Monte Carlo Bankroll Sim

Why simulated paths beat closed-form ruin formulas

A textbook risk-of-ruin equation hands you one number. That number assumes unlimited playtime and says nothing about what your bankroll chart actually looks like along the way — how far below starting balance you’ll travel before recovering, or how quickly zero can arrive on an ugly stretch of cards.

Simulation replaces that single estimate with a crowd of outcomes. The tool projects thousands of independent random walks under your own inputs, then draws the lucky road, the median road, and the miserable one. You see the terrain before you walk it with real money.

Inside the simulation engine: three moving parts

Each trial mimics real gambling conditions using three core components:

1. Dynamic path generation

Every session begins at your initial bankroll and steps through $N$ individual bets. At each step the tool rolls a random result weighted by your expected value (EV) and volatility inputs:

Bankroll_t = Bankroll_{t-1} + Net_Result

Touch zero or dip below it? That path stops cold and gets logged as a **ruin** event.

2. The Box-Muller transform for normal distribution

Flat random numbers don’t look like gambling results; bell curves do. The **Box-Muller Transform** converts two independent uniform draws into normally distributed values so large swings cluster exactly the way casino math expects:

Z = √(-2 * ln(U1)) * cos(2 * π * U2)

Here U1 and U2 are independent uniforms between 0 and 1, and Z is the resulting standard normal variable.

3. Percentile bands (P10, P50, P90)

Once all paths finish, the final bankrolls are sorted and three boundaries get flagged:

• P90 (Best Case): Only 10% of runs finished above this line. A fortunate run that outperformed expectation.
• P50 (Median Case): Half of all sessions ended above, half below. Treat this as your baseline expectation.
• P10 (Worst Case): The bottom decile. This is the downswing magnitude you must survive financially and emotionally.

Data Sandwich: Blackjack downswings in action

Concrete numbers help. Picture a card counter holding $10,000, playing with a 1.0% edge at $50 per unit, planning 1,000 hands.

Naive arithmetic promises 1,000 * ($50 * 1.0%) = $500 in profit.

Then reality shows up wearing a normal distribution. Blackjack’s per-hand standard deviation sits near 1.15 units, so across 1,000 hands the P10 line routinely falls more than -$3,500 below start — and roughly 12% of the 5,000 simulated paths hit absolute zero before hand 1,000.

Drop the unit to $20 and everything changes: ruin probability falls under 0.5%, and the P10 line finishes above water. Run both scenarios yourself. The gap between them is your risk threshold.

Frequently asked questions