Calculator

Arbitrage Calculator

About this calculator

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

When two books disagree hard enough, backing both sides costs less than either one pays. Enter both prices and this checks.

Already holding one side? This page splits a fresh bankroll across both. The hedge calculator starts from your actual stake and price and sizes the other side directly, no bankroll guessing needed.

Live arb flags across your books as lines move: open the Arb Finder in the app →

An arbitrage calculator checks whether the best prices on the two sides of a market, at different venues, cover both outcomes for less than the payout. When they do, the position returns the same amount whichever way the game goes.

The test, and the catch

Convert each price to decimal, take one over each, add them up. Under 1.00 and every outcome pays more than the pair cost you. Over 1.00 and there is nothing there, which is the usual answer.

Then split the stake in proportion to those inverses, and both outcomes return the same amount. That is the whole trick.

The catch is that you have to actually get both legs on. Prices move in seconds, the second book can reject or void you, and one leg alone is a large uncovered position. A gap you cannot execute is not a gap.

Anything over about 5% return is almost always a stale price rather than free money. Treat a big one as a warning, not a windfall.

Want more math?the Nerd Corner

\sum_i \dfrac{1}{d_i} < 1, \qquad s_i = S \cdot \dfrac{1/d_i}{\sum_j 1/d_j}, \qquad r = \dfrac{1}{\sum_j 1/d_j} - 1

where:

$d_i$ : the best available decimal odds on side $i$ , total return per dollar with the stake included. +110 gives $d = 2.10$ ; −105 gives $d = 1.952$ .
$1/d_i$ : the break-even probability that price implies; summed across both sides, the cost of covering the whole market.
$S$ : total dollars staked across both legs.
$s_i$ : dollars on side $i$ . Sized this way, $s_A d_A = s_B d_B$ , so both outcomes return the same.
$r$ : return on total stake, identical on either outcome. Positive only when the inverse sum is below one.

Worked example: the numbers in the form below

Book A prices side A at +110, Book B prices side B at +115, the best on each side:

d_A = 2.10, \quad d_B = 2.15 \qquad \Rightarrow \qquad \tfrac{1}{2.10} + \tfrac{1}{2.15} = 0.4762 + 0.4651 = 0.9413

s_A = 1000 \cdot \dfrac{0.4762}{0.9413} = \$505.88, \qquad s_B = 1000 \cdot \dfrac{0.4651}{0.9413} = \$494.12

505.88 \times 2.10 = 494.12 \times 2.15 = \$1{,}062.35 \qquad r = +6.24\%

$1,000 out, $1,062.35 back either way: a $62.35 margin, and only if both legs actually fill at the prices shown.

How the arbitrage calculation works

Convert the best price on each side to decimal odds (total return per dollar staked, stake included) and invert. A price at decimal odds d has break-even probability 1/d, so the two inverses added are the cost of covering the whole market. Side A comes from whichever book prices it highest, side B from the other:

\dfrac{1}{d_A} + \dfrac{1}{d_B} < 1

That inverse sum is the two-venue equivalent of the vig. On one book it is the overround the no-vig calculator strips out, and it is always above one. Across two venues it can dip below one, not because either book mispriced the game, but because the pair disagrees by more than their combined margin. Sizing each leg in proportion to its inverse makes both payouts identical, so the return is the same whichever side hits: a hedge, not a gamble on one outcome.

Above one there is no arb, and the calculator prints the negative number rather than rounding a non-arb up into something actionable. Book A at −110 / −110 against Book B at −108 / −112 inverts to 1.0430: $1,000 covering both outcomes returns $958.74 either way, a $41.26 loss that is exactly the two venues’ combined hold. The distance from −4.13% there to +6.24% above, on a two-cent difference in one price, is what the second book is worth on this game.

Why a “sure bet” rarely is

The arithmetic is clean; the execution is not. One tick of movement flips a positive return negative. Arbs decay in seconds. A price can move between the two legs and leave the position one-sided, stakes get voided, and books routinely limit or ban accounts that arb. The margin is a best case, not a promise.

Size is its own tell: a genuine two-way arb is rarely more than a few percent, so anything returning 12% or more (ARB_SUSPECT_RETURN = 0.12) is demoted from a green result to a “probably a stale line” caution. Full method and risks: arbitrage betting.

Where this fits, and what goes wrong

Two venues, one two-outcome market, both prices in hand. That is the entire precondition. Both legs at one book always sum above one (that sum is its hold), and the calculator flags it. Three-way markets need the same test across all three prices.
Equal stakes are not equal payouts. At 2.10 / 2.15, $500 each returns $1,050 or $1,075: still positive, but no longer the same number either way, which is the whole property being bought. Rounding $505.88 / $494.12 to $500 / $500 re-introduces a directional position.
The return is on this stake, not on capital over time. +6.24% is one market; turnover, limits and voided legs decide what it is worth.
Fees and the second leg are not in the split. It assumes both fills at the quoted prices and no commission. A Kalshi taker fee moves the effective $1/d$ up, and a 1% two-way margin does not survive a 1.75¢-per-contract fee. Price it first with the Kalshi fee calculator.

Check this number yourself

The page runs the same math as the MIT-licensed teachersbettextbook package: find_arbitrage(quotes, total_stake), over best_prices(), decimal_odds() and risk_warnings().

pip install teachersbettextbook

>>> from teachersbettextbook import find_arbitrage
>>> r = find_arbitrage([
...     {'book': 'Book A', 'ml_a': 110, 'ml_b': -105},
...     {'book': 'Book B', 'ml_a': -102, 'ml_b': 115}], 1000)
>>> r['inverse_odds_sum'], r['stake_a'], r['stake_b'], r['payout']
(0.9413067552602437, 505.88..., 494.11..., 1062.35...)

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

Arbitrage is the discontinuous edge. The same no-vig machinery, with a different precondition, drives the continuous +EV edge, a hedge on an open position, and free-bet conversion; single bets are sized by the Kelly calculator.

Frequently asked questions

What is an arbitrage calculator?

An arbitrage calculator checks whether the best available price on each side of a market, taken across two books, covers both outcomes for less than you stand to collect. If the inverse decimal odds sum to less than one, a sure bet exists, and it returns the exact stake for each side so the payout is the same either way.

How do you calculate an arbitrage bet?

Convert the best price on each side to decimal odds and add their inverses. Below one, the market is arbitrageable. Stake each side in proportion to its inverse and both outcomes return the same amount; one over the inverse sum, minus one, is the margin: at 0.9413, 6.24% of the total stake.

Is arbitrage betting risk-free?

The math is risk-free only if both bets land at the prices shown. In practice arbs decay in seconds, a price can move between the first and second leg and leave you one-sided, stakes can be voided, and books routinely limit or ban accounts that arb. The locked margin is a best case, not a guarantee.

What does it mean when the calculator says no arb at these prices?

The inverse decimal odds sum to more than one, so covering both outcomes costs more than either side pays back. The calculator reports the shortfall as a negative return rather than hiding it: at an inverse sum of 1.0430, a $1,000 two-sided position returns $958.74 whichever side wins.

Why does the calculator flag very large arbitrage returns as suspect?

Because a genuine two-way arb is rarely more than a few percent. Any detected arb returning 12% or more (the ARB_SUSPECT_RETURN threshold) is demoted to a verify-this-price caution, since a market that far apart usually means one venue has not repriced yet.