The fair odds for selecting any particular card from a standard deck of 52 are 51/1, with a probability of 0.0192 or 1.92%. As one might expect, the sum of probabilities for all cards will be 52 x 0.0192, which equals 1 or 100%. To gain an edge over the punter, a bookmaker will reduce those odds, for example to 48/1. These odds are then “unfair”, since their associated probability is now higher, at 0.0204 or 2.04%, than the true chance of picking any particular card. The sum of the probabilities for all cards is now 52 x 0.0204, that is 1.061 or 106.1%. Mathematically, of course, the sum of probabilities for all possibilities must be 1.00 or 100%. The difference between this and the bookmaker’s sum of probabilities represents the bookmaker’s profit margin. A book with a total percentage over 100 is said to be overround. In the case just mentioned, the book is overround by 6.1%. This may be expressed by saying that the overround is 106.1%, or 1.061 as a decimal. That is, for every 100 units paid out to punters, the bookmaker can expect to take 106.1, or a profit of 6.1% on turnover. If a bookmaker offered 9/2 for numbers 1 through to 6 from a throw of a standard 6-sided dice, the overround would be 109.1% (1.091).
Since the true probabilities associated with card drawing or dice rolling are mathematically fixed, a punter would be very unwise to bet at the unfair odds offered by a bookmaker. Initially he may be lucky, but over the long term he would find himself at a loss, the magnitude determined by the size of the overround. In view of this, it is remarkable how many gamblers are still happy to place bets on such games at a casino. When an edge is achievable, for example through card counting, the casino’s regulations will usually prevent such a professional from benefiting from his knowledge. In sports betting, however, the fair odds of a particular event occurring cannot be known exactly, and this is perhaps why so many punters, with a belief that they know more than the bookmakers, are prepared to accept the disadvantage that they face through the overround. For his chosen bets, the punter will hope that the bookmaker has made a mistake in the estimation of the fair odds, allowing him to overcome this disadvantage.
With fixed odds for 3 possible outcomes in a football match bet – the home win, draw, and away win – a typical overround is about 111 to 112%, although some Internet bookmakers may go as high as 118% for the less popular European football leagues. Calculating the overround for any book is a simple task of summing the inverse of the home, draw and away odds and multiplying by 100%. Here, the inverse of the decimal odds for one result, of course, is the bookmaker’s (unfair) estimation of the probability of that result occurring. Of course, whether the bookmaker’s idea is accurate about what exactly the true chance of a particular result occurring is, is open to debate. If his customer disagrees, there may be an opportunity for him to make a profit, provided he is more accurate in estimating the true chance of an outcome than the bookmaker.
Other types of bets attract different overrounds, and it is usually the case that the greater the number of possible outcomes to a sporting event or one of its elements, the greater the bookmaker’s overround. The correct score bet in football can have as many as 24 possible options on which to bet. A typical overround for this type of bet may be anything from 130 to 160%, depending on the bookmaker. In contrast to correct score betting, total goals betting in football, where there are usually only 2 possible outcomes (over 2.5 goals or under 2.5 goals), attract overrounds that are commonly less than 110%.
Punters with a keen interest in keeping the bookmaker’s disadvantage to a minimum may very well be attracted to other 2-way betting opportunities. Asian handicap betting, where the draw is eliminated, generally has a low overround, sometimes as little as 106%. In addition to total goals betting and Asian handicap in football, match bets in tennis, snooker, darts, and in fact any two-player sport where there is no possibility of the draw offer excellent betting opportunities. Standard handicap and total points betting in American sports like basketball, ice hockey and American Football have some of the smallest overrounds available, sometimes even as low as 103 or 104%.