Model how a finite blackjack bankroll can reach zero under explicit assumptions. This simulator separates a planned-horizon depletion estimate from eventual risk of ruin; they answer different questions.
Probability model
Simulate bankroll depletion
Amounts are currency-neutral. Use one currency throughout.
Model output
Bankroll risk estimate
Seeded estimate
Bands describe the modeled finite-horizon probability; none means “safe.”
Modeled bankroll survival by horizon
Analytical Brownian survival approximation; the table is the accessible alternative to the bars.
| Hands | Survival approximation |
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Unit-size comparison
Bankroll, edge, per-hand SD in units and horizon stay constant. Only the money value of one unit changes.
| Scenario | Unit | Bankroll units | Finite-horizon approximation | Eventual approximation |
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Reproducible calculation summary
Run the simulation to generate a summary.
What this model calculates
Fixed-unit drift μ = player edge ÷ 100, in units per hand
Fixed-unit volatility σ = entered SD, in units per √hand
Expected result = μ × hands
Horizon SD = σ × √hands
Positive-drift eventual ruin ≈ exp(−2μB ÷ σ²)
Zero/negative-drift eventual ruin = 100% with unlimited continued play
The finite-horizon estimate uses arithmetic Brownian motion beginning at bankroll B. Each trial samples the horizon endpoint from a normal distribution. For a positive endpoint, a Brownian-bridge crossing test samples whether the continuous path touched zero earlier. A Wilson 95% interval quantifies only Monte Carlo sampling uncertainty.
Enter the edge from the player’s perspective
The sign matters. A game with a 0.50% house edge should be entered as −0.50% player edge. Entering +0.50% describes a player advantage instead; the default is an illustration of positive drift, not a claim that ordinary basic strategy earns that advantage. Use a positive value only when matching analysis supports it.
With a bankroll of 1,000, a unit of 10 and 10,000 hands, −0.50% gives an unconstrained expected result of −500. At +0.50%, the expected result is +500. With SD of 1.15 units per hand, the horizon SD is 1,150 in either case. The expected-result and SD fields describe the underlying process before stopping at zero; they are not the average or spread of final balances after bankrupt paths have been stopped.
Read zero estimates and survival correctly
If none of 1,000 trials reaches zero, the displayed estimate is 0%, but the Wilson 95% interval still extends to approximately 0.38%. That means a finite sample has not established an impossible event. More trials improve sampling precision; they cannot validate an assumed player edge or fix missing game details.
“Survival” means the modeled bankroll has not touched zero before the selected horizon. It does not mean the player finishes ahead, avoids every drawdown or has enough money for the table minimum and all possible splits. A path may touch zero and later have a positive unconstrained endpoint; the crossing test is designed to count that earlier depletion.
Keep the bankroll, unit, edge, SD, horizon, trial count and seed together when comparing runs. Compare one changed assumption at a time, and use the session planner separately for actual spending limits.
Assumptions and limitations
- Approximation: real blackjack changes in discrete hands; this model uses a continuous diffusion path and can cross zero between nominal hand times.
- Hand results are represented by constant drift and variance. Serial dependence, deck composition, penetration, rules, errors, wonging, expenses, table limits and bankroll withdrawals/replenishment are not modeled.
- The 1.15-unit SD default is a rounded conventional teaching value. Representative simulated blackjack variance is near 1.30 units² per hand, whose square root is about 1.14; use matching game-specific data when available.
- A true card-counting betting spread does not determine EV and SD by itself. Variable-bet mode therefore accepts independently calculated expected profit and SD per 100 hands.
- The eventual formula is a Brownian infinite-horizon approximation. For positive drift it assumes constant parameters and unlimited play; for zero or negative drift it is 100% under those assumptions.
- The confidence interval reflects finite trial count, not uncertainty in your edge, SD or the Brownian model.
- No output promises profit, success, safety or a bankroll that will last.
Finite horizon is not eventual ruin
“Touched zero within 10,000 hands” is a bounded-time question. “Ever reaches zero if play continues” is unlimited. With zero or negative expectation, the second answer is 100% for a finite bankroll even when the selected-horizon estimate is much smaller.
Use the right tool for the question
This simulator estimates probability under a statistical model. The Bankroll & Session Planner handles budgets, limits and planned exposure; it does not estimate risk of ruin. For counting play, obtain EV and SD from a game-specific simulator before using variable-bet mode; a spread alone is insufficient. See the card-counting guide for the separate strategy context.
Sources checked 30 August 2026
- Wizard of Odds: simulated variance and covariance for representative blackjack rules
- Fields Institute course notes: first-passage time for Brownian motion with drift
- NIST: binomial confidence limits and boundary limitations of symmetric normal intervals
- NIST: Wilson binomial-proportion confidence interval method