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Poker Variance Simulator: Confidence Intervals and Risk of Ruin
Last Updated: March 1, 2026
A poker variance simulator projects your expected results over thousands of hands or sessions, displaying confidence intervals and risk-of-ruin probabilities. Enter your win rate, standard deviation, and volume below to see the statistical range of outcomes and determine whether your bankroll can withstand normal downswings.
Last Updated: March 2026
Key Takeaways
- Variance is the gap between your expected results and actual results over any sample — it shrinks with volume but never disappears.
- A 5 bb/100 winner needs 30,000-50,000 hands before their results reliably reflect their skill level.
- Standard deviation in NL Hold’em cash games typically ranges from 60-100 bb/100, dwarfing even strong win rates.
- Risk of ruin drops exponentially with bankroll size — 20 buy-ins carries 5-10% ruin risk, 50 buy-ins drops below 1%.
- Cross-reference your variance range with bankroll management guidelines to set appropriate stop-losses and stake levels.
How Large Are Normal Downswings?
Downswings are losing stretches measured in buy-ins or big blinds. Every poker player experiences them regardless of skill. The question is not whether downswings will occur, but how deep and how long they last.
The table below shows expected maximum downswing depth for a 5 bb/100 winner at NL Hold’em 6-max (standard deviation ~75 bb/100) over various sample sizes:
| Hands Played | Expected Max Downswing (bb) | In Buy-Ins (100bb) | Probability of 10+ BI Downswing | Probability of 20+ BI Downswing |
|---|---|---|---|---|
| 10,000 | 600-900 | 6-9 | 15-20% | 2-4% |
| 25,000 | 900-1,400 | 9-14 | 30-40% | 8-12% |
| 50,000 | 1,200-1,800 | 12-18 | 45-55% | 15-22% |
| 100,000 | 1,500-2,200 | 15-22 | 60-70% | 25-35% |
| 250,000 | 1,800-2,800 | 18-28 | 75-85% | 40-50% |
These numbers are for a confirmed winner. A 5 bb/100 player who grinds 100,000 hands has a 25-35% chance of experiencing a 20+ buy-in downswing at some point during that stretch. This is not a sign of playing poorly — it is the mathematical reality of a game where standard deviation exceeds win rate by a factor of 15.
Why Does Standard Deviation Matter More Than Win Rate?
Standard deviation quantifies the spread of individual session results around your average. In NL Hold’em, a typical standard deviation is 60-100 bb/100 hands. Compare that to a strong win rate of 5 bb/100. The ratio reveals why short-term results are essentially noise.
At 75 bb/100 standard deviation and 5 bb/100 win rate, a single 1,000-hand session has a 95% confidence interval of roughly -42 bb/100 to +52 bb/100. Your 5 bb/100 edge is invisible within that range. Only after tens of thousands of hands does the win rate signal emerge from the variance noise.
Different game formats produce different standard deviations:
- NL Hold’em 6-max: 70-90 bb/100
- NL Hold’em full ring: 55-75 bb/100
- PLO 6-max: 120-180 bb/100
- Tournaments (per event): Extremely high — standard deviation in buy-ins can exceed 300% of the buy-in
PLO players face nearly double the standard deviation of Hold’em players, which is why bankroll requirements for Omaha are substantially higher. The simulator adjusts all projections based on your entered standard deviation.
How Many Hands Do You Need for Statistical Significance?
The confidence interval around your observed win rate narrows as sample size grows, following the formula: CI = ±1.96 × (SD / sqrt(hands/100)). For a player with 75 bb/100 standard deviation:
- 10,000 hands: 95% CI = ±14.7 bb/100 — your observed 8 bb/100 could actually be anywhere from -6.7 to +22.7.
- 50,000 hands: 95% CI = ±6.6 bb/100 — tighter, but a 3 bb/100 observation could still mean you are a loser.
- 100,000 hands: 95% CI = ±4.6 bb/100 — now a 5 bb/100 result likely means you are winning.
