Roulette betting system guide
Grand Martingale Roulette Strategy: How the 1-3-7-15 System Works
Grand Martingale doubles the previous losing stake and adds one more base unit. With a £1 starting unit, the sequence becomes £1, £3, £7, £15, £31 and £63 until a win resets the next bet to £1.
A later recovery win produces more profit than standard Martingale, but the required stake and cumulative loss also grow faster. The system does not change the probability of the next spin or roulette’s house edge.
A £1 Grand Martingale Sequence
The easiest way to understand the system is to separate the profit on the winning wager from the result of the complete sequence. In this example, the first three even-money bets lose and the fourth wins.
The winning £15 stake returns £30 in total, but £15 of that is the original wager being returned. The wager profit is £15. Subtract the £11 already lost and the final sequence result is +£4.
If the £15 wager also loses, the sequence is £26 down and the next required stake is £31. The increase in recovery profit is bought with a faster-growing stake ladder.
Check the Roulette Table Before Starting
Grand Martingale depends on the exact even-money minimum and maximum. Open the live game first and work backwards from those limits instead of assuming every table uses the same range.
Mr Jones
Check the current even-money minimum and maximum before setting a base stake.
Swift Casino
Compare the displayed wheel type and table limits before starting a progression.
7 Gold Casino
Confirm the current roulette table range can support each planned step.
18+. Terms apply. Affiliate links. Play responsibly.
What Counts as Grand Martingale?
Grand Martingale is a negative progression built around an even-money roulette bet. A loss increases the next stake. A win ends the sequence and returns the next wager to the original base unit.
The version used on this page
After every full loss, double the previous stake and add the original starting unit. If the base is £1, the sequence is £1, £3, £7, £15 and £31.
Why other ladders sometimes differ
Some descriptions add a fixed chip amount or delay the extra unit until a later step. Those rules create a different sequence. Every table and formula below uses the original base-unit version consistently.
- Choose one even-money selectionUse red or black, odd or even, or 1-18 or 19-36. Changing the selection does not change the progression maths.
- Set the base unitThe original stake is also the extra unit added after each full loss.
- Increase after a full lossMultiply the previous stake by two, then add the original base unit.
- Reset after a winRecord the complete sequence result and return the next stake to the base unit.
Grand Martingale is normally explained on even-money bets because the 1:1 payout makes the recovery calculation exact. Applying the same stake ladder to an inside bet with a different payout produces a different result.
The Grand Martingale Formula
Let B be the base unit and let n be the bet number, beginning at one. The recurrence is simple, but the closed formulas make the exposure much easier to check.
For bet six with a £1 base, the required stake is £1 × (26 – 1) = £63. If that bet loses, the complete sequence is £120 down. If it wins, the sequence finishes £6 ahead.
Swipe sideways to view the complete progression.
| Bet | Stake | Total if this loses | Result if this wins |
|---|---|---|---|
| 1 | £1 | -£1 | +£1 |
| 2 | £3 | -£4 | +£2 |
| 3 | £7 | -£11 | +£3 |
| 4 | £15 | -£26 | +£4 |
| 5 | £31 | -£57 | +£5 |
| 6 | £63 | -£120 | +£6 |
| 7 | £127 | -£247 | +£7 |
| 8 | £255 | -£502 | +£8 |
| 9 | £511 | -£1,013 | +£9 |
| 10 | £1,023 | -£2,036 | +£10 |
Grand Martingale Exposure Calculator
Enter a base unit, session bankroll and even-money table maximum. The calculator shows which of the first eight progression bets can actually be placed. It assumes standard European full-loss rules, including zero.
Bankroll blocks bet 8 because placing £255 after £247 of losses needs £502 in total.
Swipe sideways to inspect each calculator step.
| Bet | Stake | Total if it loses | Result if it wins | Fits inputs? |
|---|---|---|---|---|
| 1 | £1 | -£1 | +£1 | Fits |
| 2 | £3 | -£4 | +£2 | Fits |
| 3 | £7 | -£11 | +£3 | Fits |
| 4 | £15 | -£26 | +£4 | Fits |
| 5 | £31 | -£57 | +£5 | Fits |
| 6 | £63 | -£120 | +£6 | Fits |
| 7 | £127 | -£247 | +£7 | Fits |
| 8 | £255 | -£502 | +£8 | Bankroll stop |
The probability shown is the chance of losing every fundable bet from one fresh starting point on a standard European wheel. It is not the chance of seeing that run somewhere during a longer session.
