Shorter series need fewer recovery hits and raise scale-in cash

How the number series sets share size

The numberSeries is an ordered integer list whose remaining extremes set the next share increment. Share size equals the sum of the first and last remaining series numbers times a fixed baseShareUnit. A 1-6 series with a 100-share base opens at 700 shares.

The opening fill price becomes the actionPrice, the last filled price that recenters the paired limits. Matching limits sit one limitSpread above and one limitSpread below that price. That recentering repeats until every number in the series is gone.

Scale-in adds and scale-out reductions

A lower-limit fill runs a scaleInAdd: it appends the current extreme-sum to the series and the position grows. An upper-limit fill runs a scaleOutReduce: it deletes those two extremes and the position shrinks.

Fill counts that empty the series

A finished cycle satisfies the cycleIdentity A+B=2C. A is the starting series length. B is the count of lower-limit fills, with an odd A+B rounded up to the next even number. C is the count of upper-limit fills.

After four lower-limit fills, a six-number series still needs five upper-limit fills to close, while a two-number series needs only three. With no lower-limit fills, a six-number series needs three consecutive upper-limit moves to empty, and a two-number series needs one.

Pre-cost cycle amount

The pre-cost cycle amount equals the initial extreme-sum times the baseShareUnit times the no-drawdown upper-move count times the limitSpread. At a 1-dollar spread that identity is 3 dollars a share for the six-number case and 1 dollar a share for the two-number case.

Capital ratio after scale-in paths

The capitalRatio is dollars currently at work divided by dollars used on the first fill. On a path of three consecutive lower-limit fills with 1-dollar spreads, capitalRatio values after the first buy are higher for two-number series than for a six-number series.

Two-number capitalRatio values change rank across hit sequences. Pairing a 1-2 series with a higher pair such as 4-5, using the same opening share count and the same limits, averages those paths.

The opposite martingale tradeoff

A martingaleLadder is a recovery-oriented sizing path that can cut the capitalRatio while lengthening the upper-fill count required to exit. That money-management alternative lowers the current-to-initial capital ratio but increases the upper-limit fills required to finish a cycle, the opposite tradeoff from shortening the series.