How many buy-ins a player loses in NLH, PLO, PLO5 and PLO6 — downswings, chance of a loss and bankroll from thousands of simulations
NLH 6-max, stakes $0.1/$0.2 (buy-in $10). Winrate +5 bb/100 at σ 90 bb/100: after 100k hands your observed winrate lands between +0.3 and +9.7 bb/100 90% of the time. To be 95% sure you are a winner you need 88k hands.
| Game | σ bb/100 | Typical | Bad (5%) | Bankroll 5% |
|---|---|---|---|---|
| NLH | 90 | 19 BI | 35 BI | 24 BI |
| PLO | 140 | 35 BI | 67 BI | 59 BI |
| PLO5 | 170 | 45 BI | 86 BI | 87 BI |
| PLO6 | 200 | 54 BI | 106 BI | 120 BI |
Same winrate, stakes and 100k-hand sample, 6-max tables; σ is the typical value for each game. The more hole cards, the closer the equities and the deeper the downswings: in PLO6 they are roughly twice as deep as in Hold'em at the same winrate.
A downswing is the deepest drop from a bankroll peak to the following low within the sample. A stretch without a new high counts the hands you went without beating your previous best.
| Percentile | Profit | BI | bb/100 |
|---|---|---|---|
| 5% | … | … | … |
| 25% | … | … | … |
| 50% | … | … | … |
| 75% | … | … | … |
| 95% | … | … | … |
The main question people open a cash game variance calculatorfor: how deep can a winning player's downswing get. It depends on three things — the winrate, the game's standard deviation (σ) and the length of the sample. Below are this model's numbers for a 5 bb/100 winrate over 100,000 hands at 6-max tables, in 100 bb buy-ins:
| Game (6-max) | σ bb/100 | Typical downswing | Bad (5%) | Bankroll, 5% risk | Chance of a loss | Hands to prove the winrate |
|---|---|---|---|---|---|---|
| NLH | 90 | 19 BI | 35 BI | 24 BI | 4% | 88k |
| PLO | 140 | 35 BI | 67 BI | 59 BI | 13% | 212k |
| PLO5 | 170 | 45 BI | 87 BI | 87 BI | 18% | 313k |
| PLO6 | 200 | 55 BI | 108 BI | 120 BI | 21% | 433k |
The typical downswing is the median: half of players see a shallower worst drop over 100,000 hands, half a deeper one. Badis the worst-5% line. In Hold'em a regular at 5 bb/100 usually lives through a drop of about 20 buy-ins and, once in twenty samples, 35 or more. In PLO the same figures almost double, in PLO6 they triple: with five or six hole cards equities converge, pots grow and a single session's result barely depends on skill.
At 2.5 bb/100 over the same sample downswings grow to 24 / 41 / 52 / 62 buy-ins (bad ones 47 / 82 / 103 / 124), and at 10 bb/100 they shrink to 14 / 27 / 35 / 45. Heads-up σ is about 1.6 times higher: at 5 bb/100 the typical NLH drop is already 36 buy-ins, in PLO6 96. Enter your own numbers and the calculator redoes everything for your winrate, stakes and sample.
Average profit in big blinds per 100 hands after rake — exactly as your tracker shows it. At micro stakes and in club apps typical regular winrates are 3–8 bb/100, at mid stakes 2–4. If you are not sure about your winrate (and after 50,000 hands nobody is), run two versions: the expected one and one 2–3 bb/100 lower.
| Game | 6-max | Full ring | Heads-up |
|---|---|---|---|
| Hold'em (NLH) | 80–100 | 65–80 | 130–160 |
| Omaha (PLO) | 130–160 | 105–130 | 200–250 |
| PLO5 | 160–190 | 130–150 | 250–300 |
| PLO6 | 190–230 | 150–180 | 300–360 |
The calculator uses the middle of each range (90 / 140 / 170 / 200 for 6-max), multiplies by 0.8 for full ring and by 1.6 for heads-up. Find your own σ in your tracker: Hold'em Manager and PokerTracker show Std Dev bb/100 in the session report. An aggressive style, deep stacks, straddles and bomb pots in club games raise σ by 20–40%, so for club tables with antes and straddles use the top of the range.
