Calculator

Vig and Hold Calculator

About this calculator

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

Juice, vig, hold, margin, overround. Five words for three different numbers. Here is which is which.

Remove the margin and see the fair line →

The vig is the margin a sportsbook builds into its prices. The two sides of a market sum past 100%, and that surplus is the book’s cut. This calculator measures it and names it both ways: overround and hold.

The three numbers

Convert both sides of a market to probabilities and add them up. You get more than 100%. That excess, in probability points, is the overround.

The hold is the same margin measured against the money at risk instead. It is always the smaller number, and it is the one that describes what the book actually keeps.

Vig, juice and margin are names for the thing itself. They are not a fourth quantity, however much it looks like it.

A standard −110 / −110 market runs about 4.76 points of overround and about 4.55% hold. When somebody quotes “the vig” without saying which, that gap is usually what they are papering over.

Want more math?the Nerd Corner

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 each side’s own margin 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 0 to 1.
$s$ : their sum, the book total. Above 1 at any real sportsbook.
$v$ : the overround, in probability points. 4.76% on a −110 / −110 market.
$h$ : the hold, as a fraction of every dollar risked. 4.55% on that market, always below $v$ .
$p_i$ : the fair, no-vig probability of side $i$ , from the de-vig step. The method chosen decides how the margin is attributed between 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”.

Five words, three quantities

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

Overround and hold sit 0.22 points apart on a −110 market, enough to make two published “average vig” figures disagree for no reason but definition. 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. De-vig proportionally, so side $i$ has fair probability $p_i = q_i / s$ at posted odds $d_i = 1/q_i$ . Expected value per dollar staked:

\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 costs exactly the hold per dollar risked: exactly, not approximately, and identically on both sides.

Common lines, measured

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
−120 / +100	104.55%	4.55%	4.35%	−109 / +109
−152 / +138	102.33%	2.33%	2.28%	−144 / +144
−2000 / +900	105.24%	5.24%	4.98%	−952 / +952

Where the margin sits on a lopsided line

Total margin belongs to the pair; which side pays it is a modelling choice worth several hundred points on a heavy favorite. Take −2000 / +900:

−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, in proportion to each side’s implied probability; power and Shin push it toward the longshot. The overround stays 5.24% under all three: only the split moves.

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\%

4.55% became 13.03% with no change in the prices, because $1/s^3$ falls away three times as fast. The parlay calculator runs any number of legs.

Theoretical hold is not booked hold

Everything above describes the price. It describes results only on a balanced book, and real action is not balanced, so realised hold lands above or below the theoretical figure (below zero when the popular side wins). Published operator hold is revenue over handle across every market, a different measurement.

What the number is good for

Two books quoting different prices are not comparable until both are measured, and the lower hold is closer to fair on either side. A 4.76% overround is also roughly 2.4 points of phantom edge per side if it is never removed: an edge estimate smaller than the hold it was computed through is measuring margin, not opinion.

What it cannot do is identify a sharp price: a low hold is a competitive market, not necessarily an accurate one. The sharp-consensus fair line covers that.

Common mistakes

Quoting the overround as the cost of a bet. It is a probability measurement; the cost per dollar risked is the hold, always smaller.
Comparing holds across different outcome counts. A three-way soccer market sums three implied probabilities, so its overround is not comparable to a two-way total.
Assuming the exchange version is zero. Order books carry no vig, but fees and the bid–ask spread are the same cost in a different shape, priced here.

Check this number yourself

The overround is one function in the MIT-licensed teachersbettextbook; 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. More: open source.

Measuring the margin is the first half; removing it is the second. Everything downstream (expected value, Kelly sizing, closing line value) runs on the de-vigged number, not the posted one.

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.