1988issue C071-5
Modified-martingale progression lists and ruin bounds
A modified-martingale keeps outstanding sizes on a progression list and sets the next trade to the sum of the earliest and latest remaining entries. Treat that list as a next-size ledger: refuse the next sum when it would breach a pre-set ruin budget, and reset a series only while trade-independence and the expected-value condition still hold.
- A series begins at one unit, and each later size is the sum of the earliest and latest quantities still on the progression list.
- After a win the first and last remaining entries are dropped, so the modified-martingale does not require a full double after every loss.
- No finite reserve can make a successful series certain, so the next summed unit should be refused when it would breach a small expendable stake set as the ruin budget.
- List-subdivision can keep the next wager smaller, but a series should be reset only while trade-independence and the expected-value condition still hold.
What the progression list records
A series is a run of independent trades that starts at one unit. The progression list is an ordered record of outstanding unit quantities after losses. Each later size is the sum of the earliest and latest quantities still on that list.
How the modified-martingale changes the list
The modified-martingale raises the next unit count after a loss. After a win, it drops the first and last remaining list entries rather than doubling after every loss.
When a series is complete
The series is treated as complete when a win leaves the account one trading unit ahead of the losses recorded in that run. Exposure is described as lowest at the start of a new series, so a run already ahead may be stopped early rather than forced to a one-unit close.
Finite reserves and risk-of-ruin
No finite reserve can make a successful series certain, and the largest possible loss grows as more capital is committed to the progression.
A series stake is to be capped at a small share of expendable funds. Stopping a losing series at that cap is treated as cheaper than letting the reserve be exhausted.
List-subdivision
A large remaining list may be rewritten as a gentler rising sequence with the same total so the next wager, margin need, and capital at risk stay smaller.
In the worked comparison, a subdivided list kept a single-trade peak at 7 units, while a pure doubling rule would have required 64 units on the seventh wager of a comparable streak.
The expected-value condition
The sizing rule is presented as risk-reducing only when the ratio of average profit to average loss is at least as large as the ratio of losing trades to winning trades.
Trade-independence
Each wager must be an independent trade. Adding to an open loser or winner inside the same position is treated as breaking that independence.
All readings on this track · 9 readings
- 1988Modified-martingale progression lists and ruin bounds
- 1989Scale-in-on-loss on a tempered-martingale-series with a fixed unit-factor
- 1989Shorter series need fewer recovery hits and raise scale-in cash
- 1990Recovery sizing as a series procedure
- 1990Reverse-martingale pyramiding after clustered wins
- 1993Test Martingale against fixed size before you pyramid
- 1998The runs-test as a contract-sizing gate
- 2004Scale-in on a two-close reversal instead of using a price stop
- 2012Four-level risk sizing when stock margin caps fixed fractions