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Odds are a numerical expression, typically expressed as a pair of numbers, used in both gambling and statistics. In statistics, the chances for or odds of some event reflect the chance that the event will take place, while chances against reflect the likelihood it will not. In gaming, the odds are the proportion of payoff to stake, and do not necessarily reflect exactly the probabilities. Odds are expressed in many ways (see below), and at times the term is used incorrectly to mean the likelihood of an event. [1][2] Conventionally, betting odds are expressed in the form”X to Y”, where X and Y are numbers, and it’s implied that the chances are odds against the event on which the gambler is considering wagering. In both gambling and statistics, the’chances’ are a numerical expression of the likelihood of a potential event. Should you bet on rolling one of the six sides of a fair die, using a probability of one out of six, the odds are five to one against you (5 to 1), and you would win five times up to your bet. Should you gamble six occasions and win once, you win five times your bet while at the same time losing your bet five times, so the odds offered here by the bookmaker reflect the probabilities of this die. In gaming, odds represent the ratio between the amounts staked by parties to a wager or bet. [3] Therefore, chances of 5 to 1 mean the very first party (normally a bookmaker) bets six times the amount staked by the next party. In simplest terms, 5 to 1 odds means if you bet a buck (the”1″ from the expression), and also you win you get paid five bucks (the”5″ in the expression), or 5 occasions 1. If you bet two dollars you’d be paid ten bucks, or 5 times 2. If you bet three dollars and win, you’d be paid fifteen bucks, or 5 times 3. Should you bet a hundred bucks and win you’d be paid five hundred dollars, or 5 times 100. If you lose any of those bets you would lose the dollar, or two dollars, or three dollars, or one hundred bucks. The odds for a possible event E will be directly associated with the (known or estimated) statistical probability of the occasion E. To express odds as a probability, or the other way round, necessitates a calculation. The natural approach to interpret odds for (without calculating anything) is because the ratio of occasions to non-events at the long term. A very simple example is that the (statistical) odds for rolling a three with a reasonable die (one of a set of dice) are 1 to 5. ) That is because, if one rolls the die many times, and keeps a tally of the results, one expects 1 three event for every 5 times the die does not show three (i.e., a 1, 2, 4, 5 or 6). By way of example, if we roll up the acceptable die 600 times, we’d very much expect something in the neighborhood of 100 threes, and 500 of the other five potential outcomes. That’s a ratio of 100 to 500, or simply 1 to 5. To state the (statistical) chances against, the order of the pair is reversed. Hence the odds against rolling a three with a reasonable die are 5 to 1. The probability of rolling a three using a fair die is the single number 1/6, approximately 0.17. Generally, if the odds for event E are displaystyle X X (in favour) into displaystyle Y Y (against), the likelihood of E occurring is equal to displaystyle X/(X+Y) displaystyle X/(X+Y). Conversely, if the probability of E can be expressed as a fraction displaystyle M/N M/N, the corresponding odds are displaystyle M M to displaystyle N-M displaystyle N-M. The gaming and statistical applications of odds are tightly interlinked. If a wager is a fair person, then the odds offered to the gamblers will perfectly reflect relative probabilities. A fair bet that a fair die will roll up a three will cover the gambler $5 for a $1 wager (and return the bettor their wager) in the event of a three and nothing in any other case. The terms of the bet are fair, as on average, five rolls lead in something aside from a three, at a cost of $5, for each and every roll that results in a three and a net payout of $5. The gain and the cost just offset one another and so there is no advantage to gambling over the long term. If the odds being offered on the gamblers do not correspond to probability this way then one of the parties to the bet has an edge over the other. Casinos, for example, offer chances that place themselves at an edge, and that’s how they promise themselves a profit and live as businesses. The fairness of a particular bet is more clear in a match involving relatively pure chance, such as the ping-pong ball system used in state lotteries in the USA. It’s much more difficult to gauge the fairness of the chances offered in a wager on a sporting event such as a football match. Read more: