Unlike traditional games of chance, where the pay-out probability is known before the beginning, in fixed-odd bets, is the odd assigned to an event which express the probability that that event will occur. The odd is a subjective value, assigned to each event by the authorized operator, through statistical processing, knowledge, information and so on.
Let's make an example of a football match, and the odds associated with the final result of the match:
REAL MADRID - SEVILLE 1 (1.9) - X (3.4) - 2 (4)
The less is the odd offered on an event (the victory of Real Madrid for example) the greater is the probability that this event will occur. In order to obtain the percentage probability, you must divide 100 with each odd (e.g. 100 / 1.9 = 52.6), obtaining these quotients:
REAL MADRID - SEVILLE 1 (52.6) - X (29.4) - 2 (25)
With a quick calculation, it is evident that the sum of the three quotients, does not make 100, but an ever greater value, which is called “blackboard” and which represents the theoretical profit of every bookmaker, in our case: blackboard = 107.
This means that the real probability associated with Real Madrid's win, the draw and the win of Seville, will be obtained by dividing the quotients obtained by the calculated blackboard. For example, the probability percentage of Real Madrid's win is given by the equation: 107 : 52,6 = 100: X resulting in X = 49,1%.
REAL MADRID - SEVILLE 1 (49.1%) - X (27.5%) - 2 (23.4%)
The theoretical pay-out associated with the event (the one who would win the bettor that bets on all possible outcomes of the match, proportionally to the odds) would be 93.45% (100/107= 0.9345).