Convert favorable-to-unfavorable ratio odds into probability. The displayed implied probability includes enough working to inspect signs and scale.
Odds appear in games, risk communication, forecasts, and betting markets, though prices may include margins.
Odds for an event compare favorable weight a with unfavorable weight b. Probability is a/(a+b).
Read Implied probability against Odds for the event, not in isolation. Use Odds against the event to estimate the Odds to Probability magnitude. When Odds against the event is altered, label the new Odds to Probability trial. Its Implied probability should not replace the original Odds to Probability answer.
Odds 3:2 imply 3/(3+2)=0.6, or 60%.
Add the two odds parts and divide the favorable part by that total.
Store Odds for the event, Odds against the event with the Odds to Probability output and identify the event in words. Inputs alone may not reveal whether odds were for or against, whether a row began at zero, or whether a cumulative boundary was inclusive. A short convention note prevents a correct value from being attached to the wrong question.
For Odds to Probability, before saving, check one invariant appropriate to the page: an integer count stays whole, a probability remains bounded, complementary areas total one, or a union does not exceed the summed set sizes.
Keep orientation clear: odds for differ from odds against. Both parts must use the same scale. If the Odds to Probability assumptions do not fit, consider reverse conversion.
Before using Implied probability downstream, substitute a simple Odds for the event into the same Odds to Probability relation. Preserve Odds against the event so the comparison remains fair. The resulting Implied probability provides a benchmark for detecting a misplaced sign, decimal, or input order.
Keep extra digits in Implied probability until the next step is known. Early rounding can obscure whether Odds for the event and Odds against the event satisfy the Odds to Probability relation. Round the final Implied probability once, using precision appropriate to the original Odds to Probability data.
No.
Probability one half.
No.
No; use 3/5.