Roulette martingale simulator

Doubling on red is the textbook martingale. This simulates it on a European wheel (18 red of 37 pockets), preloaded with a $1,000 bankroll and a $10 base bet. Add a table maximum under Advanced to see the wall every real casino puts in the ladder’s way.

Scenario

Current game: Roulette · red (EU) — each round wins with probability 48.65%, paying 1 to 1.

Drag this first. It changes the conclusion more than anything else on the page.

Advanced — win chance, payout, push, table limits, seed

Rounds are capped at 100,000.

16.8% of sessions finish ahead — typically by $2,410.

88.5% run out of bankroll or can no longer place the next required bet, typically down $530.

Across all 50,000 simulated sessions the expectation is −$166.

Estimated from 50,000 simulated sessions and still converging. Figures carry a margin of error that narrows as the run completes.

startmedian · mean
Ending bankroll. Grey shows flat betting on the same scenario. Estimated by simulation.

Expected versus typical

Expected ending bankroll
$834

The average across every simulated session (−$166).

Typical ending bankroll
$500

What the middle session experienced (−$500).

These differ because the distribution is lopsided. The average is pulled by outcomes that occur rarely; the median describes the session in the middle.

Preparing sample paths…

Outcomes

Finish ahead
16.8%
Finish behind
83.0%
Bankroll exhausted
0.7%

Could not place even the minimum bet.

Strategy could not continue
87.8%

The next required bet exceeded the bankroll or the table maximum, with money still left.

Full detail — percentiles, risk metrics, and the exact figures

Distribution of ending bankroll

P1
$10
P5
$70
P25
$380
P50
$500
P75
$720
P95
$3,500
P99
$3,630

Risk

Average largest bet
$579
Median maximum drawdown
$1,270
Average longest losing streak
7
Average total wagered
$5,982

Exact figures

Computed in closed form. No simulation, no margin of error.

Expected loss per $100 wagered
$3
Fair payout for this win chance
1.0556 to 1
Break-even win chance at this payout
50.00%
Chance the next 10 resolved rounds all lose
0.13%
Chance of at least one 10-loss streak within 500 rounds
26.45%

A different question from the one above, and a much larger number.

Typical longest losing streak
8

95th percentile: 12.

The ladder against the wheel

Over 50,000 simulated sessions, 16.8% finish ahead and 88.5% cannot place the next doubled bet, typically down $530. The expected loss is $3 per $100 wagered — the single-zero wheel's 1/37, untouched by the progression. A typical session's longest losing streak is 8 spins; each loss doubles the required bet, and the ladder only has to hit one streak it cannot afford.

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