{ "schemaVersion": 1, "datasetId": "csr-crypto-signal-losing-streak-probability-calculator-2026-07-13", "title": "Crypto Signal Losing Streak Probability Calculator", "description": "Calculate the exact probability of at least one crypto signal losing streak, compare the overlapping-window shortcut, and inspect 144 reproducible scenarios.", "canonicalUrl": "https://cryptosignalsreview.com/crypto-signal-losing-streak-probability-calculator/", "researchDate": "2026-07-13", "datePublished": "2026-07-13", "dateModified": "2026-07-13", "sourceCommit": "1e2b0f2a3765c3ac08d0682d6f3db6ea962e5983", "source": { "researchPath": "data/research/crypto-signal-losing-streak-probability-calculator-20260713.json", "researchSha256": "e29d0c5bffbee91d310eaa907d29f69aa75fe2ff21f26dd9efcfe69b98480fad", "generatorPath": "tools/generate-crypto-signal-losing-streak-probability-calculator.mjs", "generatorSha256": "b802875d298991adfeacb2ffd1ad1f5b064bd402f96ddad401824107580d1fd0", "checkerPath": "tools/check-crypto-signal-losing-streak-probability-calculator.mjs", "checkerSha256": "b5fa4ce9389134fcd2e6a9cf41dd42a9848ebefd4f96d38ce9b51d3481b8c76d", "immutableResearchUrl": "https://raw.githubusercontent.com/TheCryptoSimon/CryptoSignalsReview/1e2b0f2a3765c3ac08d0682d6f3db6ea962e5983/data/research/crypto-signal-losing-streak-probability-calculator-20260713.json" }, "selectionEvidence": { "property": "sc-domain:cryptosignalsreview.com", "searchType": "Web", "dateRange": "2026-05-22 through 2026-07-09", "sourceArchive": "data/research/crypto-signals-ervaringen-gsc-baseline-20260712.zip", "supportingPages": [ { "canonical": "https://cryptosignalsreview.com/crypto-signal-risk-reward/", "impressions": 29, "clicks": 0, "averagePosition": 11.62, "use": "Page-level evidence that the site already earns visibility for a quantitative signal-risk decision cluster." }, { "canonical": "https://cryptosignalsreview.com/telegram-crypto-signals-red-flags/", "impressions": 204, "clicks": 0, "averagePosition": 12.55, "use": "Page-level evidence that Google surfaced the site for signal-claim risk checks, including unrealistic performance framing; the row records impressions, not visits." } ], "selectionBoundary": "These are supporting page rows, not exact-query demand for a losing-streak calculator, general market volume, or a ranking forecast. The win-rate confidence calculator was published after this export and has no comparable baseline row. This canonical is selected for information gain: it solves a distinct run-probability problem with an exact, inspectable recurrence instead of creating query-variation pages." }, "method": { "name": "Finite-state dynamic program for the complement event", "stateSpace": "j = 0 through r - 1 trailing losses; each state is the joint probability mass that no run of r losses has occurred and the current trailing loss run has length j", "initialization": "dp[0] = 1 and every other state is 0 before the first outcome", "recurrence": [ "Let safe = sum(dp[j]) for j = 0 through r - 1.", "Add dp[r - 1] * q to an absorbing target-run accumulator using compensated summation.", "A win resets the trailing-loss state: next[0] = safe * p.", "A loss extends each nonabsorbing state: next[j + 1] += dp[j] * q for j = 0 through r - 2.", "The transition from state r - 1 on a loss reaches the target run, is accumulated directly, and is excluded from the no-run states.", "Replace dp with next and repeat for all n outcomes." ], "noRunProbability": "sum(dp[j]) after n outcomes", "atLeastOneRunProbability": "compensated sum of every absorbed dp[r - 1] * q transition; mathematically equal to 1 - noRunProbability but numerically stable when the run probability is extremely small", "complexity": "O(n * r) time and O(r) memory", "assumptions": [ "Every included outcome is classified using one predeclared binary win-loss rule.", "Outcomes are independent under the model.", "The win probability p is fixed across all n outcomes.", "The sequence