Ruin Probability Calculator
The formula
What the ruin probability tells you
The plain odds behind ruin probability: single-event probability, the fair-price payout it implies, and how repetition moves the chance of at least one success.
Calculation: p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n. Enter your inputs and every substitution is shown below the result.
Reading the result
The fair-payout line is the decision column — any offered price above it carries positive expected value, below it funds the house.
Limitations and best practice
Independence is the assumption; card draws, weather and streaks correlate, which shrinks the repetition column’s real value.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Do odds “even out”?
What changes with repetition?
Source & methodology
Classical probability (Laplace) for equally-likely outcomes.
Ruin Probability explained: formula, worked example and honest limits
Every bet is a price, and this page computes whether the price is fair. Ruin Probability is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Single-trial probability in real time, and see every substitution printed below.
Most confusion about Ruin Probability comes from mixing up the input you control with the input you merely observe. The formula treats them identically, but your decisions should not: one deserves measurement, the other deserves a defensible estimate.
A calculation like this one is worth roughly as much as a careful sentence: it forces several vague considerations into one comparable quantity. Once Ruin Probability is on the table, the argument can stop being about impressions.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here single-trial probability = 33.33%, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Possible outcomes first, at ≈11.1 % of the headline for a ten-percent error either way in that input. Read the sections in order and you will be able to reproduce every figure by hand.
Every input in Ruin Probability, and what it does to the answer
The engine implements a single stated model: p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n. There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Favourable outcomes (example value 2) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Possible outcomes (example value 6) is a quantity rather than a category — precision here is cheap and worth having. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
Repetitions (independent) (example value 2) is a plain measured quantity — the unit shown in the label is the unit the formula expects. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
The default Ruin Probability calculation, written out in full
The tool prints its own working; this is the same arithmetic on the example values, reproduced so you can follow it by hand. Starting figures: Favourable outcomes, Possible outcomes, Repetitions (independent). The endpoint of that chain is 33.33% of single-trial probability, sitting in the “Live odds — worth calculating the payoff” band.
- p = 2 ÷ 6 = 0.3333
- Odds against = (1−p)÷p = 2.00:1
- P(hit within 2 tries) = 1 − 0.6667^2 = 55.6 %
Odds against — 2.00 :1. This is the number experienced users quote when the headline alone would mislead.
At least one hit in 2 — 55.6%. This is the number experienced users quote when the headline alone would mislead.
Fair payout to break even — 3.00 :1. Read next to the headline, this is the figure that shows the shape of the trade-off.
Re-running with your own figures is instant; re-running by hand once is the best way to know the tool is telling you the truth.
The Ruin Probability corridor: your result across a realistic band
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent?
| Possible outcomes setting | Single-trial probability |
|---|---|
| 80 % of the example value | 41.67% |
| 90 % of the example value | 37.04% |
| example inputs | 33.33% |
| 110 % of the example value | 30.30% |
| 120 % of the example value | 27.78% |
That spread — 27.78% at the low end, 41.67% at the high — is what a careful read of Ruin Probability looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Possible outcomes alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Ruin Probability the most
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the single-trial probability was recalculated from scratch. For Ruin Probability the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Nudge Possible outcomes by ±10 % and Ruin Probability lands between 30.30% and 37.04% (sensitivity ≈11.1 %)
- Nudge Favourable outcomes by ±10 % and Ruin Probability lands between 30.00% and 36.67% (sensitivity ≈10.0 %)
Possible outcomes is the dominant lever here: ten percent either way moves the result by about 11.1 %, from 30.30% to 37.04%. That is where a careless figure does the most damage, so check it against a source, and treat Favourable outcomes as the second priority (≈10.0 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
Reading the result: bands, zones and thresholds
Nobody acts on a bare figure — they act on a figure with a comparison attached. The default case lands in the “Live odds — worth calculating the payoff” band, and bands are deliberately wide because real situations overlap. Before treating the band as fact, note its width: ten percent either way on Possible outcomes already spans 30.30% to 37.04%. The practical reading rules: compare against your own history before comparing against other people; treat band boundaries as zones, not walls — one point on the wrong side of a threshold rarely changes a real outcome; and when a companion output contradicts the headline, believe the pair.
In Miscellaneous & Fun, Ruin Probability is one instrument in an orchestra: on its own it is a number, next to Odds against and At least one hit in 2 it becomes a diagnosis. The tools linked above exist so the headline never has to carry that weight alone.
The errors that quietly break a Ruin Probability figure
Independence is the assumption; card draws, weather and streaks correlate, which shrinks the repetition column’s real value. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Reporting the headline and quietly discarding Odds against. The companions are where the shape of the trade-off survives the rounding.
Attention is also misallocated between fields. Having measured this engine, we can say where it belongs: Possible outcomes first, everything else second.
The subtlest error is answering the wrong question precisely. Confirm that single-trial probability is actually the quantity your decision needs — the arithmetic is flawless either way, which is what makes the mistake invisible.
Six things to confirm before acting on Ruin Probability
- Confirm the example values are plausible for your own situation before replacing them.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Check Possible outcomes before anything else: it is the measured dominant input, ≈11.1 % of Ruin Probability per ten percent.
