Durable reference map
A three-stage method to reuse whenever conditions change
Keep the sequence of inputs, calculation and exception testing stable instead of relying on a market forecast.
- Align inputs and unitsGo to equations and definitionsPlanned reward-to-risk・Base size from stop budget・Hypothetical binary expectancy
- Reconcile the worked exampleGo to table and calculation stepsCompare 2R, 3R and 3R at an unapproved 1.5 multiplier
- Test exceptions and next checksGo to rules and counterexampleCalculate base size from stop distance and budget first.
What changes between 2R and 3R
A 100-point target against a 50-point stop is 2R; a 150-point target is 3R. The planned profit distance changes, but stop loss per lot does not.
Dividing a USD 400 budget by USD 500 stop loss per lot produces 0.80 lot. Target distance is not an input to that division.
- Store stop and target prices in separate fields.
- Fix the loss budget before evaluating the target.
- Carry partial profits and time exits into realized results.
Read expectancy with target attainment
A farther target increases the payoff when reached, but its attainment probability must be tested separately. With hypothetical attainment of 40% for 2R and 30% for 3R, both rows have USD 80 binary expectancy.
Positive expectancy does not describe the loss sequence or tail. Do not use an average estimate to raise the single-trade loss budget after the fact.
The two amounts raised by a 1.5 size multiplier
Increasing 0.80 to 1.20 lots raises 3R target gain from USD 1,200 to USD 1,800. It also raises stop loss from USD 400 to USD 600.
Binary expectancy scales from USD 80 to USD 120 because capital at risk scaled by 1.5. The 3R label did not justify the extra USD 200 loss allowance.
Compare target and size assumptions in common units
The table is hypothetical and exists only to verify calculation order. Attainment rates are assumptions for the expectancy formula, not empirical observations.
The 2R and 3R base rows use the same 0.80 lot and USD 400 stop loss. Only the final row breaches the budget.
Keep confidence and win rate outside this decision
Article 4 calibrates ex-ante probabilities; Article 5 evaluates observed win frequency and payoff magnitude. This article is limited to the planned ratio of target distance to stop distance.
A confidence label, high historical win rate or distant target is not an automatic multiplier for the same loss budget. Each metric answers a different question.
- Store planned R and realized R separately.
- Record time exits at their actual P&L rather than as target hits.
- Recheck stop loss after any target or quantity change.
Calculation framework
Planned reward-to-risk
Read the role of each equation first, then follow the numerical example to check the decision path.
Planned reward-to-risk
RR = D_target / D_stop- D_target: price distance from entry to profit target
- D_stop: price distance from entry to stop
- RR: planned reward distance per unit of loss distance
In plain language: Moving the target farther raises RR but does not enter the loss-budget formula.
When this conclusion does not apply: Calculate only when D_stop > 0 and D_target ≥ 0. This differs from realized reward-to-risk after spread, slippage, partial exits and fees.
Base size from stop budget
Q_base = B / (D_stop × V)- B: account-currency loss budget
- D_stop: stop distance
- V: value per lot per distance unit
In plain language: Size follows the stop loss, not the profit target.
When this conclusion does not apply: Calculate only when B is non-negative and D_stop and V are positive. Round down to the volume step and allow separately for execution overrun and fees.
Hypothetical binary expectancy
E = p_target × G − (1 − p_target) × L- p_target: assumed probability of reaching the target
- G: account-currency gain at target
- L: account-currency loss at stop
In plain language: A target distance is economically incomplete without an attainment estimate.
When this conclusion does not apply: Calculate only when 0 ≤ p_target ≤ 1 and G and L are non-negative amounts sharing one currency and cost basis. This educational two-outcome model omits partial exits, time exits, gaps and costs.
Keep the target ratio outside the loss-budget equation
Planned reward-to-risk divides target distance by stop distance. A 100-point target against a 50-point stop is 2R, while a 150-point target against the same stop is 3R. The numerator changes the possible favorable move; it does not alter the amount lost per lot if the 50-point stop and monetary point value remain fixed.
Base quantity uses the authorized account-currency loss divided by stop loss per lot. Under the hypothetical USD 400 budget and USD 10 per point per lot, a 50-point stop costs USD 500 per lot. The resulting 0.80 lot is therefore identical for the 2R and 3R target rows before execution additions and step constraints.
