Odds, Probability & Bankroll
Odds
Odds compare the chance of something happening to the chance of it not happening, written as a ratio rather than a fraction of the whole.
- Formula
odds = p / (1 - p), wherepis the probability of the event 3- Range
- Zero to infinity, because odds compare event to non-event rather than taking a fraction of the whole 4
- Example
- A probability of 0.2 gives odds of 0.25, often written as 1:4 5
- Also called
- Odds in favor; odds against when expressed in the opposite direction 12
Key points
- Odds compare the chance of an event to the chance of it not happening, using the formula
p / (1 - p)3. - Unlike probability, which is bounded between 0 and 1, odds range from 0 to infinity because they are a ratio of two complementary outcomes 4.
- In finite equally likely cases, odds can be written as favorable outcomes : unfavorable outcomes 1.
- Betting odds are a different concept: they represent the payout format offered by bookmakers, not the abstract probability ratio 67.
Common odds expressions and their meaning
| Fractional odds | Implied probability | Meaning |
|---|---|---|
| 1/2 | 66.7% | Event is twice as likely to happen as not |
| 1/1 (evens) | 50% | Event is as likely to happen as not |
| 2/1 | 33.3% | Event is half as likely to happen as not |
| 4/1 | 20% | Event is four times more likely not to happen |
| 4/5 | 55.6% | Event is slightly more likely to happen |
| 1/5 | 83.3% | Event is five times more likely to happen |
| 2/5 | 71.4% | Event is 2.5 times more likely to happen |
| 6/5 | 45.5% | Event is slightly less likely to happen |
| 1/6 | 85.7% | Event is six times more likely to happen |
How to convert probability to odds
- Take the probability
pof the event (e.g., 0.20). - Subtract
pfrom 1 to get the probability of the event not happening (0.80). - Divide
pby1 - p(0.20 / 0.80 = 0.25). - Express the result as a ratio: 0.25 = 1:4, meaning 1 chance in favor to 4 against.
Common questions
What are the odds to win powerball?
The odds of winning the Powerball jackpot are about 1 in 292 million. This means for every 292 million tickets, on average one will win the top prize.
What are odds of winning powerball?
The odds of winning any Powerball prize are about 1 in 24.9. The jackpot odds are about 1 in 292 million, making it extremely unlikely to win the top prize.
What are odds and even numbers?
What are the odds of getting pregnant?
For a healthy couple trying to conceive, the odds of pregnancy in a single menstrual cycle are about 20–30%. Over one year, about 80–90% of couples will conceive.
Where this term is used
Related terms
Sources
- Odds en.wikipedia.org Provides the general definition of odds and its use in probability theory and gambling.
- 3.10 Odds | Probability, statistics, and the likelihood ratio for non-experts [1st Edition] lrcfs-ap2.dundee.ac.uk Offers an academic explanation of odds as a ratio of event to non-event.
- LibGuides@Southampton: Relative Risk and Odds Ratios library.soton.ac.uk Gives the formula for odds and explains the conversion from probability.
- Relative vs absolute risk and odds: Understanding the difference pmc.ncbi.nlm.nih.gov Explains the zero-to-infinity range of odds compared to probability.
- 10. The Odds Ratio (or) pmc.ncbi.nlm.nih.gov Provides the example of probability 0.2 converting to odds of 0.25 (1:4).
- Mathematics of bookmaking en.wikipedia.org Distinguishes betting odds from the abstract probability ratio.
- Gambling mathematics en.wikipedia.org Further clarifies the difference between betting odds and mathematical odds.
Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.