Why does Martingale fail with table limits?
Because the table maximum caps how many times you can double. A losing streak that reaches it costs far more than the series you won before it, and on average exactly enough to keep the house edge.
On red at a single-zero wheel, with a 10-chip base bet and a 1,000-chip maximum, you can lose 7 bets in a row (10 up to 640) before the next double is over the limit. That streak costs 1,270 chips and happens once every 106 series, each of which otherwise wins 10. Overall you lose 2.70% of every chip bet, the house edge.
Run these sessions in the simulatorRoulette odds for every bet
Martingale on red, 10-chip base bet, by table maximum
| Table maximum | Bets before the limit | Streak that hits it costs | Happens once every | Average per series |
|---|---|---|---|---|
| 100 | 4 | 150 | 14 series | −1.13 |
| 500 | 6 | 630 | 55 series | −1.74 |
| 1,000 | 7 | 1,270 | 106 series | −2.05 |
| 5,000 | 9 | 5,110 | 403 series | −2.71 |
| 10,000 | 10 | 10,230 | 784 series | −3.06 |
Exact. A series ends at the first win (+10 chips) or when the next double would pass the table maximum, after which the system starts over at 10. Average per series is the expected result in chips, with every bet a red bet on a single-zero wheel.
Why
With a 10-chip bet and a 1,000-chip maximum you can double only until the bet would pass the maximum. A streak that long is rare, but it costs the sum of every doubled bet, while each series you win pays just one base bet. A higher maximum or a bigger bankroll makes the disaster rarer and bigger in exactly the proportion that keeps the average loss on every chip bet at the house edge. Table limits aren’t what beats Martingale; they just set the size of the inevitable loss.