Vig and Hold Calculator

By Alex Thornton · author of the MIT-licensed teachersbettextbook library · Last reviewed 24 July 2026

Juice, vig, hold, margin, overround. The field uses the five words interchangeably and two of them are different numbers. Here is which is which, on your own price.

The vig is the margin a sportsbook builds into a two-sided price. Both sides are quoted so their implied probabilities sum to more than 100%, and the surplus is the book’s edge. That surplus in probability points is the overround; the same margin expressed as a share of the money risked is the hold, and it is always the smaller number.

Both quantities come from one sum:

s = q_A + q_B, \qquad v = s - 1, \qquad h = 1 - \dfrac{1}{s} = \dfrac{v}{1 + v}

and the margin each side carries individually is the gap between its posted probability and its fair one:

\text{margin}_i = q_i - p_i, \qquad \sum_i \text{margin}_i = v

where:

$q_A,\ q_B$ — the vig-inclusive implied probabilities of the two posted prices, each between 0 and 1.
$s$ — their sum, sometimes called the book total. Above 1 at any real sportsbook.
$v$ — the overround, in probability points. Also called the vig or the margin. 4.76% on a −110 / −110 market.
$h$ — the hold, as a fraction of every dollar risked. 4.55% on that same market. Never equal to $v$ , always below it.
$p_i$ — the fair, no-vig probability of side $i$ , from the de-vig step. Which de-vig method is used decides how the margin is attributed between the sides; it never changes $v$ or $h$ .

Worked example — the line in the form below

The standard point-spread price, −110 on both sides:

q_A = q_B = \dfrac{110}{210} = 52.381\%, \qquad s = 104.762\%

v = 104.762\% - 100\% = 4.762\%, \qquad h = \dfrac{4.762}{104.762} = 4.545\%

The market is priced 4.76 points over fair, which costs 4.55¢ of every dollar risked — $4.55 on a $100 bet, on either side. Two different numbers, both correct, routinely quoted as “the vig”.

Remove the margin and see the fair line →

Five words, three quantities

The vocabulary is genuinely inconsistent across the industry, and the inconsistency hides a real distinction. Here is what each term denotes when it is used carefully.

Term	What it denotes	At −110 / −110
Juice	The price notation itself — “laying −110 juice”. Describes a price, not a percentage.	−110
Overround	Implied probabilities summed, minus 100%. Measured in probability points.	4.76%
Margin	Usually a synonym for overround. Sometimes used per side, where it means q_i − p_i.	4.76% (2.38 per side)
Hold	The margin as a share of money risked: v ÷ (1 + v). The casino-side definition — expected win over handle.	4.55%
Vig / vigorish	All of the above, depending on who is speaking. The word carries no fixed definition in practice.	4.55% or 4.76%

Overround and hold sit 0.22 points apart on a −110 market — 4.76 against 4.55, about 4.5% of the figure itself. Small enough to go unnoticed, large enough to make two published “average vig” numbers disagree for no reason other than which definition each one used. This calculator prints both, labelled.

The identity that connects them

The hold is not an approximation of the overround. It is the exact expected cost of a bet, and the proof is two lines. De-vig the market proportionally, so side $i$ has fair probability $p_i = q_i / s$ , and price it at its posted decimal odds $d_i = 1/q_i$ . Then expected value per dollar staked is:

\mathrm{EV}_i = p_i \, d_i - 1 = \dfrac{q_i}{s} \cdot \dfrac{1}{q_i} - 1 = \dfrac{1}{s} - 1 = -h

The $q_i$ cancels. Every side of every two-way market, at any prices, costs exactly the hold per dollar risked when the fair probabilities are the proportional de-vig of the posted line. Not approximately — exactly, and identically on both sides.

Checking it at −110

p = 0.5, \quad b = \tfrac{100}{110} = 0.9091

\mathrm{EV} = 0.5 \times 0.9091 - 0.5 = -0.04545 = -4.545\%

Which is the hold, to the digit. A $100 bet at −110 on a market whose fair price is even money expects to lose $4.55. The overround, 4.76%, is a probability measurement and is not the amount lost.

Common lines, measured

Every row is a real two-way price shape. The fair line is the proportional de-vig.

Posted line	Implied sum	Overround	Hold	Fair line
−105 / −105	102.44%	2.44%	2.38%	even
−110 / −110	104.76%	4.76%	4.55%	even
−115 / −105	104.71%	4.71%	4.50%	−104 / +104
−120 / +100	104.55%	4.55%	4.35%	−109 / +109
−152 / +138	102.33%	2.33%	2.28%	−144 / +144
−250 / +205	104.22%	4.22%	4.05%	−218 / +218
−2000 / +900	105.24%	5.24%	4.98%	−952 / +952

Two-way moneylines at major US books commonly sit in the 2–5% band. The gap between overround and hold widens with the margin: 0.06 points apart at a 2.44% overround, 0.26 points apart at 5.24%.

