vigorish

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Vigorish, or simply the vig, also known as juice or the take, is the amount charged by a bookmaker, or bookie, for his services. In the United States it also means the interest on a shark's loan. The term is Yiddish slang originating from the Russian word for winnings, vyigrysh. Bookmakers use this concept to make money on their wagers regardless of the outcome. Because of the vigorish concept, bookmakers should not have an interest in either side winning in a given sporting event. They are interested, instead, in getting equal action on each side 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 line, to attract equal action on each side of an event.

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 = +^o⁄_{(1 + o)} and o = +^v⁄_{(1 − v)} where o is 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.

Common misconceptions about vigorish are that it is paid by only the "loser", only the "winner", or both in all circumstances. A claim on when and to what extent a gambler pays vigorish fees, however, cannot be abstracted from an individual gambler's behavior. A gambler's behavior with respect to different odds on an event must first be defined and only then can a determination be made on how the vigorish affects him when he wins and loses.

Example

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 their $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

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. −110 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 receives a lower payout factor on his 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

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

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.

Other kinds of vigorish

• In table poker, the vigorish, more commonly called the rake, is a fraction of each bet placed into the pot. The dealer removes the rake from the pot after each bet (or betting round), making change if necessary. The winner of the hand gets the money that remains in the pot after the rake has been removed. Most casinos take 5-10% of the pot, capping the total rake at $3 or $4.
• 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 don't 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.
• In pai gow poker, a 5% commission charged on all winning bets is referred to as vigorish. Unlike baccarat, the commission is paid after each winning bet, either by the player handing in the amount from his stack of chips, or by having the vig deducted from the winnings. Pai gow poker is an even game, without any built-in advantage for the house; the commission restores the advantage.
• In craps, vigorish refers to the 5% commission charged on a buy bet, where a player wishes to bet that one of the numbers — 4, 5, 6, 8, 9 or 10 — will be rolled before a 7 is rolled. The commission is charged at the rate of $1 for every $20 bet. The bet is paid off at the true mathematical odds, but the 5% commission is paid as well, restoring the house advantage. For many years, this commission was paid whether the bet won or not. In recent years, many casinos have changed to charging the commission only when the bet wins, which greatly reduces the house advantage; for instance, the house advantage on a buy bet on the 4 or 10 is reduced from 5% to 1.67%, since the bet wins one-third of the time (2:1 odds against). In this case, the vig may be deducted from the winnings (for instance, a $20 bet on the 4 would be paid $39 — $40 at 2:1 odds, less the $1 commission), or the player may simply hand the commission in and receive the full payout. This rule is commonplace in Mississippi casinos, and becoming more widely available in Nevada.
• Vig may generically refer to the built-in house advantage on most bets on any game in a casino.
• Vig is sometimes used by investment bankers to describe profits from advisory and other activities.
• In backgammon, the recube vig is the value of having possession of the doubling cube to the player being offered a double.
• The payouts and winning combinations available on most slot machines and in other electronic gambling systems are often designed such that an average of between 0.1% to 10% (varying by machine and facility) of funds taken in are not used to pay out winnings, and thus becomes the house's share. Machines or facilities with a particularly low percentage are often said to be loose.
• Pittsburgh Pirates announcer Bob Prince coined the term "hidden vigorish" to describe an underdog's ability to beat the odds in a given situation.

See also

• Rake (poker)
• Loan shark