Anti-martingale system — sizing up positions on wins

In a hypothetical sizing comparison, a trader holds 0.3 lots while equity changes. At the same stop distance and account-currency pip value, the nominal planned loss is unchanged but its percentage of equity rises after a drawdown and falls after growth. Fixed-fractional sizing recalculates volume from a chosen equity percentage; it does not improve the entry signal or guarantee recovery.

What an anti-martingale system actually is

An anti-martingale rule scales a specified stake upward after gains and downward after losses. In fixed-fractional sizing, the modeled cash budget follows current capital. This changes exposure, not whether the position is safe; market gaps, costs, constraints and strategy validity still matter.

Position sizing does not establish an entry edge. Scaling can affect monetary expectancy and geometric growth, especially when size depends on information related to outcomes. In the simplified model of a fixed payoff distribution with sizing independent of future outcomes, scaling does not turn a negative per-unit expectancy into a positive one. No sizing rule guarantees growth.

Martingale versus anti-martingale

Fixed fractional — a percentage-based variant

Fixed-fractional sizing uses a chosen percentage of a stated current capital base for a modeled loss budget. Volume also depends on stop distance, instrument value, currency conversion, costs and allowed steps. A constant chosen budget percentage does not keep the entire risk profile constant or guarantee actual loss will match that budget.

For a hypothetical USD 10,000 account, 2% is USD 200. Assuming EUR/USD pip value USD 10 per standard lot, a 50-pip exact stop fill and no costs, the modeled loss per lot is USD 500, so volume is 0.40 lot. On USD 12,000 and USD 8,000 bases it is 0.48 and 0.32 lot. A EUR account requires conversion of USD pip value at an explicit exchange rate. Broker volume steps and execution costs must be checked separately.

The arithmetic of a loss sequence

For this hypothetical sequence, each loss is exactly the chosen fraction r of capital immediately before the trade. With no costs, gaps, cash flows or volume rounding, capital after n losses is initial capital × (1 − r)ⁿ. The following drawdowns are conditional on that sequence; they do not estimate its probability or establish a survivable level.

• 2% across ten losses: 1 − 0.98¹⁰ = 18.29% drawdown.
• 2% across twenty losses: 1 − 0.98²⁰ = 33.24%.
• 2% across thirty losses: 1 − 0.98³⁰ = 45.45%.
• 5% across ten losses: 40.13%; twenty losses give 64.15%, leaving 35.85% of starting capital.
• 10% across twenty losses: 87.84% drawdown. Recovery to the starting value would require about 722.53% growth from the remainder.

The fixed ratio method of Ryan Jones

The fixed-ratio method associated with Ryan Jones’s The Trading Game (1999) adds units using cumulative closed profit and a chosen delta. Starting at one unit, the additional profit to move from n to n + 1 units is n × delta. The cumulative threshold for n units is delta × n(n − 1)/2. This rule does not itself incorporate stop distance or current equity; specify a separate loss budget and how size decreases when profit retreats.

The Kelly criterion and its practical limits

The Kelly criterion maximises expected logarithmic capital growth under a specified model. In a binary model with win probability p, net win b times the stake and loss of the stake, its fraction is f = (pb − (1 − p))/b. This requires known, stable payoff assumptions; estimates from a trading sample do not make the calculated fraction a safe recommendation.

For the ideal binary-payoff example p = 0.6, win +2 stakes and loss −1 stake, full Kelly f = (0.6 × 2 − 0.4)/2 = 0.4. The expected logarithmic growth per trial is 0.6 ln(1+2f) + 0.4 ln(1−f). Half Kelly f = 0.2 gives about 75.92% of full Kelly’s modeled log growth, not a guaranteed relationship for arbitrary strategies. Estimation error, costs, dependence and drawdown make direct application hazardous; this is a mathematical illustration, not a sizing recommendation.

How to implement the system in practice

Define the sizing rule before comparing its results. The following steps make the inputs and changes traceable; there is no universal trade count or review timetable that proves a strategy is valid.

1. State the chosen variant and fraction. Specify balance or equity as the capital base and explain why the modeled loss budget fits the constraints being tested.
2. Separate fitting from evaluation. Test on representative data, include costs and inspect results outside the sample used to select parameters. A positive sample mean is an estimate, not confirmation of future expectancy.
3. Build a position-size calculator. Include the capital base, chosen fraction, stop distance, account-currency value, costs and permitted volume steps.
4. Keep a trade journal with a position-size field. Without it, you cannot later verify whether the system was applied mechanically or whether intuition crept in.
5. Update at the stated decision point. A rule based on current equity before each entry must use that value before each entry; a weekly update is a different rule.
6. Compare complete equity paths. Check cash flows, drawdowns, overlapping exposure and rounded volumes for the same entry and exit sequence.
7. Control parameter changes. Record a change and evaluate it on separate data. A smooth past curve alone does not justify a higher fraction.

The most common mistakes in applying the system

The following checklist covers errors to inspect when applying a sizing rule. Compare each one with the recorded account equity, volume, stop distance and account-currency pip value rather than treating an anecdote as performance evidence.

• A fixed lot size unrelated to equity. The same volume on EUR5,000 and EUR15,000 produces a planned risk percentage three times larger on the smaller account if stop distance and pip value are unchanged. The exact percentages cannot be calculated without those inputs.
• Sizing up after a loss in revenge. This is a classic psychological martingale, even if the rulebook nominally specifies an anti-martingale system.
• Confusing drawdown arithmetic with ruin probability. A given fraction determines the effect of exact modeled losses; their probability and the threshold for operational failure require additional assumptions.
• Treating a positive sample mean as a guaranteed edge. Include costs and estimation uncertainty, and test whether conclusions survive different periods.
• Using a stale capital base. Recalculate at the rule’s chosen decision point. Balance and equity can differ while positions are open.
• Confusing sizing with an entry edge. Changing exposure does not validate the signal. In a fixed payoff model with size independent of future outcomes, scaling cannot reverse negative per-unit expectancy.
• Changing the rule without recording it. Specify when and why a variant changes so that results can be attributed to the rule actually used.
• Ignoring combined exposure. Long positions in several XXX/USD pairs share short-USD exposure, but are not identical positions: their base currencies, values and correlations differ.
• Not adjusting for volatility. The same risk percentage in a calm market and in an environment full of NFP, CPI and central-bank decisions represents two very different regimes — an ATR-based check on stop-loss distance helps to keep position size sensible.
• Discretionary overrides of the formula. “I feel good after two winners, so I will trade a bit bigger” turns a mechanical anti-martingale into intuitive chaos.

What does the change actually give a small account?

Return to the hypothetical sizing comparison. Hold the entry and exit sequence fixed and compare volumes derived from current equity with a fixed-volume rule. State the starting balance, stop distances, pip values and costs before comparing the resulting equity paths.

Fixed-fractional sizing reduces the next planned monetary risk after an equity loss if the chosen percentage is unchanged. Whether the resulting maximum drawdown is lower than under fixed volume depends on the complete trade sequence and assumptions; the sizing rule alone does not establish a measured annual improvement.

And the thing the change did not do: it improved not a single entry. The anti-martingale organises scale, not the quality of decisions. That distinction is worth keeping in mind every time you are tempted to think that because you size positions better, the strategy has started to work.

What to do tomorrow

1. Compare two sizing models on the same recorded trades. Recalculate the complete equity path for a predefined fixed-fractional rule and the original rule, including costs and volume rounding. Report whether drawdown increased or decreased rather than assuming an improvement.
2. Create a simple position-size calculator in a spreadsheet. Set up a formula that automatically calculates the correct lot size for EUR/USD once you input your current account equity, desired risk percentage (such as 1.5 percent), and stop-loss distance in pips. Keep this spreadsheet open on your desktop before every session.
3. Write a complete budget rule. State the capital base, chosen fraction, aggregate exposure limit and response to losses. Any reduction after a streak is an additional rule to evaluate, not a universal instruction.

Related reading: the martingale trap — doubling after losses and the limits of finite capital; the Kelly criterion — log-growth optimisation under stated assumptions; position size for different stop-loss distances — detailed calculations across currency pairs and scenarios.