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Fee charged by a bookmaker for accepting a gambler's wager From Wikipedia, the free encyclopedia
Vigorish (also known as juice, under-juice, the cut, the take, the margin, the house edge or the vig) is the fee charged by a bookmaker for accepting a gambler's wager. In American English, it can also refer to the interest owed a loanshark in consideration for credit. The term came to English usage via Yiddish slang (Yiddish: וויגריש, romanized: vigrish) which was itself a loanword from Russian (Russian: вы́игрыш, romanized: výigryš, lit. 'gain, winnings').[1][2]
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As a business practice it is an example of risk management; by doing so bookmakers can guarantee turning a profit regardless of the underlying event's outcome. As a rule, bookmakers do not want to have a financial interest creating a preference for one result over another in any given sporting event. This is accomplished by incentivizing their clientele to wager offsetting amounts on all potential outcomes of the event. The normal method by which this is achieved is by adjusting the payouts for each outcome (collectively called the line) as imbalances of total amounts wagered between them occur.
Within the mathematical disciplines of probability and statistics this is analogous to an overround,[3] though the two are not synonymous but are related by the connecting formulae below.[4] Over round occurs when the sum of the implied probabilities for all possible event results is above 100%, whereas the vigorish is the bookmaker's percentage profit on the total stakes made on the event. For example, an overround of 20% results in 16.66%[lower-alpha 1] vigorish. The connecting formulae are
where v represents vigorish and o represents over round.
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 "fair odds" betting line of 2.00/2.00[lower-alpha 2] without vigorish would decrease the payouts of all outcomes equally, perhaps to 1.95/1.95, once it was added. More commonly though, disproportional vigorish will be applied as part of the efforts to keep the amounts wagered balanced, such as 1.90/2.00, making the outcome with fewer dollars wagered appear more attractive due to the larger payout.
In the context of betting, two individuals may choose to place a wager on opposite outcomes of an event, agreeing on "fair odds" or evens. This arrangement involves each party risking an equal amount, such as $100, with the potential to win the same amount. The arrangement is made directly between the individuals, bypassing a bookmaker. Consequently, the winner is entitled to the total amount staked by both parties, while the loser forfeits their stake. This direct betting approach implies that both parties accept the counterparty risk, acknowledging the possibility that the losing party may not honor the payment upon the event's conclusion, a risk typically mitigated by a bookmaker through the payment of vigorish.
In sports betting, vigorish is applied in scenarios with a 50/50 probability outcome, such as a coin toss, where the bookmaker adjusts the odds to ensure a profit regardless of the bet outcome. For a practical illustration of how vigorish is calculated in sports betting, consider an NBA game with odds set at +210 (32.26%) and -250 (71.43%), where the combined implied probabilities equal 103.69%, resulting in a vigorish of 3.69%.[5]
By contrast, when using a sportsbook with the odds set at 1.90/2.00 (10 to 11) 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.
Vigorish can be defined independent of the outcome of the event and of bettors' behaviors, by defining it as the percentage of total dollars wagered retained by the bookmaker in a risk-free wager. This definition is largely theoretical in practice as it makes the assumption that the bookmaker has balanced the wagers perfectly, such that they make equal profit regardless of the contest result.
For a two-outcome event, the vigorish percentage, v is
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, 1.90/2.00 pricing of an even match is 4.55% vigorish, and 1.95/1.95 pricing is 2.38% vigorish.
Vigorish percentage for three-way events may be calculated using the following formula:[6]
where p, q and t are the decimal payouts for each outcome. For comparison, for over round calculation only the upper part of the equation is used, leading to slightly higher percentage results than the vigorish calculation.
More generically, vigorish can refer to the bookmaker/casino's theoretical advantage from all possible wagers on any Baccarat, in the house-banked version of baccarat (also mini-baccarat) commonly played in North American casinos, vigorish refers to the 5% commission (called the cagnotte) charged to players who win a bet on the banker hand. The rules of the game are structured so that the banker hand wins slightly more often than the player hand; the 5% vigorish restores the house advantage to the casino for both bets. In most casinos, a winning banker bet is paid at even money, with a running count of the commission owed kept by special markers in a commission box in front of the dealer. This commission must be paid when all the cards are dealt from the shoe or when the player leaves the game. Some casinos do not keep a running commission amount, and instead withdraw the commission directly from the winnings; a few require the commission to be posted along with the bet, in a separate space on the table.