How the Base Unit Changes the Ladder
A smaller base unit reduces the pound amounts, but it does not slow the multiplier. Bet four is always 15 times the base, bet six is 63 times the base and bet eight is 255 times the base.
Swipe sideways to compare base units.
| Base unit | Bet 4 | Bet 6 | Bet 8 |
|---|---|---|---|
| £0.50 | £7.50 | £31.50 | £127.50 |
| £1 | £15 | £63 | £255 |
| £2 | £30 | £126 | £510 |
| £5 | £75 | £315 | £1,275 |
| £10 | £150 | £630 | £2,550 |
There is no universal correct base stake. The practical test is whether the chosen bankroll and exact table maximum can fund every planned step, including the losses already accumulated before the next wager.
Grand Martingale vs Standard Martingale
Both are loss progressions and both reset after a win. Standard Martingale simply doubles. Grand Martingale doubles and adds the base unit, so it offers a larger recovery profit but normally reaches the same table maximum sooner.
The figures below use a hypothetical £5 base stake and £500 even-money table maximum. They are an illustration, not a claim about a particular casino table.
Swipe sideways to compare the two systems.
| Measure | Standard Martingale | Grand Martingale |
|---|---|---|
| Stake ladder | £5, £10, £20, £40, £80, £160, £320 | £5, £15, £35, £75, £155, £315 |
| Bets below £500 | 7 | 6 |
| Loss if all allowed bets lose | -£635 | -£600 |
| Next required stake | £640 | £635 |
| Profit if final allowed bet wins | +£5 | +£30 |
| European chance all allowed bets lose | 0.94% | 1.83% |
Under these assumptions, Grand Martingale stops one loss earlier. The failed-sequence losses are similar, but the Grand sequence has a larger recovery profit and almost twice the fixed-start chance of exhausting the available ladder.
Why Frequent Positive Sequences Can Mislead
Consider a Grand Martingale sequence capped after six bets with a £1 base. Most fresh sequences finish with a small positive result, but the sequence that loses all six bets costs £120.
| Sequence ending | Net result | European probability |
|---|---|---|
| Win bet 1 | +£1 | 48.65% |
| Win bet 2 | +£2 | 24.98% |
| Win bet 3 | +£3 | 12.83% |
| Win bet 4 | +£4 | 6.59% |
| Win bet 5 | +£5 | 3.38% |
| Win bet 6 | +£6 | 1.74% |
| All six lose | -£120 | 1.83% |
The chance of winning before all six lose is 98.17%, but that does not create positive expectation. The expected turnover is about £10.82 per £1-base sequence and the theoretical expected result is approximately -£0.29. The many small positive endings are offset by the much larger failed sequence.
A high sequence completion rate is not the same as an advantage. It describes how the results are distributed, not whether the average result becomes positive.
How Likely Are the Losing Runs?
On a standard European Roulette even-money bet, 19 of 37 pockets produce a full loss. The first table measures a losing run from one fixed starting point. The second measures whether at least one six-loss run appears somewhere within a longer session.
From one fixed starting point
| Full losses | Probability |
|---|---|
| 4 | 6.95% |
| 5 | 3.57% |
| 6 | 1.83% |
| 7 | 0.94% |
| 8 | 0.48% |
At least one six-loss run
| Session length | Probability |
|---|---|
| 50 spins | 35.28% |
| 100 spins | 59.73% |
| 200 spins | 84.41% |
The session figures are higher because a losing run can begin at many overlapping positions. The probability that six particular spins all lose is not the same as the probability that a six-loss run appears somewhere across 100 spins.
Zero, La Partage and Wheel Choice
The progression can be applied mechanically on different wheels, but the green pockets determine how often an even-money wager loses and whether the loss is full or partial.
Swipe sideways to compare the wheel rules.
| Wheel or rule | Zero result | Progression treatment | Even-money edge |
|---|---|---|---|
| European standard | Full stake lost | Use the normal double-plus-base step | 2.70% |
| French La Partage | Half the qualifying stake returned | Record the half-loss and reset for a clear new sequence | 1.35% |
| French En Prison | Stake remains unresolved | Wait for the table rule to resolve it before changing stake | Normally 1.35% |
| American 0 or 00 | Full stake lost | Use the normal step, with a higher loss probability | 5.26% |
La Partage does not fit the clean full-loss formula because only half the current stake is lost when zero lands. Resetting after that result keeps the accounting clear, but it is a practical convention rather than a universal Grand Martingale rule.
