Blackjack Risk-of-Ruin Simulator

By Originally published

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 mode

Money reserved for blackjack, not essential funds.

Effective average unit used by your EV and SD inputs.

Positive, zero and negative values accepted. Enter 0.5 for 0.50%.

1.15 is a rounded conventional example, not a universal blackjack constant.

Whole number from 1 to 10,000,000.

1,000–100,000. More trials narrow simulation uncertainty but do not fix model error.

Whole number from 1 to 4,294,967,295. Same inputs and seed reproduce the estimate.

Model output

Bankroll risk estimate

Seeded estimate

Bankroll in betting units100 units
Expected result over horizon+500.00
Standard deviation over horizon1,150.00
Finite-horizon touch-zero estimate—
95% Monte Carlo confidence interval—
Eventual risk-of-ruin approximation—

Interpretation bandAwaiting simulation

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.

Probability bankroll has not touched zero
Hands Survival approximation

Unit-size comparison

Bankroll, edge, per-hand SD in units and horizon stay constant. Only the money value of one unit changes.

Half, selected and double unit
Scenario Unit Bankroll units Finite-horizon approximation Eventual approximation

Reproducible calculation summary

Run the simulation to generate a summary.

JavaScript is unavailable. The interactive simulation cannot run. The formulas, assumptions and long-run warning below remain available; do not treat the default display as a calculated result.

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.

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