Grand Martingale Roulette Strategy

Steps and formula

Pick an even-money betbetEven-money betRed/black, odd/even, high/low. 18 numbers, pays 1:1.Read full → and a base b. Begin with b; after a loss stake twice the just-lost amount plus b, and reset to b after a win. For b = 1, the stakes are 1, 3, 7, 15, 31, 63, 127, 255, 511. The nth stake is 2^n − 1 unitsmoneyUnitThe base stake a system or a player works in. Progressions are described in units so they apply at any table.Read full →. A winning n-th wager produces n units net for the whole run, rather than a constant one-unit recovery.

Growth table

Cumulative loss is the amount gone before placing the listed next wager.

Worked example

After losses at 1, 3, and 7, 11 units have been lost. A 15-unit win returns 30 units including the winning stake. Subtracting the total 26 units wagered gives +4, which agrees with 15 − 11. If that 15-unit bet loses instead, cumulative losses become 26 and the next stake is 31. Gross return and net profit must not be treated as the same figure.

Expectation and bankroll risk

An even-money wager loses on 19 of 37 single-zerowheelZeroThe single green pocket that no even-money, dozen or column bet covers; the source of the house edge. Also: single zero, 0.Read full → outcomes. With a 1,000-unit bankrollmoneyBankrollThe total amount set aside for play. Bankroll management is deciding how much of it to risk per bet and per session.Read full →, losses through the 255-unit eighth wager have cost 502, leaving 498. That is not bankruptcy, but it is insufficient for the next 511-unit stake; having enough to make it from the start would require 1,013 units. Increasing bankroll merely postpones the boundary because the required stakes approximately double each loss. Each unit exposed still has expected lossmathExpected lossExpected value times total amount wagered; the average amount lost over a session or a period.Read full → 1/37 on a European wheel.

Questions