Triple Martingale Roulette Strategy

Rule and stake convention

The core rule is simple: start with one unitmoneyUnitThe base stake a system or a player works in. Progressions are described in units so they apply at any table.Read full →, multiply the next stake by three after a loss, and reset after a win. That gives 1, 3, 9, 27, 81, 243, 729 after uninterrupted losses; repeating a number would contradict tripling. For the two-dozenbetDozen1–12, 13–24 or 25–36, pays 2:1.Read full → example here, one displayed unit means one unit on each chosen dozen. Thus the opening round stakes two units total, not one.

Two-dozen payout table

Two disjoint dozens cover 24 European pocketsequipmentPocketOne of the 37 numbered compartments on the rotor. Also: slot, cup.Read full →. The stake columnbetColumnTwelve numbers in one vertical column of the layout, pays 2:1.Read full → is per component.

Worked example

Put one chipmoneyChipA token representing a fixed amount, placed on the layout to make a bet. Also: check.Read full → on the first dozen and one on the second. A 17 makes the second-dozen chip return three units including itself; after subtracting both chips, the net is +1. A 31 returns nothing and loses two. If the two-chip layoutequipmentLayoutThe printed betting grid on the table. Also: table, felt, cloth.Read full → is called a loss after 31, tripling the per-component stake makes the next layout 3 and 3, costing six total. Calling “one unit” the total instead would require a different allocation and different numbers.

Expectation and risk

At the one-per-component level, the expected result is (24 × 1 − 13 × 2) / 37 = −2/37 units. The 24/37 coverage is 64.865%, but coverage is not a guarantee of positive expected valuemathExpected valueThe average result per bet over the long run. −1/37 of the stake for every standard European bet.Read full →. Every loss triples total exposure: 2, 6, 18, 54, 162 and so forth under this convention. A single even-money interpretation has a different payoutmoneyPayoutWhat a winning bet returns, quoted as “X to 1” on top of the returned stake.Read full → and loss chance, so it must not be combined with the two-dozen arithmetic.

Questions