For the underlying probabilities and payouts, use the Roulette odds guide. The staking sequence itself does not reduce the wheel’s house edge.
Grand Martingale vs Reverse Martingale
The similar names cause confusion, but the systems move in opposite directions. Grand Martingale increases after losses. Reverse Martingale or Paroli increases after wins.
| Rule | Grand Martingale | Reverse Martingale |
|---|---|---|
| After a loss | Double + base | Reset to base |
| After a win | Reset to base | Double up to a chosen cap |
| £1 example | £1, £3, £7, £15 after losses | £1, £2, £4 after wins |
| Main exposure | Cash and earlier losses | Earlier winnings re-staked |
| House edge changed? | No | No |
Does Grand Martingale Work?
It works as a set of staking instructions. It correctly tells the player what to bet next and a recovery win does produce a larger sequence profit than standard Martingale. It does not turn Roulette into a positive-expectation game.
What the system defines clearly
- The next stake after each full loss.
- The exact profit when a later bet wins.
- The table and bankroll exposure at every step.
- A simple reset after a winning result.
What the system does not change
- The probability of the next spin.
- The effect of zero or double zero.
- The house edge on the underlying wager.
- The possibility of a run exceeding the available ladder.
A larger bankroll allows more steps but does not make a losing run impossible. A higher table maximum allows the progression to continue but does not improve the expected return. Grand Martingale changes the size and timing of the results, not the underlying odds.
How We Checked the Maths
This guide uses the base-unit version of Grand Martingale. The first stake is B and every full loss changes the next stake to twice the previous stake plus B. The closed formulas were checked against the displayed £1 progression through bet ten.
European full-loss probability uses 19 losing pockets from 37 for a standard even-money wager. Fixed-start losing-run figures are (19/37)n. Session-run figures track overlapping starting positions rather than treating each possible window as separate.
The six-bet expected result uses every possible winning stage plus the all-loss outcome. Expected turnover includes a later wager only when every earlier wager in that sequence has lost. The UK Gambling Commission explains that RTP is a long-run average rather than a promised result from one short session. Read the UKGC RTP guide.
The calculator models standard European full-loss rules only. It does not model La Partage, En Prison, changing the base unit during a sequence, multiple simultaneous bets, inside-bet payouts or casino-specific table rules.
Calculation review: Mark Taylor, RouletteUK Editor-in-Chief. Last checked 24 August 2026.
Grand Martingale FAQs
What is the Grand Martingale Roulette strategy?
It is a negative progression used mainly on even-money bets. After a full loss, double the previous stake and add the original base unit. After a win, reset to the base stake.
What is the 1-3-7-15 betting sequence?
It is the Grand Martingale ladder produced by a one-unit base: 1 unit, 3 units, 7 units, 15 units, 31 units and so on. Each new stake is twice the previous stake plus one original base unit.
Why do some Grand Martingale guides show a different sequence?
Descriptions are not fully consistent. Some add a fixed chip amount or introduce the extra unit later. This page always adds the original base unit after every full loss, which produces 1, 3, 7, 15 and 31.
How is Grand Martingale different from standard Martingale?
Standard Martingale doubles after a loss and normally recovers one base unit when a later bet wins. Grand Martingale doubles and adds the base unit, so its recovery profit increases by one base unit at every step while its stakes grow faster.
How is Grand Martingale different from Reverse Martingale?
Grand Martingale increases after losses. Reverse Martingale increases after wins and resets after a loss. They create different exposure even though both use multiplication.
What happens when zero lands?
On standard European Roulette, zero is a full loss on an even-money bet and the next stake follows the normal double-plus-base rule. La Partage returns half the qualifying stake, while En Prison leaves it unresolved under the table’s rules.
Can Grand Martingale beat the Roulette house edge?
No. The progression changes stake size, turnover and the distribution of outcomes. It does not change the probability of the next result or the house edge of the selected wheel and bet.
What happens when the next stake exceeds the table maximum?
The sequence cannot continue as written. The player must accept the current sequence loss rather than place a smaller wager and describe it as the same recovery calculation.
Keep the Progression Within a Fixed Spending Limit
A progression does not control random results. Decide the maximum amount and time before play rather than increasing either because the sequence has reached a later step. If gambling is causing concern, contact the National Gambling Helpline free on 0808 8020 133, available 24 hours a day, or use GAMSTOP to block access to licensed UK gambling sites and apps.