contains the complete eligible chronology rather than a selected subset.", "The result is a model calculation, not an estimate of the provider's unknown true process." ] }, "metrics": { "scenarioRows": 144, "comparisonRows": 144, "winRates": 6, "outcomeCounts": 6, "streakLengths": 4, "providerScores": 0, "providerRankings": 0, "forecasts": 0 }, "defaults": { "defaultWinRatePercent": 60, "defaultCompletedOutcomes": 100, "defaultLosingStreakLength": 5, "inputLimits": { "winRatePercentMin": 0, "winRatePercentMax": 100, "completedOutcomesMin": 1, "completedOutcomesMax": 10000, "losingStreakLengthMin": 1, "losingStreakLengthMax": 100, "completedOutcomesRule": "finite base-10 integer input only", "losingStreakLengthRule": "finite base-10 integer input only", "relationalRule": "losing streak length must not exceed completed outcomes" }, "variables": { "p": "assumed probability of a win on each completed outcome", "q": "assumed probability of a loss on each completed outcome, equal to 1 - p", "n": "number of completed binary outcomes", "r": "target number of consecutive losses", "dpJ": "probability that no target run has occurred and the current trailing loss run has length j" }, "modelAssumptions": [ "Every included outcome is classified using one predeclared binary win-loss rule.", "Outcomes are independent under the model.", "The win probability p is fixed across all n outcomes.", "The sequence contains the complete eligible chronology rather than a selected subset.", "The result is a model calculation, not an estimate of the provider's unknown true process." ], "exactMethod": { "name": "Finite-state dynamic program for the complement event", "stateSpace": "j = 0 through r - 1 trailing losses; each state is the joint probability mass that no run of r losses has occurred and the current trailing loss run has length j", "initialization": "dp[0] = 1 and every other state is 0 before the first outcome", "perOutcomeRecurrence": [ "Let safe = sum(dp[j]) for j = 0 through r - 1.", "Add dp[r - 1] * q to an absorbing target-run accumulator using compensated summation.", "A win resets the trailing-loss state: next[0] = safe * p.", "A loss extends each nonabsorbing state: next[j + 1] += dp[j] * q for j = 0 through r - 2.", "The transition from state r - 1 on a loss reaches the target run, is accumulated directly, and is excluded from the no-run states.", "Replace dp with next and repeat for all n outcomes." ], "noRunProbability": "sum(dp[j]) after n outcomes", "atLeastOneRunProbability": "compensated sum of every absorbed dp[r - 1] * q transition; mathematically equal to 1 - noRunProbability but numerically stable when the run probability is extremely small", "numericalRule": "Accumulate absorbed mass with compensated summation, calculate the shortcut as -expm1(candidateWindows * log1p(-q^r)), compare the direct and complement totals within tolerance, and clamp final floating-point probabilities to the inclusive range 0 through 1.", "complexity": "O(n * r) time and O(r) memory" }, "derivedOutputs": [ { "id": "exact-at-least-one-run", "label": "Chance of at least one target losing streak", "formula": "compensated sum of absorbed target-run transitions from the finite-state recurrence", "status": "primary exact result" }, { "id": "exact-no-run", "label": "Chance of avoiding the target streak", "formula": "sum of the final nonabsorbing states", "status": "exact complement" }, { "id": "specific-fixed-block", "label": "Chance that one specified block is all losses", "formula": "q^r", "status": "exact for one prespecified block only" }, { "id": "overlapping-window-shortcut", "label": "Common independent-window shortcut", "formula": "-expm1((n - r + 1) * log1p(-q^r)), algebraically equal to 1 - (1 - q^r)^(n - r + 1)", "status": "comparison only; generally nonexact when multiple candidate windows overlap. It is exact when there is one candidate window, when r is 1, or at degenerate p = 0 or p = 1 boundaries." }, { "id": "shortcut-error", "label": "Shortcut