Probability Calculator

Features

• Combinations C(n,r) and permutations P(n,r) with exact BigInt values, not scientific notation
• The formula and its simplified form are given as well
• Conditional probability via Bayes, with the substitution written out step by step
• Decimal, fractional, American and implied odds all converted
• With two odds, the sum of implied probabilities and the bookmaker margin
• Expected value, variance and standard deviation, with each outcome’s contribution
• Probabilities that do not sum to 1 raise an error instead of being normalised
• All four calculations run on your machine; nothing is uploaded

How to use

1. Choose a mode: combinations, probability, odds, or expected value
2. Enter the data for that mode (n and r; P(A), P(B|A), P(B); one or two odds; or “outcome, probability, payoff” per line)
3. The result appears as you type and every row can be copied

FAQ

Can C(100, 50) really be computed exactly?

Yes. The whole calculation uses BigInt, free of the 53-bit limit of a double. The answer is 100891344545564193334812497256 — thirty digits — and the trailing `497256` would simply be lost with ordinary floating point.

How is the bookmaker margin worked out?

Take the reciprocal of each decimal odds to get its implied probability; they usually add up to more than 100%, and the excess is the bookmaker’s profit. For odds of 1.5 and 2.8 the implied probabilities sum to about 102.38%, so the margin is about 2.38%.

Why does a probability sum other than 1 stop the tool?

Because not normalising is deliberate. If the tool quietly turned 0.3 + 0.3 into 1, you would believe your probabilities were fine when a row is missing or wrong. Reporting the error and the actual sum is what lets you fix the data.

Why show the substitution for conditional probability?

Because P(A|B) and P(B|A) are very easy to mix up. Writing out the step where P(B|A), P(A) and P(B) go into the formula lets you check at a glance that the two directions were not swapped.