1993issue C091-7
Test Martingale against fixed size before you pyramid
A tempered Martingale series can be attached to a standalone system, but it still has to beat a same-size control on the identical trade list. The archive found that after-loss series beat constant size only after that list was degraded, and that a small reverse add after a new equity high was the only size change that improved reward-to-risk on the original list.
- Treat contract count as a second rule and score it against a control that holds the same count on every trade from the same list.
- On the undegraded list, lengthening a tempered Martingale series moved its reward-to-risk curve toward the constant-contract line, and no series beat fixed contract sizing.
- After the list was degraded, some Martingale series beat constant size, but the winning series could not be identified beforehand, and the advantage appeared only after reward-to-risk had fallen.
- The only size rule that beat constant contracts on the original list was a restricted reverse add: a larger fixed count after profitable trades and a new equity high, then a cutback after a loss until equity made a new high.
Attaching a size series to a standalone system
A tempered Martingale size series can be attached to a standalone system that sets its own entries, exits, and stops and is not assumed to win half the time.
Fixed contract sizing holds the same number of contracts on every trade and is the baseline against which variable-size series are judged.
How the size series were scored
Size trials included both changing the contract count from a tempered numerical series and a control that held the same contract count on every trade.
Each series was scored by drawing trades at random from one hypothetical profit-and-loss list and repeating that draw. Reward-to-risk was final equity per contract divided by the worst closed-out drawdown per contract.
Martingale on the undegraded list
On the undegraded list, lengthening the Martingale series moved its reward-to-risk curve toward the constant-contract line, but no series beat trading a fixed contract count.
What changed after the list was reduced
After every trade was reduced, a few Martingale series beat constant size, yet the winning series could not be identified before the fact.
After a deeper reduction, most Martingale series beat constant size, but the smallest closed series still averaged a large contract count, and the list's reward-to-risk ratio had to fall before that advantage appeared.
The reverse add that beat the control
The only size rule that beat constant contracts on the original list used a larger but still fixed contract count while trades were profitable and equity was at a new high, then cut back after a loss until equity made a new high.
That rule is pyramiding: a restricted reverse-size rule with high-water step-up, meaning permission to use the larger contract count only while account equity is at a new peak. When the same list was upgraded and degraded, that small add-on size remained the preferred step across a wide band of final-equity-to-worst-closed-drawdown values.
The comparison frames Martingale as a response to near-even odds and large drawdowns, and frames a restricted reverse add, more contracts after strength and a base count after a loss, as the only change that improved the reward-to-risk map.
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