En estadística, la cuota es el inverso de la probabilidad, de forma que cuanto mayor es la cuota menor es la probabilidad teórica de que aparezca ese resultado. La cuota a favor de un evento o proposición se calcula mediante la fórmula dónde p es la probabilidad del evento o proposición. La cuota en contra del mismo evento se calcula mediante la fórmula Por ejemplo, al escoger al azar un día de la semana (7 días), la cuota asociada a favor de un domingo cualquiera es no , como podría parecer. La cuota en contra del mismo domingo es ; eso significa que es 6 veces más probable que no sea domingo a que sí sea domingo. Estas cuotas son relativas a la probabilidad de suceder. Generalmente las cuotas no son determinadas por el público en general a causa de la confusión natural que se tiene con la probabilidad de un suceso expresada de forma fraccionaria. De esta forma, la probabilidad al escoger al azar un domingo respecto a todos los días de la semana es de uno a siete (1/7). Un corredor de apuestas (para sus propios propósitos) utilizará las cuotas en formato uno contra seis, expresada generalmente por la mayoría de personas como 6 a 1, 6-1, o 6/1 (leído como seis a uno) donde la primera cifra representa el número de días contrarios al éxito del suceso, y la segunda cifra corresponde al los días a favor del éxito del suceso (cuotas a favor). En otras palabras, un evento con m a n de cuotas en contra, tendrá una probabilidad de n/(m + n), mientras que un evento de m a n de cuotas a favor, la probabilidad será de m/(m + n). La teoría de la probabilidad expresa que las cuotas juegan un papel más natural o más conveniente que las probabilidades. Para algunos juegos de azar, puede ser también la forma más conveniente para que el apostante entienda mejor cuantas ganancias tendrá si su selección es la correcta: al individuo le pagaran seis por cada unidad apostada. Por ejemplo, una apuesta ganadora de 10 € se pagará a 6 x 10€ = 60€, retornando también los 10 € originales de la apuesta.

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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 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. The gambling and statistical uses of odds are closely interlinked. If a bet is a fair one, then the odds offered to the gamblers will perfectly reflect relative probabilities. A fair bet that a fair die will roll a six will pay the gambler $5 for a $1 wager (and return the bettor his or her wager) in the case of a six and nothing in any other case. The terms of the bet are fair, because on average, five rolls result in something other than a six, at a cost of $5, for every roll that results in a six and a net payout of $5. The profit and the expense exactly offset one another and so there is no disadvantage to gambling over the long run. If the odds being offered to the gamblers do not correspond to probability in this way then one of the parties to the bet has an advantage over the other. Casinos, for example, offer odds that place themselves at an advantage, which is how they guarantee themselves a profit and survive as businesses. The fairness of a particular gamble is more clear in a game involving relatively pure chance, such as the ping-pong ball method used in state lotteries in the United States. It is much harder to judge the fairness of the odds offered in a wager on a sporting event such as a football match.

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