How this calculator works
For a finite collection of equally likely outcomes, count the favourable and unfavourable possibilities. Their ratio gives odds for success, while reversing the ratio gives odds against it. Count ratios are reduced to their simplest whole-number form. The odds-for and odds-against input modes keep explicit success and failure labels to prevent accidental reversal. Direct probability mode displays a decimal ratio with ten significant digits; numeric probability outputs retain full precision.
Formula
P(success) = favourable/(favourable + unfavourable). Odds for = favourable:unfavourable. Odds against = unfavourable:favourable. Fair decimal odds = 1/P(success).
Worked example
Two favourable and three unfavourable outcomes give success probability 2/5 = 40%, odds for 2:3, odds against 3:2 and fair decimal odds 2.5.
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Frequently asked questions
Are odds 1:4 the same as a 25% probability?
Odds for 1:4 mean one success part and four failure parts, so the probability is 1/5 = 20%.
How do I enter odds against of 4:1?
Choose odds against, then enter success part 1 and failure part 4. The output labels show both directions.
What happens at probabilities zero and one?
Odds become 0:1 or 1:0. Zero probability has infinite fair decimal odds, shown as text.