The Over-round or Vigorish (vig or juice)

The over-round (Vigorish, or simply "vig", or "juice") is what gives the bookmaker his profit.

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 49/1. These odds are then "unfair", since their associated probability is now higher, at 0.02 or 2%, than the true chance of picking any particular card. The sum of the probabilities for all cards is now 52 x 0.02, that is 1.04 or 104%. 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 vig. In the case just mentioned, the book is vig by 4%. This may be expressed by saying that the vig is 104%, or 1.04 as a decimal. That is, for every 100 units paid out to punters, the bookmaker can expect to take 104, or a profit of 4% on turnover. If a bookmaker offered 19/4 for numbers 1 through to 6 from a throw of a standard 6-sided dice, the vig would be 104.35% (1.0435).

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 vig, a negative expected value. 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 in blackjack, 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 since the odds are just an estimation by the casino/sportsbook, 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 vig. 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 (the edge).

In a standard point spread of American Football or Basketball, Las Vegas Casinos would set the odds to be -110 (1.91) on both sides. If a player wants to win $100, he risks $110. The difference between the odds they offer, and the true price represents the bookies’ margin or ‘juice’, in this case a $10 profit or 4.55% on turnover. This is known as -110 pricing and because of the vigorish, a player has to win 52.3% of his bets just to break even! If you are a good handicapper and win 54% of your bets, you would show a profit of $340 after making a hundred $100 bets.

The above is just the standard point-spread. However, nowadays there are many reliable online sportsbooks offering much better odds on these exact same events. For example, you can find books that offer -104 (1.96) odds on both sides for the same event explained in the previous paragraph. With -104 odds, the punter is betting only $104 to win $100, lowering bookies margin to 1.92%.  This lower vigorish means a player would only need to win just 51% of his plays to break even. Our hypothetical 54% handicapper does even better now. He would be up $616 after 100 plays, nearly twice as much as if he had used -110 odds! Playing at low vig sportsbooks gives bettors greater advantage to maximize profit.