Definition of Odds

For the alternative rock band, see Odds (band).

In probability theory and statistics the odds in favour of an event or a proposition are the quantity p / (1 − p) , where p is the probability of the event or proposition. In other words, an event with m to n odds would have probability m/(m + n). For example, if you chose a random day of the week, then the odds that you would choose a Sunday would be 1/6, not 1/7. These 'odds' are actually relative probabilities. Generally, 'odds' are not quoted to the general public in this format because of the natural confusion with the chance of an event occuring being expressed fractionally as a probability. Thus, the probability of choosing Sunday at random from the days of the week is 'one-seventh' (1/7), and although a bookmaker may (for his own purposes) use 'odds' of 'one-sixth' the overwhelming everyday use by most people is odds of the form 6 to 1, 6/1 or 6-1 (all read as 'six-to-one') where the first figure represents the number of ways of failing to achieve the outcome and the second figure is the number of ways of achieving a favourable outcome. This is also the most convenient way for a person to understand how much winnings will be paid if the selection is successful: the person will be paid 'six' of whatever stake unit was bet for each 'one' of the stake unit wagered. For example, a £15 winning bet at 6/1 will win '6 x £15 = £90' with the original £15 stake also being returned.