Putting target distance into the lot denominator would mix a possible gain with the protective loss calculation. Multiplying quantity because the ratio looks attractive is a different error: it leaves the equation intact but raises the money exposed at the unchanged stop. Both routes confuse an outcome aspiration with loss capacity.
Distinguish a placed target from a realized payoff
A 3R order level does not mean the realized average winner is 3R. Positions can exit partially, time out, fill at different prices, or incur spread, commission, and financing. A target may also never be reached. Historical analysis should retain the planned distance and reconstruct the realized net result as separate fields.
Using planned 3R gains alongside realized one-R losses makes expectancy asymmetric in its evidence. The positive side is an intention and the negative side is an outcome. A coherent realized statistic uses actual fills and costs for both sides; a coherent planning scenario labels target attainment as an assumption and keeps it distinct from observed frequency.
This distinction also protects against selective reporting. A trade that approaches the target and reverses is not a full target success unless the predeclared outcome rule says so. Rewriting it as nearly 3R after the event exaggerates the payoff distribution and can make an unjustified quantity multiplier appear supported.
Pair reward distance with an explicit attainment assumption
A farther target can offer more money when reached, but it can also be reached less often. The hypothetical binary model makes that tradeoff visible by assigning 40-percent attainment to 2R and 30 percent to 3R. These rates are invented inputs for arithmetic, not forecasts or measured results from the calculator.
At 0.80 lot, the 2R target corresponds to USD 800 and the 3R target to USD 1,200, while both stop losses are USD 400. The simple binary expectancy is USD 80 for each row under its stated attainment rate. Equal averages do not mean the paths, tails, holding times, or execution demands are equal.
Sensitivity should vary attainment and payoff independently. Assuming the same success rate for increasingly distant targets can create an attractive result by construction. A defensible model states where the assumption came from, preserves sample count and event definition if observed, and reports when available evidence is too thin for a stable estimate.
Expose what the 1.5 multiplier changes on both sides
Increasing 0.80 lot by a factor of 1.5 produces 1.20 lots. At a 150-point target, the hypothetical gain rises from USD 1,200 to USD 1,800. At the same 50-point stop, loss rises from USD 400 to USD 600. The multiplier scales favorable and adverse money by the same factor.
The binary expectancy also rises from USD 80 to USD 120 because the capital exposed rose. Presenting that increase as evidence that 3R created more edge would be misleading; every payoff in the simplified distribution was multiplied. The extra USD 40 average comes with an extra USD 200 loss in the losing state.
A user-facing comparison should place target gain and stop loss together, rather than highlighting only the larger target. If USD 400 remains the authorized budget, the 1.20-lot row fails before any debate about expected value. If the budget changes, that decision requires a separate policy and cannot be inferred from the reward label.
Read binary expectancy as a deliberately incomplete model
The two-outcome equation assumes every case either reaches the full target or loses the full stop amount. Actual exits can occur between those points, gap beyond them, or close in pieces. Costs and conversion can also change both outcomes. The model is useful for exposing the attainment assumption, not for claiming a complete distribution.
An average of USD 80 does not reveal losing streaks or maximum drawdown. Two sequences with the same attainment count and payoff amounts can have different peak-to-trough paths. Correlation among trades can also cluster failures. These omitted dimensions matter before any capital-policy change is considered.
Expected value can remain positive while realized performance over a finite sample is negative, and an in-sample estimate can fail later. The number should therefore be labeled hypothetical or observed with its period and count. It is not a guarantee and is not a direct sizing input under the fixed-budget architecture used here.
Preserve the causal order when the stop itself changes
A valid narrower stop can raise base quantity under the same budget because stop loss per lot falls. That is not reward-to-risk inflation. The analytical record must show why invalidation moved before quantity was calculated. Moving the stop closer merely to obtain a larger lot repeats the quantity-first distortion discussed elsewhere.
A wider target can raise the planned ratio without changing invalidation. The two price decisions may share analytical evidence, but their monetary roles remain distinct. The stop defines the modeled losing distance; the target defines one possible favorable exit. Their ratio is descriptive after both are set, not an authority that overrides the loss allowance.
