betting odds

     

In probability theory an statistics the odds in favour of an event or a proposition are the quantity p / (1 − p) , where p is the probability of the event or proposition. The odds against the same event are (1 − p) / p. For example, if you chose a random day of the week, then the odds that you would choose a Sunday would be 1/6, not 1/7. The odds against you choosing Sunday are 6/1. These 'odds' are actually relative probabilities. Generally, 'odds' are not quoted to the general public in this format because of the natural confusion with the chance of an event occurring being expressed fractionally as a probability. Thus, the probability of choosing Sunday at random from the days of the week is 'one-seventh' (1/7), and although a bookmaker may (for his own purposes) use 'odds' of 'one-sixth' the overwhelming everyday use by most people is odds of the form 6 to 1, 6-1, or 6/1 (all read as 'six-to-one') where the first figure represents the number of ways of failing to achieve the outcome and the second figure is the number of ways of achieving a favourable outcome: thus these are "odds against". In other words, an event with m to n "odds against" would have probability n/(m + n), while an event with m to n "odds on" would have probability m/(m + n).

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