iGaming Journalist & Crypto Casino Analyst
Poker risk of ruin — the probability that a player with a genuine long-term edge still loses an entire bankroll before that edge materialises — is the single most misunderstood number in the game. To quantify it, we ran a Monte Carlo simulation of 40,000 independent poker careers per scenario, tracking every 100-hand block across 100,000 hands. The results below cover bust probability by bankroll depth, expected downswing severity, the sample size required to know your own win rate, and how much deeper a high-variance format like Pot-Limit Omaha needs to be rolled.
Key Findings
A 3 bb/100 winner with a 40 buy-in bankroll busts 2.4% of the time over 100,000 hands. That same player should expect a median peak-to-trough downswing of 2,275 big blinds — nearly 23 buy-ins — and has a 14.5% chance of finishing 100,000 hands in the red. Raising standard deviation from 90 to 140 bb/100 lifts risk of ruin at 40 buy-ins from 2.4% to 16.7%. Confirming a 3 bb/100 win rate at 95% confidence takes roughly 346,000 hands.
The Inputs: What Real Poker Variance Looks Like
Every simulation is only as good as its parameters, so we anchored ours to observed ranges from tracking-database analysis rather than inventing figures.
Standard deviation in online 6-max No-Limit Hold'em typically runs 90–110 bb/100, with the wider bracket across all styles spanning roughly 70–100 bb/100. Style matters: a tight, low-variance grinder may sit at 50–70 bb/100, while an aggressive player who three-bets wide and runs large bluffs pushes 90–120 bb/100. Pot-Limit Omaha runs dramatically higher, commonly around 140 bb/100.
Win rates, by contrast, are small. A strong online cash game player might win at 4 bb/100. That produces the defining feature of poker as a game: the noise is more than twenty times larger than the signal. Chess and Go have nothing comparable. The entire discipline of bankroll management exists to survive that ratio.
| Player Profile / Format | Typical Standard Deviation (bb/100) |
|---|---|
| Tight, low-variance NLHE grinder | 50–70 |
| Online 6-max NLHE, general range | 70–100 |
| Online 6-max NLHE, typical | 90–110 |
| Aggressive high-3bet NLHE style | 90–120 |
| Pot-Limit Omaha | ~140 |
Risk of Ruin by Bankroll Size: The Core Data
The table below is the primary output of our simulation. Each cell reports the percentage of 40,000 simulated careers that hit zero at any point during 100,000 hands, given a starting bankroll measured in 100 big blind buy-ins and a standard deviation of 90 bb/100.
| True Win Rate | 10 buy-ins | 20 buy-ins | 30 buy-ins | 40 buy-ins | 50 buy-ins | 100 buy-ins |
|---|---|---|---|---|---|---|
| 1 bb/100 | 61.3% | 35.4% | 18.7% | 9.1% | 4.0% | <0.1% |
| 2 bb/100 | 51.7% | 25.6% | 11.8% | 4.7% | 1.8% | <0.1% |
| 3 bb/100 | 42.0% | 17.4% | 6.7% | 2.4% | 0.8% | <0.1% |
| 5 bb/100 | 26.5% | 7.3% | 2.0% | 0.5% | 0.1% | <0.1% |
| 8 bb/100 | 12.4% | 1.7% | 0.2% | <0.1% | <0.1% | <0.1% |
Three conclusions fall straight out of this grid.
The popular "20 buy-in" rule is dangerous for anyone who is not crushing. A 2 bb/100 winner — a perfectly respectable result at mid stakes — busts a 20 buy-in roll more than a quarter of the time. That is not a tail risk; it is a coin flip's worth of career-ending outcomes stacked into one season.
Bankroll requirements scale inversely with win rate, and steeply. Halving your edge from 4 bb/100 to 2 bb/100 roughly doubles the bankroll needed for the same bust probability. This is why moving up stakes is dangerous even when you are technically a winner at the higher level: your edge shrinks against tougher opposition while your buy-in size grows.
