After two losing trades, what happens to the next position? One person keeps the same dollar amount, another reduces it with the account, and a third doubles it: “One win will recover everything.” They may face the same next opportunity yet run out of permission or cash to participate at different points.
Set the rules before the first trade. Then follow the same opportunity sequence and inspect how each rule changes losses, recovery, and the point at which the account must stop.
What is fixed: dollars or a fraction of equity?
You will recalculate three predetermined equity paths, explain the return needed to recover after losses, and identify when cash, a policy floor, or minimum trading units require no trade. The comparison examines mechanisms; it does not select a universally best risk percentage.
“Fixed risk per trade” needs a denominator. A planned scenario loss of $100 differs from 10% of the equity immediately before each order. Under the fraction rule, a smaller account produces a smaller dollar amount. Under the fixed-dollar rule, $100 becomes a larger share of what remains.
CME's educational discussion of a percentage rule explicitly acknowledges that its 2% threshold is arbitrary.1 Our 10% is chosen for readable arithmetic, not as a recommendation or proof that actual losses will stop at the planned amount. Any proposed order must still pass the joint constraints introduced in G48.
Give every rule the same opportunities and gates
C8-77 is an independent synthetic dollar subaccount starting with $1,000 in cash and equity. Necessary household funds are separate. There are no outside flows, borrowing, or other positions. Four opportunities are supplied in advance: loss, loss, loss, win. No rule receives a different market path.
Each opportunity starts with a purchase at $100 per share, followed by a complete exit. Actual exits are $50 for the first three opportunities and $150 for the fourth. Each new opportunity restarts at the supplied $100 entry price. These are four independently supplied price segments, not one continuous market history or a validated strategy.
Each share loses $50 in a losing segment and gains $50 in a winning one. A planned scenario loss of R dollars therefore corresponds to R / 50 shares and ties up 2R dollars at entry. The minimum increment is 0.001 share, rounded down. Fees, taxes, and cash returns are zero. Main-table quantities fit that increment exactly, so rounding does not change them.
All three rules must pass two gates before buying: purchase cost cannot exceed current cash, and equity after the assumed $50 exit cannot fall below the $600 policy floor. Exactly $600 is permitted. If a proposed trade fails either gate, stop this round and skip all remaining opportunities; restarting requires a separate review. This is a predetermined control, not a guarantee that actual equity can never fall below $600.
Only the quantity policy changes:
- A: R is $100 for every trade.
- B: R is 10% of equity immediately before each order.
- C: R starts at $100, doubles after a loss, and resets to $100 after a win.
C is the loss-doubling martingale betting rule discussed here. That use of the term does not describe every mathematical process called a martingale in probability theory.
Walk the accounts through the first path
A always buys two shares for $200. Its first three losses take equity from $1,000 to $900, $800, and $700. The fourth proposal still uses R = $100. Another assumed loss would leave exactly $600, so the trade is permitted. The supplied winning opportunity adds $100, leaving $800.
B recalculates the denominator each time. Its first R is $100, leaving $900 after the loss. Next, R is $90 and the purchase is 1.8 shares; a loss leaves $810. Third, R is $81 and the purchase is 1.62 shares; equity falls to $729. Fourth, R is $72.90 and the purchase is 1.458 shares. The gain of $72.90 leaves $801.90. Cash is sufficient and each projected losing outcome remains at or above $600.
| Opportunity | Supplied result | A: R / ending equity | B: R / ending equity | C: R / ending equity |
|---|---|---|---|---|
| 1 | Loss | $100 / $900 | $100 / $900 | $100 / $900 |
| 2 | Loss | $100 / $800 | $90 / $810 | $200 / $700 |
| 3 | Loss | $100 / $700 | $81 / $729 | Planned $400 rejected / $700 |
| 4 | Win | $100 / $800 | $72.90 / $801.90 | Already stopped / $700 |
C cannot simply wait for the fourth opportunity. After the second loss it has $700. The proposed R of $400 requires $800 at entry, which it cannot afford. Even ignoring cash, the assumed loss would leave $300, violating the floor. Recording a third trade and using a later win to rescue it would bypass both gates.
The accounts see the same opportunities but participate different numbers of times. A skipped opportunity is not a completed zero-return trade and does not belong in the realized trade win rate. The ending values of $800, $801.90, and $700 describe this path; they do not rank the rules universally.
A smaller risk amount also changes recovery
B finishes slightly ahead of A here because its dollar losses shrink during the streak. Its later dollar gain shrinks too. Its path is $1,000 multiplied by 0.9 three times, then by 1.1, giving $801.90. Adding three negative 10% returns and one positive 10% return would miss the changing bases.
A loses 30% over the first three trades and has $700 left. Recovering $1,000 requires $300 / $700, or about 42.86%, rather than another 30% gain. Recovery uses remaining equity as the denominator. A 50% decline leaves half the original amount and requires a 100% gain to return to the start.
B's first three losses total 27.1%, leaving $729. Returning to $1,000 requires approximately 37.17% from there. A final 10% gain is insufficient. Reducing later exposure can limit further dollar losses while also changing recovery speed; assess both sides.
A's fourth $100 risk is about 14.29% of $700, compared with 10% at the start. Fixed dollars are not a fixed percentage. Continued losses can make that unchanged amount increasingly demanding, so even a simple rule needs floors and reassessment.
Why doubling always seems to need one more trade
The arithmetic attraction is easy to see under stronger assumptions. Suppose trading could continue without limit, every order filled completely at the supplied prices, and gains and losses were symmetric. After losses of $100, $200, and $400, a gain of $800 would recover $700 and leave $100 more.
But after those three hypothetical losses, only $300 remains from the initial $1,000. The next R of $800 would require $1,600 cash. The arithmetic of recovery does not supply that money or make the next outcome a win.
