Hedge Calculator

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

Enter the bet you already hold and the price on the other side. This computes the equal-profit hedge stake, the break-even stake, any partial hedge in between — and the expected value the hedge gives up, which competing tools leave off the screen.

A hedge calculator finds the stake on the opposite side of a bet you already hold that makes both outcomes pay the same amount. The equal-profit stake is the original bet’s total return divided by the decimal odds on the other side. Equalising removes the swing and, at any price carrying margin, costs expected value.

H = \dfrac{S \cdot d_1}{d_2}, \qquad L = S\,d_1 - S - H, \qquad H_{\text{be}} = \dfrac{S}{d_2 - 1}, \qquad \mathbb{E}[\text{cost}] = H\,\big(1 - p_2 d_2\big)

where:

$S$ — the stake already at risk on the original bet, in dollars.
$d_1$ — decimal odds of the bet you hold, the price you actually took. +250 is $d_1 = 3.50$ .
$d_2$ — decimal odds on the other side now, the price the hedge would be placed at. +150 is $d_2 = 2.50$ .
$H$ — the equal-profit hedge stake, in dollars: the stake that makes both outcomes return $S d_1$ .
$L$ — the result either way, in dollars. Positive is profit; negative is an equal loss, and the calculator labels it as one.
$H_{\text{be}}$ — the break-even-only stake: the smaller hedge whose profit exactly covers the original stake if the other side wins.
$p_2$ — the de-vigged fair probability that the hedge side wins, taken from the current two-way market, not from the hedge price alone.
$\mathbb{E}[\text{cost}]$ — expected value given up by placing the hedge, in dollars. It is zero only if the hedge price is exactly fair.

Worked example — the numbers in the form below

You hold $100 at +250. The market has moved: your side is now −180 and the other side is +150.

d_1 = 3.50 \Rightarrow S d_1 = \$350.00, \qquad d_2 = 2.50 \Rightarrow H = \tfrac{350}{2.50} = \$140.00

\text{original wins: } \$250.00 - \$140.00 = \$110.00 \qquad \text{hedge wins: } \$210.00 - \$100.00 = \$110.00

\text{de-vig } (-180,\,+150) \Rightarrow p_2 = 38.36\% \quad\Rightarrow\quad \mathbb{E}[\text{cost}] = 140\,(1 - 0.3836 \times 2.50) = \$5.75

$110 either way, against an unhedged position worth $115.75 on average at the current fair prices. The $5.75 gap is what the certainty costs — 4.11¢ per dollar hedged, which is exactly the market’s margin on the side being bought.

Want the live board that shows both sides of the market as they move? Open the app →

Three hedges, three different questions

“How much do I hedge” is not one question. It is three, and they have three different answers on the same two prices.

Equal profit either way. $H = S d_1 / d_2$ . Both outcomes return $S d_1$ , so the result is a single number: $110 at the worked prices. This is the stake most people mean by “hedging”.
Break even only. $H_{\text{be}} = S/(d_2-1)$ . The smaller stake whose $100 profit cancels the original $100 loss — $66.67 here. The original side still pays $183.33 if it lands. This removes the loss, not the swing.
Partial. Any fraction $f$ of the equal-profit stake. The outcomes stay unequal and the cost scales with $f$ .

All three on the worked market — $100 at +250, hedge available at +150:

Hedge stake	If the original wins	If the hedge wins	Swing	Expected
$0 — no hedge	+$250.00	−$100.00	$350.00	$115.75
$35.00 — 25%	+$215.00	−$47.50	$262.50	$114.32
$66.67 — break even	+$183.33	$0.00	$183.33	$113.01
$70.00 — 50%	+$180.00	+$5.00	$175.00	$112.88
$105.00 — 75%	+$145.00	+$57.50	$87.50	$111.44
$140.00 — equal profit	+$110.00	+$110.00	$0.00	$110.00

Expected column uses the fair probabilities from de-vigging the current −180 / +150 market proportionally: 61.64% / 38.36%. Read the table left to right and the trade is visible in one line — the swing column falls from $350 to $0 and the expected column falls from $115.75 to $110.00.

What the hedge costs

This is the number the rest of the category omits. A hedge is a bet, placed at a posted price, and posted prices carry margin. Buying the other side at +150 when its fair price is 38.36% means paying more than the outcome is worth.

