Grand Martingale: the extra unit adds up

Grand Martingale doubles the stake after a loss and adds one starting unit. A win returns the next stake to one unit. That extra unit makes the sequence grow faster than ordinary Martingale.

A complete loss-and-recovery path

With one-chip units, the first stakes are 1, 3, 7, 15 and 31. Four losses consume 26 chips. If the fifth bet wins at 1 to 1, its 31-chip profit leaves five chips of net profit across the cycle. The apparent improvement comes from risking more chips at every step.

A 100-chip budget can fund losses of 1+3+7+15+31=57, but cannot fund the next 63-chip bet with only 43 left. The failure condition is an unaffordable required stake, even though the wallet still holds chips.

Compare equal starting conditions

Ordinary Martingale reaches 1, 2, 4, 8, 16 over the same first five bets. Grand Martingale reaches 1, 3, 7, 15, 31. Comparing the systems by their cycle profit alone hides the difference in exposure. Keep bankroll, unit, table maximum and spin sequence identical when comparing them.

The audited native catalog contains a named Grand Martingale plan using double-plus-one after losses. It is separate from the legacy capped Martingale template. Our arithmetic uses the named rule; a manually capped version needs its cap and reset behavior stated separately.

What the additional stake changes

On a fair European wheel, red still wins on 18 of 37 pockets at every step. The larger wager scales both possible profit and possible loss. It does not alter the pocket probabilities. Check the bankroll and table-limit explanation before tracing a longer sequence, or use the Martingale calculator for the ordinary doubling baseline.