Beyond about 50 buy-ins, ruin risk collapses toward zero. The marginal safety bought by the 51st through 100th buy-in is tiny. Once you clear roughly 50 buy-ins for a solid win rate, additional bankroll is better deployed as stake mobility than as insurance.
Bankroll Required for a Target Risk of Ruin
The simulation above answers "how risky is this bankroll?" The inverse question — "how big must my bankroll be?" — has a closed-form answer. For a player with win rate μ and standard deviation σ per 100 hands, lifetime risk of ruin for a bankroll B is approximately e^(−2Bμ/σ²). Solving for B gives the table below, in 100 bb buy-ins, at σ = 90 bb/100.
| True Win Rate | For 5% ruin risk | For 1% ruin risk | For 0.1% ruin risk |
|---|---|---|---|
| 1 bb/100 | 121 buy-ins | 187 buy-ins | 280 buy-ins |
| 2 bb/100 | 61 buy-ins | 93 buy-ins | 140 buy-ins |
| 3 bb/100 | 40 buy-ins | 62 buy-ins | 93 buy-ins |
| 4 bb/100 | 30 buy-ins | 47 buy-ins | 70 buy-ins |
| 5 bb/100 | 24 buy-ins | 37 buy-ins | 56 buy-ins |
| 8 bb/100 | 15 buy-ins | 23 buy-ins | 35 buy-ins |
The lifetime formula is more conservative than our 100,000-hand simulation because it assumes an infinite horizon — given unlimited time, more careers eventually touch zero. Use the simulation numbers to reason about a season; use the formula to reason about a career.
The Pot-Limit Omaha Adjustment
Because risk of ruin depends on the square of standard deviation, moving from NLHE's 90 bb/100 to PLO's 140 bb/100 does not increase bankroll requirements by 56% — it increases them by roughly 142%. At a 3 bb/100 win rate, a 5% lifetime ruin target requires 40 buy-ins in Hold'em and 98 in Omaha. At 5 bb/100 it is 24 versus 59.
| Win Rate | NLHE (σ=90), 1% ruin | PLO (σ=140), 1% ruin |
|---|---|---|
| 2 bb/100 | 93 buy-ins | 226 buy-ins |
| 3 bb/100 | 62 buy-ins | 150 buy-ins |
| 5 bb/100 | 37 buy-ins | 90 buy-ins |
Downswing Depth: What Losing Actually Looks Like
Ruin is the extreme case. Far more common — and far more damaging to the average player's decision making — is the ordinary downswing. Our simulation tracked the maximum peak-to-trough drawdown across each 100,000 hand career with unlimited bankroll, isolating pure variance from bust risk.
| True Win Rate | Median Max Downswing | 95th Percentile Downswing | Chance of Losing Over 100k Hands | 5th–95th Percentile Result |
|---|---|---|---|---|
| 0 bb/100 (breakeven) | 3,171 bb | 6,280 bb | 50.3% | −4,706 to +4,672 bb |
| 1 bb/100 | 2,789 bb | 5,582 bb | 36.0% | −3,683 to +5,702 bb |
| 2 bb/100 | 2,504 bb | 4,938 bb | 23.9% | −2,633 to +6,736 bb |
| 3 bb/100 | 2,275 bb | 4,390 bb | 14.5% | −1,654 to +7,704 bb |
| 5 bb/100 | 1,919 bb | 3,571 bb | 4.0% | +297 to +9,657 bb |
| 8 bb/100 | 1,562 bb | 2,718 bb | 0.3% | +3,294 to +12,693 bb |
Read the 3 bb/100 row carefully, because it describes a genuinely good regular. Half of all such players will endure a downswing of at least 22.75 buy-ins during 100,000 hands. One in twenty will endure 43.9 buy-ins. Roughly one in seven will play the entire 100,000 hand stretch — a full year of serious volume for most players — and end it with less money than they started with, while playing well the whole time.
The 5th-to-95th percentile column is the number most players find hardest to accept. That same 3 bb/100 winner has a plausible outcome range spanning more than 9,300 big blinds. At NL200, that is a $18,700 spread between reasonable good luck and reasonable bad luck over a single year. The expected value of the year is 3,000 bb; the noise around it is three times larger.