Where the margin sits on a lopsided line

Total margin is a property of the pair. Which side pays it is a modelling choice, and on a heavy favorite the choice is worth several hundred points of price. Take −2000 / +900, a 5.24% overround:

−2000 / +900, margin attributed proportionally

q_A = 95.24\%, \quad q_B = 10.00\%, \quad s = 105.24\%

p_A = \dfrac{0.9524}{1.0524} = 90.50\%, \qquad p_B = \dfrac{0.1000}{1.0524} = 9.50\%

\text{margin}_A = 4.74\ \text{pts}, \qquad \text{margin}_B = 0.50\ \text{pts}

Proportional attribution hands 90% of the margin to the favorite, because it hands each side margin in proportion to its own implied probability. The power and Shin methods redistribute it toward the longshot instead, on the evidence that longshot prices are the ones padded hardest. The overround stays 5.24% under all three — only the split moves. The selector above switches between them; the no-vig calculator shows what each does to the fair price.

Margin compounds across parlay legs

A parlay multiplies the prices, so it multiplies the book totals too. Three legs at −110:

d_{\text{offered}} = 1.9091^3 = 6.958, \qquad d_{\text{fair}} = 2^3 = 8.000

h_3 = 1 - \dfrac{6.958}{8.000} = 13.03\%

The hold went from 4.55% to 13.03% without any change in the prices — a three-leg parlay of standard spreads carries close to three times the margin of one bet, because $1/s^3$ falls away three times as fast. The parlay calculator runs any number of legs and shows the compounded figure alongside the payout.

Theoretical hold is not booked hold

Everything above describes the price. It describes the book’s results only when the money splits so that both outcomes pay the same — a balanced book. Real action is not balanced, so a market’s realised hold can land far above or below the theoretical number, including below zero when the popular side wins.

Two consequences worth keeping straight. Published operator hold percentages are revenue divided by handle across every market and every bettor, which is a different measurement than the 4.55% here. And a market with a wide posted margin is not automatically expensive to a particular bettor: the cost of a specific bet is the gap between its price and the fair price of that side, which is what the expected value calculator measures.

Two things the number is good for

Comparing venues on one market. Two books quoting different prices are not comparable until both are measured. The one with the lower hold is quoting closer to fair, whichever side you look at.
Sizing the estimation problem. A 4.76% overround is roughly 2.4 points of phantom edge per side if it is never removed. Any edge estimate smaller than the hold it was computed through is measuring the margin rather than an opinion.

What it cannot do: identify a sharp price. A low hold is a competitive market, not necessarily an accurate one. Where a defensible reference price comes from is covered in the sharp-consensus fair line.

Common mistakes

Quoting the overround as the cost of a bet. It is a probability measurement. The cost per dollar risked is the hold, which is always smaller.
Splitting the margin evenly. Subtracting half the overround from each side is a different operation from normalising, and it disagrees with every de-vig method on any market that is not symmetric.
Comparing holds across markets with different outcome counts. A three-way soccer market sums three implied probabilities, so its overround is not comparable to a two-way total without adjusting for the count.
Reading a low hold as a good price for one side. Hold is a property of the pair. A book can hold 2% overall while pricing the side you want a point worse than everyone else.
Assuming the exchange version is zero. Order books have no vig, but they charge fees and quote a bid–ask spread, which is the same cost in a different shape. The Kalshi fee calculator puts a number on it.
Treating the theoretical figure as money the book is certain to collect. It is the expected result of a balanced book, and books are not balanced.

Check this number yourself

The overround is one function in the MIT-licensed teachersbettextbook package, and the hold is one line of arithmetic on it:

pip install teachersbettextbook

>>> from teachersbettextbook import overround, devig
>>> v = overround(-110, -110)
>>> v
0.04761904761904767
>>> v / (1 + v)          # the hold
0.045454545454545504
>>> devig(-110, -110, method='proportional')
(0.5, 0.5)

Same inputs, same digits, no account required. More on what is open and what is not: open source.

Measuring the margin is the first half; removing it is the second, and everything downstream — expected value, Kelly sizing, closing line value — runs on the de-vigged number rather than the posted one. How to de-vig odds covers the three methods in full.

Frequently asked questions

What is the vig in sports betting?

The vig (vigorish, or juice) is the margin a sportsbook builds into its prices. Both sides of a market are priced so their implied probabilities sum to more than 100%, and that surplus — the overround — is the book’s edge. On a standard −110 / −110 market it is 4.76 percentage points.

Are vig and hold the same thing?

They are two different numbers that the industry uses interchangeably. Overround is the surplus in probability points: implied sum minus 100%, or 4.76% at −110 / −110. Hold is that surplus expressed as a share of money risked: overround divided by (1 + overround), or 4.55% on the same market. Hold is always the smaller of the two.

How do you calculate the vig on a betting line?

Convert both posted prices to implied probabilities, add them, and subtract 100%. For −110 and −110 that is 52.38% + 52.38% − 100% = 4.76%. Dividing the surplus by the total, 4.76 ÷ 104.76, gives the 4.55% hold — the share of each dollar risked that the price is expected to cost.

What is a normal amount of vig?

Two-way moneylines at major US books commonly run 2% to 5% overround, with −110 / −110 (4.76%) as the reference point for point spreads and totals. Margins widen on markets with less competition and less liquidity — player props, alternate lines, longshot futures — and compound across parlay legs, where three −110 legs reach a 13.03% hold.

Does the vig mean the sportsbook always wins?

No. Hold is the book’s expected share only if the money splits evenly across both sides at those prices. Real action is lopsided, so a book’s realised hold on any single market can be far above or below the theoretical figure, and can be negative. The theoretical number describes the price, not the outcome.