Martingale progression
Starting from one unit and doubling after each loss gives:
1, 2, 4, 8, 16, 32, 64, ...
After six consecutive losses, cumulative loss is:
1 + 2 + 4 + 8 + 16 + 32 = 63 units
The next prescribed stake is 64 units. If it also loses, cumulative loss becomes 127 units. A 50-unit maximum stake makes the seventh prescribed bet unavailable even before bankroll capacity is considered.
Fibonacci progression
A common Fibonacci-style progression begins:
1, 1, 2, 3, 5, 8, ...
The first six stakes total 20 units. The exact recovery claim depends on the payoff, when the sequence moves forward or backward, and how pushes and partial wins are handled. A slower progression still changes exposure without changing the underlying outcome probabilities.
Expected value remains attached to the bets
If independent even-money trials have win probability 0.48, the one-unit expected profit is:
EV = 0.48 * 1 - 0.52 * 1 = -0.04 units
Doubling the stake doubles both possible profit and loss, so the expected profit for a two-unit version is -0.08 units. A progression rearranges the distribution of results; it does not reverse the sign of EV.
OpenStax explains that independent outcomes do not become more likely because previous outcomes occurred.
Evaluate the whole stopping rule
Record starting capital, base stake, maximum stake, maximum sequence length, operator limit, payoff, win probability, independence assumption, and what happens when the next stake is unavailable. Include abandoned sequences in the result rather than reporting only completed recoveries.
Formal probability of ruin depends on the model, costs, minimum bets, and survival condition; Ferguson treats these inputs explicitly. There is no universal ruin percentage for every Martingale implementation.
Why short records can look attractive
Most completed sequences can show a small gain while rare long sequences carry much larger losses. Reporting win frequency without loss magnitude hides this asymmetry. Publish total stake, maximum cumulative exposure, incomplete cycles, drawdown, and the full outcome distribution.
Worked limit check
| Loss number | Martingale stake | Cumulative loss | Next stake |
|---|---|---|---|
| 1 | 1 | 1 | 2 |
| 2 | 2 | 3 | 4 |
| 3 | 4 | 7 | 8 |
| 4 | 8 | 15 | 16 |
| 5 | 16 | 31 | 32 |
| 6 | 32 | 63 | 64 |
Test the sequence against both available bankroll and operator maximum before any simulation. If either boundary is crossed, mark the cycle failed at that point; do not assume the next recovery stake occurred. Add commission and non-even prices because a simple doubling rule may not recover the intended amount when net payoff per unit is below one. Report failed and abandoned cycles in the headline denominator. Record the largest permitted stake and the bankroll shortfall at failure so the boundary remains auditable.
Next step
Use Gamblers Fallacy for the next part of this topic.
Continue learning
- Next guide: Percentage Staking
- Related guide: Separate Betting Bankrolls
Assumptions and limitations
Examples use independent binary even-money outcomes with no commission. Real prices are not exact even money, limits can be user-specific, and bets may be dependent. This page explains risk and does not provide instructions for using progressive systems.
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