How Standard Deviation Changes the Picture
Holding win rate at 3 bb/100 and bankroll at 40 buy-ins, we varied only standard deviation:
| Standard Deviation | Risk of Ruin | Median Max Downswing | 95th Pct Downswing | Chance of Losing Year |
|---|---|---|---|---|
| 60 bb/100 (tight) | <0.1% | 1,329 bb | 2,496 bb | 5.7% |
| 90 bb/100 (typical NLHE) | 2.5% | 2,277 bb | 4,416 bb | 14.7% |
| 110 bb/100 (aggressive) | 7.2% | 2,935 bb | 5,728 bb | 19.4% |
| 140 bb/100 (PLO) | 16.7% | 3,931 bb | 7,761 bb | 24.9% |
Identical win rate, identical bankroll, and bust probability moves from effectively zero to one in six. Style is a bankroll decision, not just a strategic one. This is also why the choice between a GTO or exploitative approach has financial consequences beyond expected value — high-variance exploitative lines that maximise EV against weak opposition also widen the distribution around it.
Sample Size: How Long Until You Know Your Own Win Rate?
Because standard deviation dwarfs win rate, observed results converge on the truth extremely slowly. We simulated 200,000 samples at each volume for a player whose true win rate is 3 bb/100 with σ = 90.
| Hands Played | Chance of Showing a Loss | 95% Confidence Interval on Observed Win Rate |
|---|---|---|
| 1,000 | 45.9% | −52.8 to +58.8 bb/100 |
| 5,000 | 40.7% | −21.9 to +27.9 bb/100 |
| 10,000 | 37.2% | −14.6 to +20.6 bb/100 |
| 25,000 | 30.1% | −8.2 to +14.2 bb/100 |
| 50,000 | 22.8% | −4.9 to +10.9 bb/100 |
| 100,000 | 14.7% | −2.6 to +8.6 bb/100 |
| 250,000 | 4.8% | −0.5 to +6.5 bb/100 |
| 500,000 | 1.0% | +0.5 to +5.5 bb/100 |
| 1,000,000 | <0.1% | +1.2 to +4.8 bb/100 |
At 100,000 hands — a volume most recreational players never reach — a true 3 bb/100 winner still cannot statistically distinguish themselves from a losing player at 95% confidence. The interval only excludes zero somewhere past 250,000 hands. Expressed directly, the hands required for a 95% confidence interval to exclude zero are:
- 8 bb/100 winner: approximately 48,620 hands
- 5 bb/100 winner: approximately 124,468 hands
- 3 bb/100 winner: approximately 345,744 hands
- 2 bb/100 winner: approximately 777,924 hands
- 1 bb/100 winner: approximately 3,111,696 hands
The practical implication is that results-based self-assessment is almost useless at realistic volumes. Players who want a faster read on whether they are actually good should evaluate decision quality rather than outcomes — reviewing hands against solver output or equity calculations converges far faster than the money does. Our equity calculator and strategy library are built for exactly that kind of process-based review, and newer players will find the foundations in our beginner course.
Tilt as a Bankroll Variable
One finding deserves emphasis because it reframes tilt control as a mathematical rather than merely psychological concern. Applying the lifetime formula to a 40 buy-in bankroll at σ = 90, a player winning at 4 bb/100 carries a 1.9% risk of ruin. Degrade that win rate to 1 bb/100 — a modest deterioration by the standards of what actually happens to people on bad days — and risk of ruin climbs to 37.2%.
A three big blind reduction in win rate multiplies lifetime bust probability roughly twentyfold. And that estimate is conservative, because tilted play typically also raises standard deviation through larger average pot sizes and looser continuation, compounding the effect through both terms of the formula simultaneously. Within our 100,000 hand simulation the same shift moves ruin from 0.5% to 9.1% — an eighteenfold increase over a single year of volume.
