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Vigorish, or simply the vig, also known as juice, the cut or the take, is the amount charged by a bookmaker, or bookie, for taking a bet from a gambler. In the United States, it also means the interest on a shark's loan. The term originates from the Russian word for winnings, выигрыш vyigrysh.^{[1]} Bookmakers use this practice to make money on their wagers regardless of the outcome. To minimize their risk, some bookmakers do not want to have an interest in either side winning in a given sporting event. Instead, they are interested in getting equal betting on both outcomes of the event. In this way, the bookmaker minimizes his risk and always collects a small commission from the vigorish. The bookmaker will normally adjust the odds or the line. The concept is also sometimes referred to as the overround, although this is technically different, being the percentage the event book is above 100%, whereas the vigorish is the bookmaker's percentage profit on the total stakes made on the event. For example, 20% overround is vigorish of 16^{2}⁄_{3}%. The connecting formulae are v = \frac{o}{(1 + o)} and o = \frac{v}{(1 - v)} where o is the overround.
It is simplest to assume that vigorish is factored in proportionally to the true odds, although this need not be the case. Under proportional vigorish, a moneyline odds bet listed at +100 vs. +100 without vigorish (fair odds) could become −110 vs. −110 with vigorish factored in. Under disproportional vigorish, it could become −120 vs. +100. A fairly common amount of vig is ~2%. ^{[2]}
A fair odds bet: Two people want to bet on opposing sides of an event with even odds. They are going to make the bet between each other without using the services of a bookmaker. Each person is willing to risk $100 to win $100. After each person pays his $100, there is a total of $200 in the pot. The person who loses receives nothing and the winner receives the full $200.
By contrast, when using a sportsbook with the odds set at −110 vs. +100 (10 to 11, 1.9090..) with vigorish factored in, each person would have to risk or lay $110 to win $100 (the sportsbook collects $220 "in the pot"). The extra $10 per person is, in effect, a bookmaker's commission for taking the action. This $10 is not in play and cannot be doubled by the winning bettor; it can only be lost. A losing bettor simply loses his $110. A winning bettor wins back his original $110, plus his $100 winnings, for a total of $210. From the $220 collected, the sportsbook keeps the remaining $10 after paying out the winner.
In the above example, the bookmaker has taken a rake, or scaled commission fee, of $10 ÷ $220 = 4.55%. Since the winning bettor got his full $110 wager back, plus $100 in winnings, it could be considered that only the losing bettor paid the vigorish. An alternative view could be that the winner — who had risked $110 and only received $210 in the end, instead of doubling his money to $220 — is the only bettor who paid the vigorish. To discuss how the bettors are affected by the vigorish, it must first be defined what they would have bet at fair odds (without the presence of vigorish) or else there is no way to compare how much tax is placed on the winner or loser due to the vigorish. There are unlimited possibilities for how the presence of vigorish could affect the amount wagered by a bettor, since a bettor is free to bet in any arbitrary way based on the odds. There are, however, several natural options to consider which give different results on how vigorish affects a bettor.
These are three examples of possible gambler behaviors that all give different answers to the distribution of vigorish fees amongst winners and losers. One therefore cannot say precisely whether winners or losers or both are paying the vigorish until the gamblers' behaviors with respect to the fair odds and juiced odds is defined.
Vigorish percentage can be defined in a way independent of the outcome of the event and of bettors' behaviors by defining it as the percentage raked in a risk-free wager. This definition is the rake of the bookie as a percentage of total bets received if the bookie has balanced the wagers so that he makes equal profit regardless of the outcome of the event.
For a two outcome event, the vigorish percentage, v is
v = 100*\left(1 - {p*q \over p + q}\right)
where the p and q are the decimal payouts for each outcome. This should not be confused with the percentage a bettor pays due to vigorish. No consistent definition of the percentage a bettor pays due to vigorish can be made without first defining the bettor's behavior under juiced odds and assuming a win-percentage for the bettor. These factors are discussed under the debate section.
For example, −110 side pricing of an even match is 4.55% vigorish, and −105 side pricing is 2.38% vigorish.
Vigorish percentage for three-way events may be calculated using the following formula:^{[3]}
v = 100 * { (1/p + 1/q + 1/t)-1 \over 1/p + 1/q + 1/t}
where p, q and t are the decimal payouts for each outcome. For comparison, for overround calculation only the upper part of the equasion is used, leading to slightly higher percentage results than the vigorish calculation.
Vig may generically refer to the built-in house advantage on most bets on any game in a casino. The term may also refer to, and be applied in specific ways to, particular casino games.
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