Vigorish

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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 his services. In the United States it also means no interest on a shark's loan. The term is Yiddish slang originating 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, bookmakers do not want to have an interest in either side winning in a given sporting event. They are interested, instead, 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 1623%. 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.

Example[edit]

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. −110 (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.

Discussion[edit]

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, many observers will assert that only the losing bettor paid the vigorish. Others would attest 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, we must first define 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.

  1. The gambler has a target amount he wants to win, which is independent of the presence or absence of vigorish. As an example, for an even match we would have −100 vs. +100 for fair odds and the gambler wagers 100 to win 100. Under proportional vigorish the odds would become −110 vs. +100 and so gamblers must wager 110 to win 100. In this case, losers lose 110 under the juiced odds compared to 100 under fair odds, so the loser pays 10 extra. The winner gets back his 110 plus 100 profit, compared to getting back his 100 plus 100 profit under fair odds. The winner has no net difference since he is up 100 either way. So the loser pays the full vigorish of 10 under this assumption.
  2. The gambler has a given amount he is willing to risk, independent of vigorish. Under fair odds the gambler risks 100 to win 100. Under vigorish, the gambler still risks 100 to win 100 × (100 ÷ 110) = 90.9. Under this behavior, the loser loses 100 in both cases, so pays no vigorish. The winner wins 100 net under fair odds and 90.9 net under vigorish, so he pays 9.1 in vigorish. The winner pays the full vigorish under this assumption.
  3. The gambler bets more when he has a greater edge (better payout for a given chance of winning). A Kelly gambler is one such gambler, who seeks to maximize his rate of bankroll growth in the limit of infinite bets placed over time. This type of gambler will bet more when the payout reflects a bigger advantage for him. The fact that he bets at all indicates that he thinks he has an advantage in the bet, so the presence of vigorish reduces this edge by reducing the payout for a given amount wagered. Therefore, these gamblers on either side of the wager will both bet less than they would have at fair odds (assuming proportional vigorish). The losers therefore lose less than they would have under fair odds, so counter-intuitively these losers do better with vigorish. The winners not only receive a lower payout factor on their bet, but they also risked less than they would have at fair odds, so they pay the full rake of the bookmaker, plus the amount saved by the losers, since (amount cost by winners) − (amount saved by the losers) = (full vigorish raked by the bookmaker). So for these gamblers, the losers pay negative vigorish, while the winners pay more than the full vigorish raked in by the bookie.

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[edit]

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:[2]

 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.

Other kinds of vigorish[edit]

Casino games[edit]

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.

Other uses[edit]

See also[edit]

References[edit]