# Vigorish

Vigorish (also known as juice, under-juice, the cut, the take, the margin, the house edge or simply the vig) is the fee charged by a bookmaker (or bookie) 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, romanizedvigrish),[1] which was itself a loanword from Ukrainian (Ukrainian: ви́граш, romanizedvýhraš, lit.'winnings, profit') or Russian (Russian: вы́игрыш, romanizedvýigryš, lit.'gain, winnings').[2]

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] Overround 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%[a] vigorish. The connecting formulae are

${\displaystyle v={\frac {o}{(1+o)}}\quad {\text{ and }}\quad o={\frac {v}{(1-v)}}}$

where v represents vigorish and o represents overround.

## Proportionality

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[b] 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.

## Examples

### The simplest wager

Two people want to bet on opposing sides of an event and agree to "fair odds", also known as evens. They are going to make the wager between each other without using the services of a bookmaker. Each person agrees to risk $100 for the chance to win$100. The person who loses receives nothing and the winner receives both stakes. Rather than pay vigorish to someone who will guarantee that the winner will be paid, they both assume the opportunity cost in the event the backer of the losing side refuses to pay the winner at the event's conclusion.

## References

1. ^ "Vigorish dictionary definition | The American Heritage® Dictionary of the English Language, Fifth Edition". www.yourdictionary.com. Retrieved 2019-06-03.
2. ^ "Definition of VIGORISH". www.merriam-webster.com. Retrieved 2019-06-03.
3. ^ Moya, Fabián Enrique (2012-07-24). "Statistical Methodology for Profitable Sports Gambling" (PDF). www.stat.sfu.ca. p. 15. Archived (PDF) from the original on 2013-06-12. Retrieved 2019-06-02.
4. ^ "A Refresher on Overround and Vig". Matter of Stats. Retrieved 2019-06-03.
5. ^ "Profit margin calculator | Pinnacle". www.pinnacle.com. Retrieved 2019-06-03.