Methodology
We simulated poker careers as sequences of 100-hand blocks, with each block's result drawn from a normal distribution parameterised by the scenario's win rate (mean) and standard deviation. Each scenario used 40,000 independent trials of 1,000 blocks, or 100,000 hands per career. The simulation was written in Python using NumPy's PCG64 generator with a fixed seed (20260820) for reproducibility.
Risk of ruin was recorded when a career's running equity touched or fell below zero at any block boundary. Maximum drawdown was computed as the largest peak-to-trough decline in cumulative result across the full career, using a running maximum, with bankroll set effectively unlimited to isolate variance from bust risk. Sample-size confidence intervals used 200,000 draws per volume level, cross-checked against the analytic result μn ± 1.96σ√n.
Closed-form bankroll requirements use the standard continuous approximation for lifetime risk of ruin, RoR = e^(−2Bμ/σ²), with B, μ, and σ expressed in big blinds per 100 hands. Cells reported as "<0.1%" reflect zero or near-zero occurrences within 40,000 trials and should be read as an upper bound, not an exact value.
Two limitations apply. First, the normal approximation is excellent at the 100-hand block level by the central limit theorem, but real poker results have fatter tails at the individual-hand level. Second, the model assumes a constant win rate and standard deviation, whereas real players face changing game conditions, table selection effects, and their own form. Neither limitation materially changes the ordering or magnitude of the results, but both mean the figures should be treated as well-calibrated benchmarks rather than precise predictions for any individual.
Frequently Asked Questions
What is risk of ruin in poker?
Risk of ruin is the probability that a player loses their entire bankroll despite having a positive long-term expectation. It depends on three variables: bankroll size, win rate, and standard deviation. It rises steeply as win rate falls and rises with the square of standard deviation, which is why high-variance formats require disproportionately deeper bankrolls.
How many buy-ins do I need for cash games?
It depends entirely on your win rate. Our simulation shows a 5 bb/100 winner needs about 24 buy-ins for a 5% lifetime ruin risk, while a 2 bb/100 winner needs 61 and a 1 bb/100 winner needs 121. For most solid mid-stakes regulars, 40–50 buy-ins of 100 big blinds is a defensible target. The common 20 buy-in guideline is only safe for players winning well above 5 bb/100.
How big is a normal poker downswing?
Larger than most players expect. A 3 bb/100 winner with standard deviation of 90 bb/100 faces a median maximum downswing of 2,275 big blinds — roughly 23 buy-ins — over 100,000 hands, with a 5% chance of exceeding 4,390 big blinds. Breakeven players face a median maximum drawdown above 3,100 big blinds.
How many hands do I need to know my true win rate?
Roughly 346,000 hands to confirm a 3 bb/100 win rate at 95% confidence, and around 124,000 hands for a 5 bb/100 win rate. At 100,000 hands, a true 3 bb/100 winner's confidence interval still spans −2.6 to +8.6 bb/100 — it does not exclude zero. Process-based review converges far faster than results.
Why does PLO need a bigger bankroll than Hold'em?
Because bankroll requirements scale with the square of standard deviation. PLO typically runs around 140 bb/100 versus roughly 90 bb/100 for NLHE, so the same win rate needs about 2.4 times the bankroll. A 3 bb/100 winner needs 62 buy-ins for 1% ruin risk in Hold'em but 150 buy-ins in Omaha.
Sources
- PrimeDope — The Ultimate Guide to Poker Variance
- PrimeDope — Cash Game Variance Calculator
- PrimeDope — Examples and Impacts of Variance in Cash Games
- PokerCharts — Variance Calculator, Confidence Cones and Risk of Ruin
- VIP-Grinders — Variance in Poker
- NumPy — Random Generator documentation (simulation engine)
Cite This Article
If you use data from this article, please link back to https://www.deucescracked.com/blog/poker-risk-of-ruin-variance-simulation-study. Suggested citation: DeucesCracked Editorial, "Poker Risk of Ruin Study: 40,000 Simulated Careers," DeucesCracked, August 2026. All simulation outputs on this page are original to DeucesCracked and free to reproduce with attribution.
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