Scratch Card EV Calculator
The formula
What the scratch card ev tells you
The plain odds behind scratch card ev: 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.
Scratch Card EV: what this tool answers
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Scratch Card EV 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.
Like most useful measures, Scratch Card EV is a summary, and summaries hide as much as they reveal. The companion outputs and the input table are here to reopen what the headline compressed.
There is a habit that separates people who get useful answers from Gambling & Probability numbers: they decide what question the figure answers before they compute it. Scratch Card EV answers “Single-trial probability?” — and nothing else, which is precisely why the result is trustworthy.
Nothing below is stock text pasted around a number: the worked example computes single-trial probability = 40.00% from this tool’s own defaults, 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. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
Inside the Scratch Card EV calculation: formula and every input
Here is the complete model this tool runs — p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n — with each input explained below. If a competitor’s page gives you a different answer from the same inputs, this is the text that settles which of you is right.
Favourable outcomes (example value 2) is a quantity rather than a category — precision here is cheap and worth having. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Possible outcomes (example value 5) is a measured number in the unit named by the label; the formula does not convert for you. 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 numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
A fully worked Scratch Card EV example
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Favourable outcomes, Possible outcomes, Repetitions (independent). The endpoint of that chain is 40.00% of single-trial probability, sitting in the “Live odds — worth calculating the payoff” band.
- p = 2 ÷ 5 = 0.4000
- Odds against = (1−p)÷p = 1.50:1
- P(hit within 2 tries) = 1 − 0.6000^2 = 64.0 %
Odds against — 1.50 :1. Read next to the headline, this is the figure that shows the shape of the trade-off.
At least one hit in 2 — 64.0%. Read next to the headline, this is the figure that shows the shape of the trade-off.
Fair payout to break even — 2.50 :1. If your inputs change, this is usually the first companion figure to move.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
The Scratch Card EV corridor: your result across a realistic band
Single-point answers invite false confidence, so the same engine was run across a band around the input that matters most here. Each row is a full recalculation of Scratch Card EV, not an interpolation.
| Possible outcomes setting | Single-trial probability |
|---|---|
| 80 % of the example value | 50.00% |
| 90 % of the example value | 44.44% |
| example inputs | 40.00% |
| 110 % of the example value | 36.36% |
| 120 % of the example value | 33.33% |
Across 5 settings of Possible outcomes, the result spans 33.33% to 50.00%. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Possible outcomes alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Scratch Card EV the most
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the single-trial probability recomputed, so the ranking below is measured rather than asserted. Read it as a map of where Scratch Card EV is fragile — drawn for the example inputs, which is the map you want when deciding what to measure carefully.
- Nudge Possible outcomes by ±10 % and Scratch Card EV lands between 36.36% and 44.44% (sensitivity ≈11.1 %)
- Favourable outcomes +10 % → Scratch Card EV = 44.00% · −10 % → 36.00% (the single-trial probability shifts ≈10.0 %)
Possible outcomes is the dominant lever here: ten percent either way moves the result by about 11.1 %, from 36.36% to 44.44%. 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). The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
Interpreting the Scratch Card EV verdict
Nobody acts on a bare figure — they act on a figure with a comparison attached. The verdict attached to the default calculation — “Live odds — worth calculating the payoff” — is one band on a ladder your own figure may sit somewhere else on. The sensitivity list shows how far a modest input error moves you along that ladder: for Possible outcomes, ±10 % covers 36.36% to 44.44%. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
Where Scratch Card EV sits next to similar measures: this tool answers “how much is the Scratch Card EV”, while the related calculators answer “what do I do about it”. Reading the result alone tends to over-weight a single snapshot; pairing it with the companion tools above turns the number into a decision.
The errors that quietly break a Scratch Card EV 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.
Confusing a large number with an important one. Scratch Card EV can be dominated by one input whose absolute value looks unimpressive, which is why this page ranks influence separately from magnitude.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Possible outcomes dominating — a careful figure there beats false precision everywhere else.
Another is comparing across contexts: a Scratch Card EV computed with one set of conventions should never be lined up against a figure computed with another. Check the inputs behind both before ranking them.
Scratch Card EV verification checklist
- Recompute once with the dominant input deliberately set low, and see whether the decision changes.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Check Possible outcomes before anything else: it is the measured dominant input, ≈11.1 % of Scratch Card EV per ten percent.
- Note the date and the inputs beside the number so the figure can be audited later.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Confirm the answer against one independent method or published benchmark for Scratch Card EV.