- Compare the result with one independent method or published benchmark.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
How to use the Ruin Probability tool properly
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — one document, one pass. Open the statement, label or record that holds favourable outcomes, possible outcomes, repetitions (independent) and transcribe straight into the form. Transcription from a single source removes the mismatch errors that appear when figures are assembled from three different places. Re-running a number costs seconds; retracting a decision costs considerably more.
Step 2 — start from the case you can defend. Enter pessimistic-but-honest figures first; the optimistic run is a ceiling, not a plan. A conclusion that holds on conservative inputs holds everywhere. Write the figure down before moving on; memory flatters whichever number you saw last.
Step 3 — change one input at a time. Nudge a single field by ten percent, watch the headline and its companions move, then undo it. Two or three fields will dominate — the sensitivity table above already ranks them for this engine. Half of a good calculation is knowing which input you would hate to be wrong about.
Step 4 — run the scenario trio. Expected, pessimistic, optimistic. The gap between pessimistic and expected is the number to plan against; the optimistic result is useful only as a ceiling. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the 33.33% output. Six months from now the context is what turns this figure into a trend. If a result feels obviously right, that is the moment to check the inputs hardest.
The real-world conversations Ruin Probability settles
Numbers earn their keep in conversations, and Ruin Probability is no exception. In Miscellaneous & Fun discussions around Gambling & Probability, this figure decides whether an option stays on the table: it converts an opinionated debate into an arithmetic one, and arithmetic is the only referee both sides accept. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
The audience for this page is players deciding whether a wager is mathematically worth taking. In professional Gambling & Probability practice the pattern is always the same — screen with Ruin Probability, then invest slow analysis only in whatever survives the screen. A figure with a date beside it becomes evidence; without one it stays an anecdote.
There is a personal-administration use people overlook: periodic self-checking. Ruin Probability quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. Estimates improve most when the worst case is written down in ink.
Ruin Probability — frequently asked questions
What affects Ruin Probability the most?
Ruin Probability is driven above all by Possible outcomes. Perturbing only that field by ten percent either way produced 30.30% against the 33.33% baseline — a ≈11.1 % response, while Favourable outcomes manages ≈10.0 %.
Which matters more: favourable outcomes or possible outcomes?
For Ruin Probability, Possible outcomes wins the head-to-head (≈11.1 % against ≈10.0 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.
What is a typical Ruin Probability?
On the worked example above Ruin Probability comes out at 33.33%. Treat that as one point on a distribution rather than a norm: the bands, the companion outputs and the sensitivity ranking tell you how wide the plausible range really is.
How do I calculate Ruin Probability by hand?
Three steps: write the formula (p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n), insert your values, and simplify. The worked example section shows exactly that chain for the default inputs; replicating it once on paper teaches you more about Ruin Probability than any number of calculator runs.
What happens to Ruin Probability if possible outcomes changes by 10 %?
Try it in the form above and the printed substitution will follow you; the pre-computed answer for the defaults is 30.30% to 37.04% across the ten-percent probe, i.e. ≈11.1 % sensitivity on the single-trial probability.
Is the Ruin Probability result of 33.33% good or bad?
Good and bad are comparisons, so the honest test is three questions: where does your own Ruin Probability sit against the 33.33% reference above, how far would a plausible input error move it (≈11.1 % per ten percent on Possible outcomes), and what does the alternative option compute to?
Is Ruin Probability accurate?
The arithmetic is exact: p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n is evaluated with full floating-point precision and every substitution is printed in the worked example. What limits accuracy is input quality and the model’s assumptions, so treat the 33.33% result as the correct answer to the question you typed — and check the assumptions section before acting on it.
Is Ruin Probability actually useful?
As a conversation piece, yes — and the underlying method transfers: the same p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n family shows up in Miscellaneous & Fun decisions that are far less playful.
Do odds “even out”?
Each trial is memoryless — the law of large numbers guarantees averages over the long haul, not corrections soon.
What changes with repetition?
The at-least-one line compounds (1−(1−p)^n) — 3 % once per try becomes 1−0.97^30 ≈ 60 % across 30 tries.
Does this Ruin Probability tool store my numbers?
No. The entire calculation runs in your browser session; nothing entered above is transmitted or saved, which is the correct behaviour for sensitive Miscellaneous & Fun figures and the reason you can re-run this page as often as you like.
Glossary for Ruin Probability
- Odds against
- 2.00 :1 in the default Ruin Probability calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- At least one hit in 2
- 55.6% for the Ruin Probability worked case; it sits next to the main result because it carries context the headline leaves out.
- Fair payout to break even
- 3.00 :1 for the Ruin Probability worked case; it sits next to the main result because it carries context the headline leaves out.
- Single-trial probability
- The primary output of this tool: 33.33% for the default inputs, computed exactly from p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “Live odds — worth calculating the payoff”, and your inputs may not.
- Sensitivity (±10 %)
- How far the Ruin Probability moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
The model is published arithmetic implemented exactly as written: p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n. Source of record: Classical probability (Laplace) for equally-likely outcomes. Any other implementation of this model should return the same figure for the same inputs. If one does not, the difference is in its assumptions — which this page prints and that one probably does not.
This page is an estimation aid, not professional advice. The design rule is simple: two people entering identical figures must get identical answers. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
After the number: what to do with it
Compare the computed edge against the actual price being offered; a positive theoretical edge still loses to bad odds.
This page was written for players deciding whether a wager is mathematically worth taking, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.