Roulette strategy · Martingale · the ceiling
The Martingale Against a £10,000 Table Maximum
Double after every loss and the next red puts you £100 up. Watch a doubling run from £100 meet a £10,000 table maximum on a single-zero wheel, then see what the run is worth on average. You watch; you do not play.
How a doubling run meets the table maximum
This section shows roulette visuals: a staking ladder, pockets from a simulated wheel and example bets. Are you 18 or over?
An explainer, not a game. Nothing can be staked or paid out here. 18+
The numbers for this step
Example run on a single-zero wheel at an example £10,000 table, even-money bets on red. The seven losing pockets are the first run of seven non-red results in a seeded spin sequence. Probabilities are exact fractions; the million-run check uses the same seeded generator.
Step by step
01A doubling run starts with £100 on red at a table with a £10,000 maximum.
The Martingale is a staking plan, not a way of changing the game. It starts with one even-money bet, here £100 on red at an example single-zero table whose maximum is £10,000 a spin. Red covers 18 of the 37 pockets. The plan only decides how much the next bet will be.
02After each loss the bet doubles, so the first red ends the run £100 up.
The rule is simple: after a loss, double the bet; after a red, stop. Because each bet is as large as all earlier losses together plus the first stake, the first red recovers everything and leaves a gain of exactly £100. That is why the plan looks safe. The problem is how quickly the bets grow.
03Four losses: £100, £200, £400 and £800, so £1,500 is down.
Suppose red does not come. The first four bets are £100, £200, £400 and £800, and all four lose. £1,500 has gone in to chase a £100 gain. The pockets shown under the bars are real draws from a seeded sequence of spins, the first stretch in it where seven spins in a row missed red.
04Three more lose: £1,600, £3,200 and £6,400. £12,700 is gone.
The run continues with £1,600, £3,200 and £6,400, and those lose too. After seven bets the total lost is £12,700, all of it staked to recover a gain of £100. Each bet on its own had the same chance as the first; the wheel does not know that a run of losses is under way.
05The eighth bet would be £12,800, above the £10,000 maximum: the table will not take it.
The plan now calls for £12,800, but the table maximum is £10,000. The bet cannot be placed, and the run ends here with £12,700 lost. The doubling rule depends on bets growing without limit, and every table has a limit. That ceiling is where the plan stops working as described.
06Seven non-red results in a row: (19/37)^7 = 0.94%, about 1 in 106 runs.
Nineteen of the 37 pockets are not red: the 18 black numbers and zero. The chance that seven spins in a row all miss red is 19/37 multiplied by itself seven times, 0.94%. That is roughly one run in every 106. Rare for a single run, but a player who repeats the plan many times will meet it.
07The other 99.06% of runs end £100 up.
In every other run red arrives within seven bets, and the run ends exactly £100 up, however long it took. So the plan produces many small gains and an occasional large loss. Whether that is worth it is a question of averages, and the next step weighs the two outcomes against each other.
0899.0584% × £100 − 0.9416% × £12,700 = −£20.52 per run, on average.
Weigh each outcome by its probability. The runs that end up contribute 99.0584% of £100, about £99.06. The runs that hit the maximum contribute 0.9416% of −£12,700, about −£119.58. Together that is −£20.52 per run. With the percentages rounded to two places the sum would show −£20.32, so the page carries four.
09Same figure from the edge: £759.38 staked in an average run × 1/37 = £20.52.
The same number comes out of the house edge. An average run stakes £759.38, because most runs stop after one or two bets. Every pound staked on red costs 1/37 on average, and £759.38 divided by 37 is £20.52. The plan changes how much is staked and when the losses come. It does not change the edge.
10A million seeded runs: 9,345 reach the maximum; average −£19.62 against an exact −£20.52.
As a last check the page plays the plan a million times with seeded spins. 9,345 runs, 0.93%, reached the maximum, against 0.94% expected, and the average result was −£19.62 per run against the exact −£20.52. The remaining gap is the random spread a million runs still leave, because each rare loss is so large.
11No staking system changes the house edge; it only changes when the losses arrive.
The Martingale, and every other staking plan, rearranges bets in time. It cannot alter the payouts or the number of pockets, so it cannot alter the 2.70% that the single zero takes from every pound staked on red. At high stakes the table maximum makes the trade-off sharper: frequent small gains, rare losses many times larger.
How the numbers are made
Example run on a single-zero wheel at an example £10,000 table, even-money bets on red. The seven losing pockets are the first run of seven non-red results in a seeded spin sequence. Probabilities are exact fractions; the million-run check uses the same seeded generator.