After k consecutive losses, cumulative loss is 100 × (2ᵏ − 1), and next planned R is 100 × 2ᵏ. Here, 2ᵏ means doubling k times. Funding requirements grow while finite capital, concentration limits, minimum units, and execution can stop participation first.
Symmetry matters too. In a separate variant, lose $100 and $200, then let a successful R = $400 trade earn only 0.5R, or $200. The combined result is still a $100 loss, before fees. That third proposal also fails the earlier cash and floor constraints; this variant only isolates the assumption behind “one win recovers everything.”
No actual ruin probability can be inferred from one losing-streak table. You would need a joint distribution of outcome sizes and signs, dependence, costs, gaps, funding and execution constraints, and a definition of ruin. Zero equity, crossing a $600 policy floor, and becoming too small to trade are different events. This exercise supplies a deterministic path, not that probability model.
Adding after a loss is not always doubling
A planned installment, new research evidence, or restoration of a target weight can call for buying after a decline without using a martingale rule. Ask what determines the new amount, how total exposure is constrained, and when the plan stops.
“Increase enough to recover the old losses in one trade” directly turns past losses into a demand for more risk. A rebalancing rule instead uses target weights and overall constraints. It does not promise a return to the original purchase price, and changed household obligations can stop the plan.
Adding after gains needs an explanation too. A current-equity fraction increases dollar exposure when equity grows, as specified in advance. Temporarily changing 10% to 20% after one or two wins is a new rule version. Realized profits are not expendable “market money.”
MoneySense discusses purchase-price anchoring and written plans.2 Use those ideas to specify revision conditions, without diagnosing a person's psychology from a few trades. Keeping an old rule forever is not the objective either. Changed evidence or household conditions can justify a documented pause and renewed review.
An account can become unable to trade before reaching zero
The main exercise permits 0.001-share increments; an actual tool may not. Change only the trading unit to whole shares, keeping B's other conditions. The first two shares lose $100, leaving $900. The next planned R is $90, but $50 per-share scenario loss permits only one share after rounding down. That loss leaves $850.
The next targets are R = $85, then $80, each still allowing only one share. Equity moves to $800 after the third loss and $850 after the final win. This is not evidence of a smarter fraction rule. The actual exposure no longer tracks 10% precisely because the trading unit changed.
If planned R is below $50, do not round up to one share merely to participate. Zero shares and no trade may be the correct outcome. Affordability and the floor also remain distinct: from a separate $620 equity snapshot, a 10% planned loss of $62 would leave $558, below $600. Reject it even if the purchase itself is affordable.
The $50 exit is not guaranteed. FINRA explains that a triggered stop becomes a market order and can execute far from the expected price during volatility.3 If the actual exit is $30, each share loses $70; the two shares intended to carry R = $100 lose $140. A proposal that passed a reference-price floor check can therefore breach it in actual execution.
In an ideal fraction model, losing less than 100% each time keeps equity mathematically positive. That does not establish practical survival. Minimum units, necessary payments, costs, and execution differences can prevent further trading. Kelly-type methods do not bypass those conditions and are not this chapter's default funding rule.
Change the path before judging the rule
Explain. Why does A's risk percentage rise during losses? What is wrong with counting C's skipped later opportunities as realized trades that restore its money?
Reference answers · reveal
Answer. A keeps dollars fixed while equity shrinks. C cannot fund or obtain permission for its third trade. Retain planned quantity, rejection reasons, and actual equity; future opportunities cannot retroactively fund a prohibited order.
Transfer. Change only the supplied sequence to loss, loss, win, loss. Calculate all three paths without letting foreknowledge of the third opportunity waive its admission checks. Can the two examples establish an actual ruin probability?
Answer. A moves through $900, $800, $900, and $800. B moves through $900, $810, $891, and $801.90: the third R of $81 wins, then the fourth R of $89.10 loses. C still has $700 after two losses and must reject R = $400, even though this opportunity would have won. It remains at $700.
B's matching endpoints result from multiplying the same factors on these two no-flow paths, with exact proportional fills and no pause. It does not show that every sizing rule or withdrawal path is order-independent. Neither deterministic example supplies an actual ruin probability.
Save a losing-streak action rule
Extend T15 with the rule version, starting equity and currency, fixed-dollar or current-equity R, updates after wins and losses, cash required, unit precision, floor, and stop/restart conditions. Keep planned R, permitted quantity, actual fills, equity, reasons for nonparticipation, and scenario differences row by row.
Recalculate at least one denominator and one rejection. Keep the ideal-fill, whole-share, and gap examples separate. If continuing requires household money, return to its purposes and approved funding boundary; a deposit is not a strategy recovery. Without inspectable records or an executed tool run, describe the work as a mechanism exercise.
Define exposure and stopping conditions before the moment you most want to change them. Recovery uses remaining equity; continued participation requires cash, policy permission, and actual execution. An extra win cannot by itself prove a better rule, and a reference exit cannot guarantee the loss.
References
- CME Group: The 2% Rule. Percentage-based amounts and the arbitrary threshold; its percentage and loss-certainty language are not adopted as recommendations.
- MoneySense: Behavioural Science and Investing, updated September 21, 2026. Purchase-price anchoring and written plans; no fixed psychological multiplier or individual diagnosis is used.
- FINRA: Regulatory Notice 16-19, May 2016. Stop-order execution in volatile markets.
Editorial status
AI-assisted draft synchronized to the accepted second-round Chinese source. C8-77 and its variants are synthetic, without an estimated real ruin probability or strategy validation. See the author review. A separate AI reviewer has completed an independent full-text and bilingual review. Human financial review and target-reader testing have not been performed and are not scheduled for this edition.