How to use the Scratch Card EV tool properly
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Scratch Card EV takes a minute to learn and applies to every input above.
Step 1 — start from evidence. The inputs behind Scratch Card EV are favourable outcomes, possible outcomes, repetitions (independent). Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. When in doubt, prefer the boring input: the interesting one is usually the one you misread.
Step 2 — compute the version you would not be embarrassed by. If a stranger audited your inputs, which set would you hand over? Enter that set, read the result, and treat everything else as upside. The point of transparency is that a reader can disagree with a specific line rather than with you.
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. One decimal place more than your data supports is one decimal place of fiction.
Step 4 — ask what would have to be true. Take the result you want and work backwards through the inputs until you find the assumption that produces it; then decide honestly whether that assumption is defensible. Write the figure down before moving on; memory flatters whichever number you saw last.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the 40.00% output. Six months from now the context is what turns this figure into a trend. A figure nobody can reproduce is a figure nobody will act on twice.
Where Scratch Card EV matters in practice
In Gambling & Probability the figure computed here is usually the first one somebody asks to see. Having it — with the formula behind it — changes your position in the conversation from participant to reference. When two sources disagree, it is almost never the arithmetic that differs.
The companion outputs — Odds against and At least one hit in 2 — exist for the second stage of that screen: the headline sizes the prize, while the companions describe the trade-off you are accepting to get it. Say the answer out loud before you save it; if it sounds wrong, the model did not change, your understanding did.
Treat Scratch Card EV like a smoke alarm rather than a painting — its value is in being tested periodically, not in being admired once. Re-running a number costs seconds; retracting a decision costs considerably more.
People also ask about Scratch Card EV
What affects Scratch Card EV the most?
Scratch Card EV is driven above all by Possible outcomes. Perturbing only that field by ten percent either way produced 36.36% against the 40.00% baseline — a ≈11.1 % response, while Favourable outcomes manages ≈10.0 %.
Which matters more: favourable outcomes or possible outcomes?
By the numbers, Possible outcomes: a ten-percent change in it moves the result ≈11.1 %, versus ≈10.0 % for Favourable outcomes. Spend your measuring effort in that order — precision on the weaker lever buys almost nothing.
What is a typical Scratch Card EV?
With the example inputs on this page the result is 40.00%, labelled “Live odds — worth calculating the payoff”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.
How do I calculate Scratch Card EV by hand?
Use the stated model — p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n — and substitute in the order the tool prints (it starts from p = 2 ÷ 5 = 0.4000). On the example inputs the hand route lands on 40.00%, exactly what the calculator shows. A spreadsheet reproduces it in two or three cells; doing it once by hand is what makes the automated answer trustworthy.
What happens to Scratch Card EV if possible outcomes changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the single-trial probability goes across 36.36% to 44.44%, a swing of roughly 11.1 % around the 40.00% baseline. That ratio is the practical definition of how much this input matters.
Is the Scratch Card EV result of 40.00% good or bad?
The tool answers “what”, not “whether”: 40.00% carries the verdict “Live odds — worth calculating the payoff” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
Is Scratch Card EV 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.
Is Scratch Card EV 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 40.00% result as the correct answer to the question you typed — and check the assumptions section before acting on it.
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.
Do I need an account to use this Scratch Card EV calculator?
No, and no data leaves the tab. The engine runs in the page itself, which is why the worked example, the bands and the sensitivity ranking all respond instantly to your keystrokes.
What the labels on this page mean
- Odds against
- 1.50 :1 on the example inputs — a companion figure printed beside the headline of Scratch Card EV so that no result is read in isolation.
- At least one hit in 2
- 64.0% for the Scratch Card EV worked case; it sits next to the main result because it carries context the headline leaves out.
- Fair payout to break even
- 2.50 :1 in the default Scratch Card EV calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Single-trial probability
- The primary output of this tool: 40.00% 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 calculation written out in full so that nothing on this page has to be taken on trust.
- Verdict band
- The interpretation attached to a result (“Live odds — worth calculating the payoff” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Scratch Card EV moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
The provenance of this Scratch Card EV calculation
There is no black box on this page — the engine evaluates 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.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. What that buys you is reproducibility — two people, two browsers, the same arithmetic, and a printed trail from inputs to result that either of them can audit.
Next steps after the calculation
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
Whoever you are (people who need one trustworthy number before their next decision), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Miscellaneous & Fun, a dated figure is a trend, and an undated one is a rumour.