odds

   a statement of the probabilities that an event will or will not happen. If the probability is a/(a + b) that the event will happen and b/(a + b) that it will not happen, then the odds are a-b (or a to b, or a:b) in favor of the event and b-a (or b to a, or b:a) against the event. In the division of the probability into a + b parts the values of a and b are usually chosen so that both numbers are small whole numbers with the smaller number equal to 1 if possible. Generally the odds are stated in whichever form puts the larger number first, and in many cases this will be the odds against the event. Thus 4-1 odds on a horse in a horse race can be viewed as an estimate that the probability of the horse's winning is 1/5.

   In some cases, odds are used to express probabilities explicitly: for example, if a geologist says that the odds are 5-1 against a volcano erupting this year, that is an estimate that the probability of an eruption is about 1/6. In betting situations, odds are at least a rough estimate for probabilities, but what they actually establish is the payoff ratio: if an event has a-b odds, then you must bet b in order to receive a + b if the event happens. Thus the odds can be viewed as the ratio of potential profit a to wager b. This traditional use of the word "odd" is believed to come from the old English word ord for a spear point, hence something hazardous.