Glossary term
Odds
A way of expressing chance as the ratio of ways for something to happen against the ways for it not to happen.
Visual intuition
3 in 100
before new evidence
Odds: the 3 in, against the 97 out
The same crowd read two ways: probability compares the 3 highlighted people with all 100 (3 in 100); odds pit them against the 97 who are not — 3 to 97.
Formula
odds = probability / (1 - probability)
Example
If a horse wins with 0.2, its odds of winning are 0.2/0.8 — 1 to 4 in favor, which a bookmaker quotes as 4-to-1 against.
How It Works
and odds slice the same crowd differently. Probability compares the 3 highlighted people with all 100: 3 in 100, or 3%. Odds pit them against the other 97: 3 to 97. For a fair coin the odds are 1 to 1 — 'even odds' — while the probability is 50%. The distinction matters because casual speech mixes the two, bookmakers quote odds the other way around (odds against), and for rare events the numbers nearly coincide — odds of 3 to 97 work out to about a 3% probability — which is why odds ratios often stand in for risk ratios in research.
Concepts
Conditional Probability
The probability of something after new information changes what is still possible. The important move is to update the denominator: cases ruled out by the new information should no longer be counted. Many mistakes happen when people keep using the original odds after the situation has narrowed.
Expected Value
The long-run average outcome: each result weighted by how likely it is. It tells you whether a bet is favourable on average, but it ignores how badly a single rare outcome would hurt — which is why people rationally pay to avoid losses they could not absorb.
Related Facts
Probability
4 min · easy
A roulette wheel has no memory
After red lands ten times in a row, black feels 'due'. The next spin is still about 48.6% red, exactly as it was on the first.
Risk & Decisions
4 min · medium
Insurance is a bet you want to lose
On average you pay in more than you ever get back. Buying it is still the smart move.