The Two Numbers That Define Your Results
Cash game variance is governed by two parameters:
Win rate (bb/100)
Your expected profit per 100 hands, measured in big blinds. A winning player at NL50 might have a 5 bb/100 win rate, meaning they expect to earn 5 big blinds ($2.50) per 100 hands on average.
Standard deviation (bb/100)
The spread of your results around that average. A typical SD for 6-max NLH is 75-95 bb/100.
At common win rates and standard deviations, the SD is 15-20x larger than the win rate, which means short-term results are dominated by noise.
What Variance Looks Like: Simulated Examples
Example 1: Solid Winner at NL50
Parameters: 5 bb/100 win rate, 80 bb/100 SD, 100,000 hands
Expected profit: 5,000 bb ($2,500)
The simulated distribution:
| Percentile | Result (bb) | Result ($) |
|---|---|---|
| 5th | +1,850 | +$925 |
| 25th | +3,700 | +$1,850 |
| 50th (median) | +5,000 | +$2,500 |
| 75th | +6,300 | +$3,150 |
| 95th | +8,150 | +$4,075 |
At the 5th percentile, you earn less than half your expected value. That falls within normal statistical variation: one in twenty 100K-hand stretches will produce this result or worse.
Example 2: Breakeven Player at NL100
Parameters: 0 bb/100 win rate, 85 bb/100 SD, 50,000 hands
Expected profit: 0
| Percentile | Result (bb) | Result ($) |
|---|---|---|
| 5th | -3,950 | -$3,950 |
| 25th | -1,620 | -$1,620 |
| 50th | 0 | $0 |
| 75th | +1,620 | +$1,620 |
| 95th | +3,950 | +$3,950 |
A breakeven player can easily find themselves up or down 40 buy-ins over 50,000 hands. That range is the expected distribution for a player with zero edge, no downswing or upswing required.
Example 3: Small Winner at NL200
Parameters: 3 bb/100 win rate, 90 bb/100 SD, 200,000 hands
Expected profit: 6,000 bb ($12,000)
| Percentile | Result (bb) | Result ($) |
|---|---|---|
| 5th | +2,680 | +$5,360 |
| 25th | +4,580 | +$9,160 |
| 50th | +6,000 | +$12,000 |
| 75th | +7,420 | +$14,840 |
| 95th | +9,320 | +$18,640 |
Even over 200,000 hands, the range of outcomes varies by a factor of nearly 4x between the 5th and 95th percentiles.
Downswing Probabilities
The most feared aspect of variance is the downswing: a sustained period of results below expectation. Here is how likely they are:
5 bb/100 Winner, 80 bb/100 SD
| Downswing Size | Probability in 100K Hands | Expected Duration |
|---|---|---|
| 5 buy-ins | 85% | Will happen multiple times |
| 10 buy-ins | 45% | Common; expect at least one |
| 15 buy-ins | 18% | Roughly one in five 100K stretches |
| 20 buy-ins | 7% | One in fourteen stretches |
| 30 buy-ins | 1% | Rare but real |
2 bb/100 Winner, 85 bb/100 SD
| Downswing Size | Probability in 100K Hands | Expected Duration |
|---|---|---|
| 5 buy-ins | 92% | Will happen many times |
| 10 buy-ins | 65% | More likely than not |
| 15 buy-ins | 38% | Roughly one in three stretches |
| 20 buy-ins | 20% | One in five stretches |
| 30 buy-ins | 5% | Uncommon but not rare |
If your win rate is small relative to your standard deviation, which it almost always is, multi-buy-in downswings are routine.
The Rake Factor
Rake is a constant drag on your win rate, and it amplifies the impact of variance.
A player with a 5 bb/100 pre-rake win rate at a room charging 3 bb/100 effective rake has a 2 bb/100 post-rake win rate. The standard deviation stays the same (around 80 bb/100), but the ratio of SD to win rate jumps from 16:1 to 40:1.
This means the lower-rake room is not just saving you 3 bb/100 in direct costs; it is fundamentally changing your variance profile. A 5 bb/100 winner at a low-rake room experiences the variance profile of a solid winner. The same player at a high-rake room experiences the variance profile of a marginal winner.
Use the rake calculator to see the exact rake difference at your stakes across every major room.
Standard Deviation Benchmarks by Game Type
Your actual SD depends on your playing style and the game format:
| Game Type | Tight SD | Average SD | Aggressive SD |
|---|---|---|---|
| 6-Max NLH | 65-75 | 75-85 | 85-100 |
| Full Ring NLH | 55-65 | 65-75 | 75-85 |
| 6-Max PLO | 130-155 | 155-180 | 180-220 |
| Heads-Up NLH | 100-120 | 120-140 | 140-170 |
PLO players face roughly twice the variance of NLH players at equivalent stakes, which changes bankroll requirements, downswing expectations, and the sample size needed to evaluate results.
How Many Hands to Know Your Win Rate
One of the most important applications of variance math is understanding when your results become meaningful.
| Win Rate | SD | Hands for +/- 2 bb/100 (95% CI) |
|---|---|---|
| 5 bb/100 | 80 | ~246,000 |
| 3 bb/100 | 80 | ~246,000 |
| 1 bb/100 | 80 | ~246,000 |
The sample size requirement does not depend on your win rate; it depends only on your standard deviation. This is because the confidence interval formula uses SD, not the mean.
At typical volume of 500 hands/hour single-tabling, 246,000 hands takes approximately 492 hours of play. For four-tabling, roughly 123 hours.
Most recreational players never reach statistically meaningful sample sizes. If you play 10 hours per week on a single table, it takes nearly a year to get a result that is accurate to +/- 2 bb/100.
Using This Data
The variance calculator at PrimeDope runs the same Monte Carlo engine that generated the data in this article. Enter your own win rate, standard deviation, and sample size to see your personal variance profile.
The cash bankroll simulator takes it further: it simulates thousands of complete bankroll trajectories to show your probability of going broke, reaching a target, or sustaining a specific stake.
Understanding variance lets a serious player interpret results accurately instead of making decisions based on noise.
Run your own variance simulation with your actual win rate and standard deviation.
Open Variance Calculator