If a target change coincides with a stop change, the report should vary each component separately before interpreting the new ratio. A move from 2R to 3R can result from a farther target, a closer stop, or both, and those paths have different effects on loss per lot. One ratio alone cannot identify which control changed.
Treat target attainment as a population-specific estimate
An observed attainment rate needs stable strategy logic, entry definition, target rule, stop rule, holding horizon, and cost treatment. Pooling a 2R scalping target with a 3R multi-day target creates a frequency that belongs to neither process. The sample should retain trades that exited early rather than silently removing them.
Changing the target can change holding time and exposure to gaps or financing. It can also alter behavior, such as the frequency of manual exits. These consequences mean a 2R attainment estimate should not be copied to 3R without evidence. A scenario can test the assumption, but its hypothetical status must remain visible.
A small sample can generate unstable rates. Testing many target multiples and selecting the best historical expectancy compounds selection bias. The development process should disclose candidate counts and reserve later data for validation. An attractive optimized 3R row is not independent evidence that future outcomes will match it.
Include execution and costs without hiding them in R
Planned R commonly uses price distances, while realized R should use net account-currency P&L divided by the pre-trade loss budget. Spread, adverse fills, commission, financing, and conversion can make a one-stop outcome worse than negative one realized R. The denominator and cost basis must be disclosed before comparing values.
A farther target can face different execution conditions than a nearby exit. Assuming identical fill quality at 2R and 3R may be convenient but unsupported. An execution analysis should retain order type, time, venue, and partial fills. It should not retrofit slippage into the target distance while leaving stop-side execution untreated.
Known quantity-proportional costs can be included in loss per lot or replayed after rounding, while fixed reserves can reduce the available budget. Whichever method is used, the all-in check must remain tied to the original authorized amount. Renaming a gross price ratio as net reward-to-risk conceals the adjustment rather than solving it.
Separate this ratio from confidence and recent win rate
A confidence forecast estimates an event probability before the outcome. A win rate summarizes realized counts. Reward-to-risk compares planned price distances. One can use observed target attainment in an expectancy model, but the concepts retain different denominators and evidence. Combining them into a single quality score can hide contradictory assumptions.
For example, a high confidence label does not prove the 3R target is more likely to fill, and a high recent win rate may reflect much smaller realized wins. Conversely, a low win rate can coexist with favorable payoff asymmetry. Each statement needs its own sample and should not become a direct lot multiplier.
Typed fields help enforce the boundary: probability is zero to one, target and stop are points, payoff is currency or R, and quantity is lots. The active monetary budget remains a separate account-control input. A calculation should reject multiplication across incompatible units instead of relying on persuasive labels.
Use a decision table that identifies the binding assumption
A clear table shows stop distance, target distance, ratio, assumed attainment, executable lot, stop loss, target gain, and expectancy in the same row. The 2R and 3R base rows then reveal that quantity and stop loss stay fixed. The multiplier row reveals exactly where the account-currency breach enters.
The table should also expose whether values are planned, hypothetical, or realized. Combining an observed attainment rate with a hypothetical cost-free payoff can be useful as a scenario, but it is not a fully observed performance record. Column labels and source notes should prevent readers from attributing more evidence than the data carry.
A sensitivity panel can vary attainment while retaining 0.80 lot, then vary quantity while retaining the same rate. This two-axis view shows whether a favorable average comes from a stronger assumption or simply more capital. The purpose is not to find the most attractive cell; it is to reveal the condition on which the conclusion depends.
Attack common presentation tactics that conceal the loss
One misuse displays the USD 1,800 target from 1.20 lots but compares it with the USD 400 stop from 0.80 lot. The numerator and denominator then come from different quantities. A validation rule should require every row’s target and loss amounts to reconcile with the same lot, point value, and price distances.
Another misuse calls a placed 3R target a realized 3R winner even when the position exited partially. Reconstruction from fills should override labels. A third counts time exits that never reached the target as successes because they were profitable, changing the outcome definition from target attainment to positive P&L after results are known.
The workflow should also reject zero or negative stop distance, probabilities outside zero to one, missing point value, and upward step rounding through budget. If target distance is zero, the ratio can be zero but the stop-based lot may still be computed. If stop distance is zero, the size denominator is invalid and no quantity should be produced.
