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Martingale calculator: working out your own ladder
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A Martingale ladder is fully described by three numbers: the base stake, the bankroll (or table maximum, whichever binds first) and the number of steps those allow. From them you can work out the chance the losing streak arrives and what the session is expected to return. Here is the arithmetic, then a table of common configurations.
The formulas
Total staked after n losses: base × (2ⁿ − 1). After 6 losses from £5: 5 × 63 = £315.
Steps allowed: the largest n where base × (2ⁿ − 1) + base × 2ⁿ ≤ bankroll, that is, where you can afford the next bet. Equivalently, the table maximum divided by the base, rounded down to a power of two.
Chance of n losses in a row on red (single zero): (19/37)ⁿ.
Chance of at least one n-loss streak in S spins: approximately 1 − (1 − p)^(S/n) where p = (19/37)ⁿ; a rough but usable estimate.
Expected result: always minus 2.70% of total turnover, whatever the ladder.
Common ladders
| Base | Bankroll | Steps | At risk | p(streak) per sequence | Chance in 100 spins |
|---|---|---|---|---|---|
| 50p | £50 | 6 | £31.50 | 1.83% | ~50% |
| £1 | £100 | 6 | £63 | 1.83% | ~50% |
| £2 | £500 | 7 | £254 | 0.94% | ~30% |
| £5 | £500 | 6 | £315 | 1.83% | ~50% |
| £5 | £1,000 | 7 | £635 | 0.94% | ~30% |
| £10 | £1,000 | 6 | £630 | 1.83% | ~50% |
| £20 | £5,000 | 7 | £2,540 | 0.94% | ~30% |
Notice what the table does not contain: a configuration where the streak is unlikely over a normal session. Adding a step halves the chance and doubles the money at risk. There is no bankroll that makes the seventh loss cheap.
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A worked example
Base £2, bankroll £500, table max £500 on red.
Steps: £2, £4, £8, £16, £32, £64, £128 = £254 staked after seven losses; the eighth bet of £256 would take the total to £510, over the bankroll. Seven steps.
Chance of seven losses: (19/37)^7 = 0.94%. Over 200 spins, roughly one chance in two of meeting it.
Each completed sequence wins £2. To be up £254 you need 127 winning sequences without a seven-loss streak. The expected number of sequences before the streak arrives is about 106. The arithmetic is not in your favour, which is the house edge saying hello.
What the calculator cannot change
The 2.70%. Every configuration in the table returns minus 2.70% of turnover over time. The only thing the numbers change is the shape: a short ladder loses often and cheaply, a long ladder loses rarely and expensively. Choose the shape with open eyes or, better, keep the stake flat and skip the ladder.
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Good to know
How many Martingale steps does £100 allow from £1?
Six. £1, £2, £4, £8, £16, £32 total £63; the seventh step, £64, would take the total to £127. Six losses in a row happens 1.83% of the time per sequence.
What is the chance of losing a Martingale sequence?
(19/37) to the power of the number of steps. Five steps 3.56%, six steps 1.83%, seven 0.94%, eight 0.48%. Each extra step halves the chance and doubles the cost.