Square-Root Martingale

Decelerating growth: size is √i, so the ladder gets heavier with depth but by progressively less. It is the growth curve that remains affordable at depths where every other growth curve has become unfundable, which makes it the practical choice for wide grids that still want some averaging.

Size at level i is the square root of i. The gap between levels 9 and 10 is a fraction of the gap between 1 and 2, so the curve flattens as it deepens — the opposite of the compounding behaviour that makes martingale dangerous.

Below is the wizard's own ladder table and the trading terminal's chart engine, both driven by buildLadderPlan for this mode. Change the level count, spread or target and the rung prices, sizes, capital ramp and chart lines recompute exactly as they would in the grid designer.

Sub-linear in the multiplier sense: ten levels cost roughly twenty-two times base, and forty levels remain within reach of a normal account. This is the only martingale variant that is genuinely deployable at forty-plus levels.

Read the cost vs 5 levels column as the escalation test. A flat ladder doubles when the depth doubles; anything materially above that is a curve whose coverage has to be bought rather than simply configured.

With every rung filled, the volume-weighted average entry is 93.65 against a base of 100 and a deepest rung of 90.00 — so the average sits 63% of the way down the covered range. Getting back to flat from the bottom therefore needs a 4.06% bounce, against 5.00% for a flat ladder of the same depth — 0.94% less work.

Growth decelerates: the gap between level 9 and 10 is far smaller than between 1 and 2. Capital is sub-linear in the multiplier sense — ten levels cost only about 22× base.

The last row is the metric that separates modes. Profit for a full cycle is the target percentage of deployed capital in every mode, so it cannot discriminate. What differs is how much capital has to sit reserved to earn one shallow cycle: this mode reserves 22.5× base to collect 4.5 bps of it when the first rung completes.

Low-to-moderate volatility instruments and wide ladders. Anywhere the realistic adverse move is large relative to the spread, square-root growth buys depth without buying convexity.

Grows with the square root of depth, so it adds size but decelerates. A conservative way to average down: more than fixed, far less than linear. Floored at 1 lot.

Mild. The tail is thin because the deepest rungs are only modestly larger than the shallowest, so the failure mode reverts to coverage exhaustion rather than capital escalation.

This is the product's grid backtester, not a summary of one. It fetches public candles for the instrument you pick, rebuilds the ladder anchored on the first candle of the window, then applies the engine's own fill, take-profit, refill and stop-loss rules bar by bar. The caveat block inside the panel is part of the output — read it before trusting a number.

First the arithmetic, then the market. The table below is computed from the size curves alone; the sweep underneath replays every one of those ladders over the same real candle window, with grid_mode as the only variable.

• Risk-averse mean-reversion where you still want the average entry to move.
• Deep ladders (20–60 levels) where any steeper curve would be unaffordable.
• Low-volatility instruments whose pullbacks are shallow but frequent.

• You need aggressive recovery from a deep drawdown — the curve is too flat to deliver it.
• Depth is shallow, where the difference from fixed is negligible.

• Because capital is mild, spend the budget on depth: square-root at 40 levels is a very different (and often better) strategy than square-root at 10.
• If you want more recovery at the same affordability, power mode with p ≈ 1.2 is the next step up.

• Track coverage rather than exposure — this mode fails by running out of range, not out of money.
• Compare peak committed notional against the account, weekly. A growth curve that has never been deep has never been tested.
• Treat every level increase as a capital decision: adding levels to a growth curve is not a linear cost.

1. 1
   Coverage exhaustion

   The same failure as fixed: price leaves the covered range and the ladder holds. Deep configurations are the mitigation, and this mode can afford them.
2. 2
   Under-differentiation at shallow depth

   At five levels the curve is nearly flat, so the operational complexity of a growth mode buys almost nothing. Either go deeper or use fixed.

• Pairs well with trailing: light deep rungs make window shifts cheap.
• Spread sets how fast the ladder consumes depth. Widening it buys coverage for the same level count at the cost of fewer fills.
• Target sets what each cycle books. Below round-trip fees plus slippage, a grid is a fee generator regardless of the size curve.
• The stop loss is the only bound on the tail. Without it, the curve's worst case is whatever the market does, not what you planned.

1. 1
   Is this the safest growth mode?

   Among the uncapped growth curves, yes by a wide margin. Capped linear is comparable and gives you an explicit ceiling instead of a decelerating formula.

• Sizes and capital: levelMultiplier / gridModeCurve in lib/grid/gridModes.ts, mirrored from grid_modes.hpp and the Python engine's lot calculator.
• Rung and exit prices, capital ramp, init targets and the stop line: buildLadderPlan — the same builder the wizard and grid designer use.
• Backtest fills, cycles and P&L: runBacktest / runBacktestSweep over public broker candles, applying the engine's fill, exit, refill and stop rules.
• Price charts: the trading terminal's chart engine, with the ladder drawn through its own price-line API.

• 1.Grid Modes — Overview — The full taxonomy and how to choose
• 2.Martingale family — What every curve in this family has in common
• 3.Capital Allocation — Sizing an account to a Square-Root Martingale ladder
• 4.Stop Loss — Bounding this curve's tail
• 5.Reading the Ladder Plan — Verifying the curve before deploying
• 6.Grid Structure — Levels, init batch and base size