Martingale across 100,000 reproducible sessions

Martingale produces a persuasive session history: frequent small recoveries, a high chance of reaching a modest target, and losses that arrive in a different shape. The result below measures that shape without changing seeds after an inconvenient outcome.

Method

We ran 100,000 European-wheel sessions. Every session began with $1,000, wagered $5 on red, doubled after a loss, and reset to $5 after a win. A session stopped at +$100, after 250 spins, or when the next required wager exceeded the bankroll or $500 table maximum. Session seeds came from one published master seed and the same two-stage generator used by Engineer mode.

Master seed

0x6d21683b

Wheel

European single-zero

Bankroll / unit

$1,000 / $5

Exit rules

+$100 target; 250-spin cap; $500 table maximum

What the high success rate leaves out

The target rate was 82.85%. Taken alone, that number makes the system look effective. The cost is concentrated in the other 17.15%: the next double no longer fit inside the bankroll. Median terminal bankroll was $1,100, while the mean fell to $981.77. That gap is the tail doing its work. Many sessions banked $100; fewer sessions surrendered enough to pull the average below the starting balance.

Limitations

This is a stopping-rule experiment, not a claim about every possible Martingale. A larger bankroll or table maximum moves the breaking point; it does not remove it. The test models independent, fair spins and ignores casino operating constraints beyond one table maximum. It also calls a progression broken when the prescribed next wager cannot be placed, even if cash remains. That is the correct failure definition for the strategy, but it is not the same as a literal zero balance.