Retain an audit trail from plan through realized exit
At entry, save stop, target, distance units, point value, budget, raw and rounded lot, planned ratio, and any attainment assumption with its source. During the trade, append amendments rather than overwriting them. At exit, link every fill, cost, and conversion to the parent decision and calculate realized net P&L independently.
If the target or stop changes, record the timestamp, reason, and active position quantity. The new planned ratio applies only after the amendment and should not be backfilled to the entry record. This event history prevents a profitable discretionary exit from being presented later as though the original 3R plan had executed exactly.
Aggregated analysis should distinguish intended target attainment, positive trade outcomes, and realized R. Their counts can differ without inconsistency because they answer different questions. Keeping them separate allows reviewers to see whether the strategy’s distance plan, execution, and payoff distribution align rather than collapsing everything into one success percentage.
Use the cited educational logic without claiming performance evidence
CME educational examples support fixing an account loss amount, deriving contracts and stop ticks, and using a chosen risk-reward ratio for a profit exit. Separate CME sizing material likewise derives quantity from stop location and account risk rather than target distance. These relationships support the calculation order used here.
The CFTC warning supports distinguishing hypothetical results from actual conditions that include execution, spread, fees, and market changes. It does not provide the 40- or 30-percent attainment rates. Those rates and all three rows are invented solely to show how target assumptions and quantity interact.
The evidence therefore supports no claim that 2R or 3R is superior, that either expectancy will occur, or that USD 400 is an appropriate budget. It supports the narrower statement that a farther target does not enter the base stop-loss sizing equation and that multiplying the lot raises both modeled gain and modeled loss.
Translate the comparison into a defensible final statement
Given the hypothetical 50-point stop, USD 10 point value, and USD 400 budget, the base calculation is 0.80 lot. A 100-point or 150-point target changes planned reward-to-risk from 2 to 3 but leaves the stop loss at USD 400. This result is conditional on the stated units and excludes separate execution additions.
At 1.20 lots, the stop amount is USD 600, so the row exceeds the active budget by USD 200 even though its assumed binary expectancy is larger. That comparison makes the decision consequence visible: the average rose because exposure rose. The 3R label did not create a free increase in loss capacity.
The page can help a reviewer keep price planning, probability assumptions, and capital control distinct. It cannot recommend a target multiple, predict attainment, or guarantee fills. A valid narrower stop may change quantity for an analytical reason; a farther target alone does not authorize the same change. That boundary also prevents a favorable target scenario from silently changing the account’s loss authority. The same separation must survive exports and later performance reports, not only the visible comparison table.
Decision and control rules
- Calculate base size from stop distance and budget first.
- Store planned and realized reward-to-risk separately.
- Include target attainment when testing expectancy.
- Do not use a farther target as permission for a larger loss budget.
Common failure modes
- Treating a placed 3R target as a realized 3R gain.
- Showing the 1.5-times gain while hiding the 1.5-times stop loss.
- Counting partial or time exits as full target attainment.
Evidence and specifications
- CME Group — The 2% Rule
What this source supports: CME’s example fixes the account loss and derives contracts and stop ticks, then uses the chosen risk-reward ratio to set a profit exit, supporting separation of target distance from loss budget.
- CME Group — Proper Position Size
What this source supports: The exchange lesson derives size from stop location and account risk, not from the distance to a desired profit target.
- CFTC — Commodity Trading Systems Sold on the Internet
What this source supports: The CFTC warns that hypothetical results may omit actual execution, spreads, fees and market conditions, supporting the distinction between a planned target and realized payoff.
Questions to resolve
Is 3R always better than 2R?
No. Compare attainment, partial exits, costs and the loss distribution, not distance alone.
Which should be selected if expectancy is equal?
This article cannot decide. Dispersion, holding time, tail loss and capital constraints are separate considerations.
Should a farther target reduce size?
Target distance alone is not in the base-size formula. Recompute if stop distance or the loss budget also changes.
Can I tighten the stop to manufacture 3R?
Changing invalidation just to improve the ratio creates the stop-first reversal covered by Article 2.
Recalculate from current inputs
Calculate quantity from stop distance and loss budget, then evaluate target distance and attainment in separate fields.
Important: This is educational material about reward-to-risk and sizing. It does not recommend a target, attainment rate, budget or quantity. Hypothetical expectancy is not performance or a promise of future profit.