Decimal odds

Odds are a numerical expression, usually expressed as a pair of numbers, used in both gambling and statistics. In statistics, the odds for or odds of some event reflect the likelihood that the event will take place, while odds against reflect the likelihood that it will not. In gambling, the odds are the ratio of payoff to stake, and do not necessarily reflect exactly the probabilities. Odds are expressed in several ways (see below), and sometimes the term is used incorrectly to mean simply the probability of an event. Conventionally, gambling odds are expressed in the form "X to Y", where X and Y are numbers, and it is implied that the odds are odds against the event on which the gambler is considering wagering. In both gambling and statistics, the 'odds' are a numerical expression of the likelihood of some possible event.

In gambling, odds represent the ratio between the amounts staked by parties to a wager or bet. Thus, odds of 6 to 1 mean the first party (normally a bookmaker) stakes six times the amount staked by the second party.

In simplest terms, 6 to 1 odds means if you bet a dollar (the "1" in the expression), and you win you get paid six dollars (the "6" in the expression), or 6 x 1. If you bet two dollars you would be paid twelve dollars, or 6 x 2. If you bet three dollars and win, you would be paid eighteen dollars, or 6 x 3. If you bet one hundred dollars and win you would be paid six hundred dollars, or 6 x 100. Of course if you lose any of those bets you would lose the dollar, or two dollars, or three dollars, or one hundred dollars.

In statistics, the odds for an event E are defined as a simple function of the probability of that possible event E. One drawback of expressing the uncertainty of this possible event as odds for is that to regain the probability requires a calculation. The natural way to interpret odds for (without calculating anything) is as the ratio of events to non-events in the long run. A simple example is that the (statistical) odds for rolling six with a fair die (one of a pair of dice) are 1 to 5. This is because, if one rolls the die many times, and keeps a tally of the results, one expects 1 six event for every 5 times the die does not show six. For example, if we roll the fair die 600 times, we would very much expect something in the neighborhood of 100 sixes, and 500 of the other five possible outcomes. That is a ratio of 100 to 500, or simply 1 to 5. To express the (statistical) odds against, the order of the pair is reversed. Hence the odds against rolling a six with a fair die are 5 to 1. The probability of rolling a six with a fair die is the single number 1/6, roughly 0.17.

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