The classic risk-of-ruin formula: B = −ln(risk) × σ² ÷ (2 × winrate), all in bb. At σ 90 and 5 bb/100 with a 5% risk that is 2,427 bb — 24 buy-ins; at σ 200 (PLO6) — 120 buy-ins. The formula assumes an unlimited sample and a constant winrate, so it is a lower bound. Next to it the calculator shows a second number — "to survive this sample": how far below the start you go in the worst 5% (or 10%, 1%) of runs over exactly the number of hands you entered. For a short sample it is below the formula, for a long one it approaches it.
The rule for moving between stakes: move up when the bankroll exceeds the next level's requirement and move down as soon as it drops below the current one's — without waiting for zero. Matching stakes to a bankroll is what the bankroll calculator does.
After N hands the observed winrate lies within true ± 1.96 × σ ÷ √(N/100)95% of the time. At σ 90 and 100,000 hands that is ±5.6 bb/100: a player whose true winrate is 5 bb/100 sees anything from −0.6 to +10.6 on the graph. In PLO6 at σ 200 the interval is ±12.4 bb/100 — even after 100,000 hands you don't know whether you win at all. Hence the "hands to prove the winrate" line: how much you need to play to be 95% confident your winrate is above zero. For 5 bb/100 it is 88,000 hands in Hold'em and 433,000 in PLO6; for 2.5 bb/100 four times as many.
The result of every 100 hands is a normally distributed value with mean "winrate" and deviation σ (in $ — multiplied by the big blind). This is the standard model of cash game variance calculators: over hundreds of hands the sum of results is close to normal by the central limit theorem, even though single hands are not. Expectation and the chance of a loss are exact from the formulas; downswings, stretches without a new high, the longest losing streaks and the sample bankroll come from Monte Carlo: thousands of runs of your sample, each in 100-hand blocks. The game comparison uses the same winrate, stakes and sample with each game's typical σ.
Tournaments follow a different model — profit comes from rare deep runs and the distribution is skewed. Run those through the MTT variance calculator. What variance in poker is and how to live with it is in poker variance explained; where to play cash games with normal rake — cash game poker: where to find a table.
At 5 bb/100 over 100,000 hands the typical downswing in NLH 6-max is about 19 buy-ins, and 5% of players go deeper than 35. In PLO it is 35 and 67, in PLO5 45 and 87, in PLO6 55 and 108 buy-ins. The lower the winrate and the longer the sample, the deeper the worst downswing.
The standard deviation in PLO 6-max is about 140 bb/100 versus 90 in NLH, about 170 in PLO5 and 200 in PLO6. Since downswings and the required bankroll scale with σ², PLO needs roughly 2.5 times the bankroll of Hold'em at the same winrate, and PLO6 about 5 times.
By the risk-of-ruin formula at 5 bb/100 and 5% risk: NLH — 24 buy-ins, PLO — 59, PLO5 — 87, PLO6 — 120. That is the minimum for an unlimited sample with a known winrate; in practice keep a margin: 30–50 buy-ins in Hold'em and 80–150 in Omaha.
Winrate is the average profit in big blinds per 100 hands after rake. σ (Std Dev bb/100) is the standard deviation of the result per 100 hands, the measure of variance; your tracker reports it. The calculator needs both; σ defaults to a typical value for the game.
To be 95% confident that a 5 bb/100 winrate is above zero you need about 88,000 hands in NLH, 212,000 in PLO, 313,000 in PLO5 and 433,000 in PLO6. At 2.5 bb/100 the numbers grow fourfold. The calculator shows the confidence interval of your observed winrate.
For a winning player at 5 bb/100: NLH — 4%, PLO — 13%, PLO5 — 18%, PLO6 — 21%. After 50,000 hands the chances roughly double: 11%, 21%, 26% and 29%. In cash games this chance is exact from the normal distribution.
In cash games the result of a 100-hand block is close to normal, so outcomes are symmetric: the median equals the mean and downswings are counted in 100 bb buy-ins. In MTTs profit comes from rare deep runs, the distribution is skewed and downswings in buy-ins are several times larger. Tournaments have their own MTT variance calculator.
No. The winrate is entered after rake; to include rakeback, add it to the winrate (at 5 bb/100 rake and 30% rakeback that is +1.5 bb/100). Moving up, tilt and a winrate that drops during a downswing are not modelled — so keep a margin.