Calculator

Expected Value Calculator

About this calculator

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

De-vig a sharp line, then compare it to the price you were actually offered. The gap is your edge.

Full animated derivation and a live +EV feed across books: open the tool in the app →

This expected value calculator de-vigs a sharp line, compares it with the price your book offered, and turns the gap into an average profit per dollar. Positive means the price pays more than the outcome is worth.

What the number means

Expected value is what a bet averages per dollar if you could run it forever. Not what it pays this time. Nothing pays “on average” on a Sunday.

Positive means the price pays more than the outcome is worth. Negative means it does not. Zero means you found a fair price, which is most of them.

The catch is p, your win probability. You cannot read it off the book you are betting into, because that price already contains the cut you are trying to beat. De-vig a sharper line and use that instead.

Anything above about 15 cents on the dollar is not an edge. It is a stale price or a typo, and this site refuses to flag those as opportunities.

Want more math?the Nerd Corner

\text{EV} = p \cdot b - (1 - p) \;=\; p\,(b + 1) - 1

where:

$p$ : the fair, de-vigged win probability of the side being priced, 0 to 1. From a reference line, not your own book.
$b$ : net decimal payout of your price, in dollars of profit per dollar risked. +145 gives $b = 1.45$ ; −145 gives $b = 0.69$ .
$1 - p$ : how often the stake is lost.
$\text{EV}$ : expected profit per $1 staked, in dollars. Multiply by the stake for profit on the bet.
$q_{\text{price}} = 1/(b+1)$ : the break-even probability your price implies. EV is positive exactly when $p > q_{\text{price}}$ .

Worked example: the numbers in the form below

Sharp line −140 / +120, your book offers +145 on side B, de-vigged by the power method:

p_B = 43.44\%, \qquad +145 \Rightarrow b = 1.45,\quad q_{\text{price}} = \tfrac{1}{2.45} = 40.82\%

\text{EV} = 0.434435 \times 1.45 - 0.565565 = +0.064366 \Rightarrow +6.44\%\ \text{per \$1}

The edge is +2.63 probability points and the expected profit is 6.4¢ per dollar staked: on average, over many repetitions of this exact price, not on this one bet.

How the expected value calculation works

The first term is what you win when you are right, weighted by how often that happens; the second is the stake you lose the rest of the time. The whole game is getting p right, and a book’s own price cannot supply it: the vig is baked in, so its implied probability is inflated. The calculator de-vigs a reference line instead, and compares the result to what your price implies:

q_{\text{price}} = \dfrac{1}{b + 1}, \qquad \text{edge} = p - q_{\text{price}}

When the fair probability beats the probability your price implies, the edge is positive and so is the EV. The proportional, power and Shin methods split the reference book’s vig differently, so the panel computes all three at once.

Does the edge survive the method choice?

A thin edge can be an artifact of the de-vig method. Positive under all three is robust; positive under one and negative under another is fragile, and reporting the worst case is the honest version of this math:

De-vig method	Fair p (side B)	Price implies	Edge	EV	Half-Kelly
Proportional	43.80%	40.82%	+2.98 pts	+7.30%	2.52%
Power	43.44%	40.82%	+2.63 pts	+6.44%	2.22%
Shin	43.56%	40.82%	+2.74 pts	+6.72%	2.32%

All three clear zero, so this edge is robust; the half-Kelly column is what the Kelly calculator stakes on the same numbers, and a 0.36-point disagreement about p moves it by 13%. At +130 the same market turns knife-edge: proportional +0.7%, power −0.08%: same bet, opposite sign. On a −250 / +205 reference with +240 at your book, all three agree on the sign but the size runs +2.9% to +7.0%. On longshots the method is the largest single source of error.

How much precision does p deserve?

The second form of the formula makes the sensitivity explicit:

\text{EV} = p\,(b+1) - 1 \qquad \Rightarrow \qquad \dfrac{d\,\text{EV}}{d p} = b + 1

Every probability point of error in p moves EV by $b+1$ points, a multiplier of 2.45 at +145. An edge narrower than the spread between the three de-vig methods sits inside the noise of its own inputs.

Where this fits, and what goes wrong

One reference line, one different price. The two inputs have to come from different venues: de-vig a book, test that same book’s price, and the edge is exactly zero every time, by construction.
Skipping the de-vig counts margin as edge. On a 4% hold, comparing a raw implied probability to your price manufactures roughly 2 points of phantom value on each side.
It cannot judge the reference line. Feed it a soft book and you get a confident number on a weak estimate; where a defensible reference price comes from is in the sharp-consensus fair line guide.
EV is not money in hand. +6.44% per dollar is an average over many repetitions; a single bet returns $b$ or −1, never 0.0644, and it inherits its error bar from p, magnified by $b+1$ .
A huge number is usually a stale price. Anything above 15% EV per dollar (EV_SUSPECT_PER_DOLLAR = 0.15) is treated as a suspect line and left unflagged: two-way markets that far apart are usually one venue that has not moved.
It answers whether, not how much. Kelly sizes it, returning zero on a negative-EV input: the correct answer, not a bug. Fees move the break-even directly; the Kalshi fee calculator gives the fee-adjusted $q_{\text{price}}$ . Against the closing line the same arithmetic is closing line value, which converges on true edge far faster than win rate.

Check this number yourself

The page runs the same math as the MIT-licensed teachersbettextbook package, two public functions and one line of arithmetic: devig() for p, moneyline_to_odds() for b, then p*b - (1-p).

pip install teachersbettextbook

>>> from teachersbettextbook import devig, moneyline_to_odds
>>> p = devig(-140, 120, method='power')[1]
>>> b = moneyline_to_odds(145)
>>> float(p * b - (1 - p))
0.06436636547960783

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

The fair-line step on its own is the no-vig calculator; the full method is in Expected Value (+EV) Betting.

Frequently asked questions

What is an expected value calculator?

An expected value calculator estimates the long-run average return of a bet. It de-vigs the sharp or fair line to get a true probability, then compares that to the probability your book’s price implies. When the fair probability is higher, the bet has positive expected value (+EV).

How do you calculate the expected value of a bet?

Use EV = p·b − (1−p), where p is the fair (de-vigged) win probability and b is the net decimal payout of your price. A positive result means the bet returns more than it risks on average. Multiply by your stake for expected profit per bet.

What makes a bet +EV?

A bet is +EV when the de-vigged fair probability beats the probability your price implies: when a softer book’s price is generous enough that the math clears zero against a sharp or consensus line.

How big does an edge need to be to survive estimation error?

EV rearranges to EV = p(b+1) − 1, so a one-point error in the fair probability moves EV by (b+1) points. At +145 that multiplier is 2.45, larger than most edges people chase. An edge smaller than the spread between the three de-vig methods is inside the noise of its own inputs.

What does a very large positive EV usually mean?

Almost always a stale or mistyped price rather than an edge. Anything above 15% expected value per dollar (the EV_SUSPECT_PER_DOLLAR threshold) is treated as a suspect line and left unflagged, because two-way markets that far apart are usually one venue that has not moved yet.