This article is about the gambling and statistical term. For playing chess with odds, i. In gambling, the odds are the ratio of payoff to stake, and do not necessarily reflect exactly the probabilities. Conventionally, gambling odds are expressed in the form “X to Y”, where X and Y are numbers, and it is read reflected in you online free pdf 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. 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. If you lose any of those bets you would lose the dollar, or two dollars, or three dollars, or one hundred dollars. 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. Hence the odds against rolling a six with a fair die are 5 to 1. The gambling and statistical uses of odds are closely interlinked.

The profit and the expense exactly offset one another and so there is no advantage 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. Odds are expressed in the form X to Y, where X and Y are numbers. Usually, the word “to” is replaced by a symbol for ease of use. 1, 6-1 and 6:1 are all interchangeable.

When the probability that the event will not happen is greater than the probability that it will, then the odds are “against” that event happening. To a gambler, “odds against” means that the amount he or she will win is greater than the amount staked. Odds on” is the opposite of “odds against”. It means that the event is more likely to happen than not. Note that the gambler who bets at “odds on” and wins will still be in profit, as his stake will be returned.

Even odds” occur when the probability of an event happening is exactly the same as it not happening. In common parlance, this is a “50-50 chance”. Evens” implies that the payout will be one unit per unit wagered plus the original stake, that is, “double-your-money”. Looked at from the perspective of a gambler rather than a statistician, “better than evens” means “odds against”. 10 units, one would be returned 20 units, making a profit of 10 units. If the gamble was paying 4:1 and the event occurred, one would make 50 units, or a profit of 40 units.