minus exact result", "formula": "overlapping-window shortcut - exact at-least-one-run probability", "status": "method comparison, not model uncertainty" } ], "interpretationRules": [ "Describe the result as an exact calculation under the stated model, never as the exact probability of a real provider's future outcomes.", "Do not infer that a high streak probability makes a strategy unprofitable or that a low streak probability makes it safe.", "Do not infer record quality, independence, or a stable win probability from a reported win rate.", "Keep loss size, leverage, liquidation, drawdown, and account-survival questions outside the calculator output.", "Show the exact result before the shortcut comparison so the approximation cannot become the headline claim." ] }, "defaultScenario": { "rowKey": "win-rate-60-outcomes-100-streak-5", "winRatePercent": 60, "lossRatePercent": 40, "completedOutcomes": 100, "streakLength": 5, "candidateWindows": 96, "exactAtLeastOneProbability": 0.45907367434132, "exactNoRunProbability": 0.54092632565868, "specificBlockProbability": 0.01024, "overlappingWindowShortcutProbability": 0.627719542444097, "shortcutMinusExactPoints": 16.8645868103 }, "scenarios": [ { "rowKey": "win-rate-40-outcomes-20-streak-3", "winRatePercent": 40, "lossRatePercent": 60, "completedOutcomes": 20, "streakLength": 3, "candidateWindows": 18, "exactAtLeastOneProbability": 0.927681851093932, "exactNoRunProbability": 0.0723181489060682, "specificBlockProbability": 0.216, "overlappingWindowShortcutProbability": 0.987477555131921, "shortcutMinusExactPoints": 5.9795704038 }, { "rowKey": "win-rate-40-outcomes-20-streak-5", "winRatePercent": 40, "lossRatePercent": 60, "completedOutcomes": 20, "streakLength": 5, "candidateWindows": 16, "exactAtLeastOneProbability": 0.47765109724545, "exactNoRunProbability": 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"coinlike-100-5", "winRatePercent": 50, "completedOutcomes": 100, "losingStreakLength": 5, "exactAtLeastOneRunProbability": 0.810109599196358, "specificFixedBlockProbability": 0.03125, "overlappingWindowShortcutProbability": 0.9525403327041213, "shortcutOverstatementPercentagePoints": 14.243073350776324 }, { "id": "sixty-percent-100-5", "winRatePercent": 60, "completedOutcomes": 100, "losingStreakLength": 5, "exactAtLeastOneRunProbability": 0.4590736743413203, "specificFixedBlockProbability": 0.010240000000000003, "overlappingWindowShortcutProbability": 0.6277195424440976, "shortcutOverstatementPercentagePoints": 16.864586810277725 }, { "id": "seventy-percent-200-6", "winRatePercent": 70, "completedOutcomes": 200, "losingStreakLength": 6, "exactAtLeastOneRunProbability": 0.09521162970955765, "specificFixedBlockProbability": 0.0007290000000000007, "overlappingWindowShortcutProbability": 0.1325581843380913, "shortcutOverstatementPercentagePoints": 3.7346554628533646 }, { "id": 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9.989999999999867e-17 }, { "id": "ninety-nine-point-nine-percent-10000-5", "winRatePercent": 99.9, "completedOutcomes": 10000, "losingStreakLength": 5, "exactAtLeastOneRunProbability": 9.986004999946471e-12, "specificFixedBlockProbability": 1.0000000000000044e-15, "overlappingWindowShortcutProbability": 9.99599999995009e-12, "shortcutOverstatementPercentagePoints": 9.99500000361942e-13 }, { "id": "zero-percent-boundary-10000-10", "winRatePercent": 0, "completedOutcomes": 10000, "losingStreakLength": 10, "exactAtLeastOneRunProbability": 1, "specificFixedBlockProbability": 1, "overlappingWindowShortcutProbability": 1, "shortcutOverstatementPercentagePoints": 0 }, { "id": "one-hundred-percent-boundary-10000-10", "winRatePercent": 100, "completedOutcomes": 10000, "losingStreakLength": 10, "exactAtLeastOneRunProbability": 0, "specificFixedBlockProbability": 0, "overlappingWindowShortcutProbability": 0, "shortcutOverstatementPercentagePoints": 0 } ], "officialSources": [ { "id": "cornell-run-probabilities", "publisher": "Cornell University Biometrics Unit", "authors": [ "Steven J. Schwager" ], "title": "Run Probabilities in Sequences of Bernoulli Trials", "publicationDate": "1981-09", "url": "https://hdl.handle.net/1813/32857", "accessedAt": "2026-07-13", "use": "Primary technical source for the exact probability of at least one run of k successive outcomes in n Bernoulli trials and for a recursive solution.", "boundary": "The report studies Bernoulli runs generally. The implementation uses an equivalent finite-state complement recurrence and does not claim that real trading outcomes are independent or identically distributed." }, { "id": "arxiv-run-recurrence", "publisher": "arXiv", "authors": [ "Jungtaek Oh", "Chongjin Park", "Sungsu Kim" ], "title": "Recurrence algorithms of waiting time for the success run of length k in relation to generalized Fibonacci sequences", "publicationDate": "2022-10-17", "url": "https://arxiv.org/abs/2210.08797", "accessedAt": "2026-07-13", "use": "Primary research context for recurrence algorithms, waiting times, longest runs, and the distinction between independent and Markov-dependent Bernoulli trials.", "boundary": "The calculator implements only the independent, constant-probability model and prominently excludes Markov dependence." }, { "id": "nist-binomial", "publisher": "NIST/SEMATECH", "title": "1.3.6.6.18. Binomial Distribution", "url": "https://itl.nist.gov/div898/handbook/eda/section3/eda366i.htm", "accessedAt": "2026-07-13", "use": "Official reference for two mutually exclusive outcomes and the fixed single-trial probability assumption.", "boundary": "A binomial count distribution alone does not answer an order-sensitive run question; the calculator adds an explicit run-state recurrence." }, { "id": "nist-runs", "publisher": "NIST/SEMATECH", "title": "1.3.5.13. Runs Test for Detecting Non-randomness", "url": "https://www.itl.nist.gov/div898/handbook/eda/section3/eda35d.htm", "accessedAt": "2026-07-13", "use": "Official context that runs are consecutive dichotomous values and that randomness is an assumption to inspect rather than silently grant.", "boundary": "The calculator is not a runs test, does not compute a p-value, and does not diagnose nonrandomness from one observed streak." }, { "id": "cftc-trading-systems", "publisher": "U.S. Commodity Futures Trading Commission", "title": "Fraud Advisory: Commodity Trading Systems Sold on the Internet", "url": "https://www.cftc.gov/LearnAndProtect/AdvisoriesAndArticles/fraudadv_tradingsystem.html", "accessedAt": "2026-07-13", "use": "Official investor-protection context on consecutive losses, hypothetical performance, actual market conditions, omitted costs, and break-even effects.", "boundary": "The advisory concerns commodity futures and options trading systems, not every crypto product or jurisdiction. It does not validate this model, evaluate a crypto-signal provider, or turn a streak probability into a risk-sizing recommendation." } ], "decisionBoundary": "This calculator answers a narrow probability question under an independent, constant-probability Bernoulli model. It does not verify a provider's record, estimate a true win rate, prove independence, model changing market regimes, include open or omitted calls, measure payoff size, fees, slippage, funding, leverage, drawdown or account survival, predict future results, rank a provider, or recommend a trade, risk size, or subscription.", "citationGuidance": { "preferredCitation": "CryptoSignalsReview Evidence Desk (2026), Crypto Signal Losing Streak Probability Calculator, research date 2026-07-13.", "reuseBoundary": "Derived scenario rows may be reused with the canonical URL, assumed win rate, completed-outcome count, target streak length, independent constant-probability model, exact recurrence label, research date, and decision boundary intact. Do not relabel model output as verified provider performance, a forecast, profitability, safety, or trading advice." } }