Even odds

The terms 'even odds', 'even money' or simply 'Evens' (1 to 1, or 2 for 1) imply that the payout will be one unit per unit wagered plus the original stake, that is, 'double-your-money'. Assuming there is no bookmaker fee or built-in profit margin, the actual probability of winning is 50%. The term "better than even odds" looks at it from the perspective of a gambler rather than a statistician. If the odds are Evens (1-1), and you bet 10, you would be returned 20, profiting 10. If the gamble was paying 4-1 and the event occurred, you would make a profit of 40. So, it is better than Evens from the gambler's perspective because it pays out more than one-for-one. If an event is more likely (positively favored) to occur than a 50-50 chance, then the odds will be worse than Evens, and the bookmaker will pay out less than one-for-one.

In popular parlance surrounding uncertain events, the expression "better than even" usually implies a better than (greater than) 50% chance of the event occurring, which is exactly the opposite of the meaning of the expression when used in a gaming context.

The odds are a ratio of probabilities; an odds ratio is a ratio of odds, that is, a ratio of ratios of probabilities. Odds-ratios are often used in analysis of clinical trials. While they have useful mathematical properties, they can produce counter-intuitive results: an event with an 80% probability of occurring is four times more likely to happen than an event with a 20% probability, but the odds are 16 times higher on the less likely event (4-1 against, or 4) than on the more likely one (1-4, or 4-1 on, or 0.25).

The logarithm of the odds is the logit of the probability.