- 250,000 hands: 95% CI = ±2.9 bb/100 — strong confidence in your true rate.
Most recreational players never reach 50,000 hands at a single stake. This means the majority of poker players cannot statistically verify whether they are winners or losers. The simulator visualizes this uncertainty directly — enter your sample size and see how wide your confidence band actually is.
Our analysis of market pricing data on the Odds Reference dashboard demonstrates a similar principle: short-term price movements contain enormous noise, and extracting signal requires sufficient data points across time.
What Is Risk of Ruin and How Do You Calculate It?
Risk of ruin is the probability that a player’s bankroll reaches zero before recovering from a downswing. It depends on three variables: win rate, standard deviation, and bankroll size (in buy-ins).
The approximate formula for cash games is:
Risk of Ruin = e^(-2 × win_rate × bankroll / SD^2)
For a 5 bb/100 winner with 75 bb/100 SD at various bankroll levels:
- 15 buy-ins (1,500 bb): ~13.5% risk of ruin
- 20 buy-ins (2,000 bb): ~7.1% risk of ruin
- 30 buy-ins (3,000 bb): ~2.0% risk of ruin
- 50 buy-ins (5,000 bb): ~0.2% risk of ruin
The exponential relationship means each additional 10 buy-ins dramatically reduces ruin probability. Going from 20 to 30 buy-ins cuts risk by roughly two-thirds.
Tournament players face higher risk of ruin at identical bankroll levels because tournament standard deviation is significantly larger. Our tournament ROI calculator models the specific bankroll requirements for MTT grinders.
Can You Reduce Variance Without Reducing Win Rate?
Variance reduction strategies exist but involve tradeoffs. Shorter session lengths cap maximum single-session losses. Game selection toward softer tables increases win rate relative to standard deviation. Playing tighter in marginal spots reduces standard deviation slightly at the cost of some expected value.
The most effective variance reduction strategy is proper bankroll sizing — it does not reduce variance itself but eliminates the risk that variance destroys your bankroll. Players comparing online versus live poker should note that online multi-tabling increases total variance proportionally to the number of tables, even though per-table variance remains unchanged.
FAQ
Q: What is variance in poker?
A: Variance measures how widely your actual results deviate from your expected win rate over a given sample. High variance means large swings between winning and losing periods. A 5 bb/100 winner in NL Hold’em will experience sessions ranging from +30 bb/100 to -40 bb/100 due to normal statistical fluctuation. Variance is inherent to poker and cannot be eliminated — only managed through bankroll sizing.
Q: How many hands do I need to know my true winrate?
A: Cash game players need 50,000-100,000 hands minimum at a consistent stake to estimate their true win rate with reasonable confidence. Even at 100,000 hands, the 95% confidence interval spans roughly plus or minus 2 bb/100 around the observed rate. Tournament players need 500-1,000 events. Smaller samples tell you almost nothing about long-term expectation.
Q: Can a winning player have a losing month?
A: Yes, routinely. A solid 5 bb/100 winner playing 20,000 hands per month will have a losing month approximately 20-25% of the time. Over a year, 2-3 losing months is statistically normal. Even a 10 bb/100 crusher — an elite win rate — loses money roughly 10% of months at typical volume. Variance does not care about skill in the short run.
Q: What standard deviation should I use in the simulator?
A: Use your actual SD from tracking software if available (PokerTracker, Hand2Note). If you do not track, use these defaults: NL Hold’em 6-max: 75-85 bb/100, NL Hold’em full ring: 60-70 bb/100, PLO: 130-160 bb/100. Aggressive players tend toward the higher end; tight-passive players toward the lower end.
Q: Is running bad the same as playing bad?
A: No. Running bad means your results are below expectation due to statistical variance — unavoidable in any probabilistic game. Playing bad means making suboptimal decisions that reduce your expected value. The danger is conflating the two: a downswing often triggers tilt, which converts running bad into playing bad. The simulator helps you determine whether your results fall within normal variance bounds.