Applicable Mathematics/Odds

"Odds" is a way of expressing the likelihood of an event.

The more usual way of expressing the likelihood of an event is its "probability" (the percentage of future trials which are expected to produce the event: so in tossing a coin believed to be fair, we would assign a probability of 50% (or one half, or 0.5) to the event "heads").

The ODDS of an event, however, is the ratio of the probability of the event happening to the probability of the even not happening (i.e. the ODDS of a fair coin landing heads is 50%:50% = 1:1 = 1). It is the ODDS we are using when we use a phrase like "it is 50/50 whether I get the job" or "The chances of our team winning are 2 to 1".

Or, For example, when rolling a fair die, there is one chance that you will roll a 1 and five chances that you will not. The odds of rolling a 1 are 1:5, or 1 to 5. This can also be expressed as $$1/5$$ or 0.2 or 20%, but these forms are likely to be misunderstood as normal probabilities rather than odds.

To convert odds to probability, you add the two parts, and this is the denominator of the fraction of your probability. The first part becomes the numerator. Thus, 1:5 becomes 1/(1+5) or 1/6.

To convert probability to odds, you use the numerator as the first number, then subtract the numerator from the denominator and use it as the second number. Thus, 1/6 becomes 1:(6-1) or 1:5.