risk
- 360
- Buy-ins for 1% risk
- 553
RoR = exp(-2 x ROI x bankroll / stdDev²), all units in buy-ins
Assumes normally distributed results, constant stakes and unlimited play. Tournament results are heavily right-skewed, so read the output as an order of magnitude rather than a precise probability.
What is risk of ruin in poker?
Risk of ruin is the chance of losing your whole bankroll before your edge shows up in your results. It is not zero for a winning player: a long enough losing run can empty any finite bankroll, and the smaller the bankroll is next to the swings, the more likely that run arrives first.
Three numbers decide it: how big your edge is, how widely your results swing around it, and how many buy-ins you hold. The calculator combines them in the standard formula and tells you both the risk you are running now and the bankroll that would bring it down to 5% or 1%.
The risk of ruin formula
RoR = exp(−2 × ROI × bankroll / SD²)
Everything is in buy-ins: the bankroll, the ROI as a share of a buy-in per tournament, and the standard deviation per tournament. It is the diffusion approximation most poker risk-of-ruin calculators use, and it treats your results as a random walk with a steady drift — your edge — and steady volatility.
With a bankroll of 5,000 for 50 tournaments — 100 buy-ins — a 15% ROI and a standard deviation of 6 buy-ins, the risk of ruin is 43.5%. To get it under 5% you would need 360 buy-ins.
- Inputs
- Bankroll5,000
- Average buy-in50
- Expected ROI15%
- Standard deviation6
- Result
- Risk of ruin43.5%
- Bankroll in buy-ins100
- Buy-ins for 5% risk360
- Buy-ins for 1% risk553
How many buy-ins do you need?
Solving the formula for the bankroll gives the buy-ins that hold the risk at a chosen level. For tournaments with a standard deviation of 6 buy-ins — a field of several hundred players:
| ROI per tournament | 5% risk | 1% risk | 0.1% risk |
|---|---|---|---|
| 5% | 1,079 | 1,658 | 2,487 |
| 10% | 540 | 829 | 1,244 |
| 15% | 360 | 553 | 829 |
| 20% | 270 | 415 | 622 |
| 30% | 180 | 277 | 415 |
For other formats and field sizes, the poker bankroll calculator fills in a typical standard deviation for you and gives the buy-ins for any risk level.
Cash games use the same formula with 100 hands as the unit: win rate and standard deviation in big blinds per 100 hands, the result divided by 100 big blinds for a buy-in. With a standard deviation of 90 bb/100, typical for no-limit hold’em:
| Win rate (bb/100) | 5% risk | 1% risk | 0.1% risk |
|---|---|---|---|
| 1 | 122 | 187 | 280 |
| 2.5 | 49 | 75 | 112 |
| 5 | 25 | 38 | 56 |
| 7.5 | 17 | 25 | 38 |
| 10 | 13 | 19 | 28 |
Standard deviation by format
The standard deviation is the input people get wrong most often, and it matters most: the bankroll you need grows with its square. Bigger fields pay a few players a lot and most players nothing, so their results swing far more than a sit & go’s:
| Format | Standard deviation (buy-ins) |
|---|---|
| 9-player sit & go | 1.5 – 2 |
| 18 – 45 players | 2.5 – 3 |
| 100 – 200 players | 3.5 – 4.5 |
| 500 – 1,000 players | 5.5 – 7.5 |
| 5,000 players and more | 10 and more |
The difference is not academic. At 15% ROI, holding the risk at 5% takes about 29 buy-ins with a sit & go’s spread of 1.7 and about 490 with a 1,000-player field’s spread of 7. Using a sit & go figure for big tournaments understates the bankroll by an order of magnitude.
Risk of ruin vs a variance calculator
They answer different questions. Risk of ruin asks: if I play forever at these stakes, how likely am I to go broke? A variance calculator simulates a fixed number of tournaments or hands and shows the range of results you might see — how deep a downswing gets, how often a winning player is still behind after 1,000 games.
Use risk of ruin to size a bankroll, and a variance simulation to set expectations for the next few months.
Why the result is an approximation
- It assumes results are normally distributed. Tournament results are not: most are small losses, a few are large wins. Treat the output as an order of magnitude.
- It assumes constant stakes. Moving down after a losing run lowers your real risk; moving up after a winning one raises it.
- It assumes your ROI is known. A few hundred tournaments say very little about a true ROI, so test the number with a lower one too.
Lowering your risk of ruin
- Hold more buy-ins: the same money at lower stakes.
- Lower the variance: smaller fields and sit & gos swing less than large tournaments.
- Set a move-down point in advance, so a downswing changes your stakes before it changes your bankroll.
- Keep your own numbers. Tracking your sessions turns guesses about ROI and swings into figures you can enter here.
This number covers one spot. PokeAI covers your game.
The calculator answers how much. PokeAI answers why — on the hands you actually played, using this same engine for every number it gives you.
Questions about this calculator
- What is risk of ruin in poker?
- It is the probability that a player with a real edge still loses their entire bankroll because of variance before that edge shows up in results.
- How many buy-ins do I need for MTTs?
- It depends on your ROI and the size of the fields you play. At 15% ROI in fields of several hundred players, about 360 buy-ins hold the risk of ruin at 5%. Enter your own numbers above rather than following a fixed rule of thumb.
- What standard deviation should I use?
- For tournaments, roughly 1.5-2 buy-ins for 9-player sit & gos, 3.5-4.5 for fields of 100-200 and 5.5-7.5 for 500-1,000. For cash games, 80-100 big blinds per 100 hands is common. Your own results are the best source once you have enough of them.
- Can I use this calculator for cash games?
- Yes. Treat 100 hands as one unit: enter your win rate in bb/100 as the ROI (5 bb/100 is 5% of a 100-big-blind buy-in) and your standard deviation in bb/100 divided by 100. At 5 bb/100 and 90 bb/100, 5% risk takes about 25 buy-ins.
- Why does a losing player have 100% risk of ruin?
- Without a positive expectation, a large enough sample makes busting a certainty. No bankroll size fixes a negative ROI.
- Does risk of ruin assume I never move down?
- Yes. The formula keeps your stakes fixed. Moving down after losses lowers your real risk, which is why a move-down rule is the cheapest protection a bankroll can have.
Related calculators
- Poker Bankroll Calculator
Work out how many buy-ins you need for cash games, sit & gos and tournaments from your win rate or ROI, your swings and the risk of ruin you accept.
- ICM Calculator
Convert tournament stacks into prize money with the Malmuth-Harville ICM model, and compare an ICM chop with a chip chop before agreeing a deal.
- Call EV Calculator
Enter your equity, the pot and the bet to see the expected value of a call in chips, plus how much equity you are above or below break-even.
Further reading
- Downswing or Leak? How to Tell From Your Own Poker Numbers
How big downswings get for winning players, how often a winner is still behind after 50,000 hands, and the signs in your own results that point to a leak instead.
- Poker Bankroll Management: Fixed Percentage, Kelly and Stop-Loss
Three bankroll management methods worked through with real numbers: fixed percentage, the Kelly criterion and stop-losses, and the risk of ruin behind each.
- What Is a Poker Bankroll? How Much You Need and How to Manage It
A poker bankroll is money kept only for poker, counted in buy-ins. What counts, how many buy-ins cash games, sit & gos and tournaments need, and how to build one.