The hedge leg’s expected value, per dollar staked, is:

\dfrac{\mathbb{E}[\text{hedge}]}{H} = p_2 d_2 - 1 = \dfrac{p_2}{q_2} - 1, \qquad q_2 = \dfrac{1}{d_2}

At +150 the price implies $q_2 = 40.00\%$ while the fair probability is $p_2 = 38.36\%$ , so every hedged dollar is worth $0.3836/0.40 - 1 = -4.11\%$ . On $140 that is −$5.75.

The identity is exact, and worth seeing written out. The unhedged position is worth

\mathbb{E}[\text{unhedged}] = S\,(p_1 d_1 - 1) = 100\,(0.6164 \times 3.50 - 1) = \$115.75

and adding the hedge leg gives

\$115.75 + (-\$5.75) = \$110.00 = L

— the locked figure, to the cent. The hedge converts $115.75 of expected value into $110.00 of certainty. That difference is the entire content of the decision, and it is arithmetic, not opinion.

The cost is the vig on the side you buy

Rewriting the per-dollar cost makes its source obvious:

1 - \dfrac{p_2}{q_2} = \dfrac{q_2 - p_2}{q_2}

The numerator is the probability points of margin sitting on the hedge side; the denominator normalises it into a rate per dollar. At the worked prices that is $(0.4000 - 0.3836)/0.4000 = 4.11\%$ . Under proportional de-vig this collapses to a single number for the whole market — $\rho/(1+\rho)$ , where $\rho$ is the overround — so both sides cost the same rate to hedge into. A tighter market is cheaper by exactly the amount it tightens: a −105 / −105 pair carries 2.44% overround, and hedging into it costs 2.38¢ per dollar instead of 4.11¢.

Two consequences follow. Shopping the hedge price matters as much as shopping the original price — it is the same arithmetic, applied to the leg most people place in a hurry. And an exchange quote, where the margin is a fee rather than a spread on the line, prices the same hedge differently; the Kalshi fee calculator puts that cost in the same units.

When the arithmetic says the hedge costs nothing

Occasionally the two prices are far enough apart that the equal-profit hedge returns more than the total staked no matter what happens. That is not a hedge any more; it is an arbitrage, and the same two-price test detects it:

\dfrac{1}{d_1} + \dfrac{1}{d_2} < 1

At the worked prices that sum is $1/3.50 + 1/2.50 = 0.6857$ — below 1, which looks like an arb but is not one here, because $d_1$ is a price already taken rather than a price available now. That distinction is the whole difference between hedging and arbitrage: an arb needs both prices live at the same moment, a hedge needs only the second one. Compare against the current price on your side (−180, decimal 1.556): $1/1.556 + 1/2.50 = 1.0429$ , above 1, so there is no arb in the live market — just 4.29% of margin.

A negative expected cost means the same thing: the hedge side is priced above fair. The calculator prints $0.00 for the cost in that case rather than dressing a favourable price up as a saving, and points at the arbitrage calculator, which is built for it.

The de-vig method moves the cost, not the locked figure

The locked $110 depends only on the two prices and does not move at all. The cost depends on the fair probability, and that is an estimate. On the worked market the three methods disagree:

De-vig method	Fair p, hedge side	Unhedged EV	Cost of the hedge	Locked
Proportional	38.36%	$115.75	$5.75	$110.00
Power	37.60%	$118.39	$8.39	$110.00
Shin	37.86%	$117.50	$7.50	$110.00

A $5.75-to-$8.39 range on a $110 position. The sign never changes — every method agrees the hedge gives something up — but the size is an estimate carrying its own error bar, which is why the calculator names the method it used. How to de-vig odds covers what separates the three.

Second example: hedging into a loss

$200 at −110, and the market has moved the other way. Your side is now +260 and the other side is −340.

d_1 = 1.9091 \Rightarrow S d_1 = \$381.82, \qquad d_2 = 1.2941 \Rightarrow H = \tfrac{381.82}{1.2941} = \$295.04

L = \$381.82 - \$200.00 - \$295.04 = -\$113.22

Equal on both sides, and equal to a $113.22 loss. Hedging cannot manufacture a profit out of a position that has lost value; it can only make the two outcomes identical. Unhedged, this position is worth −$99.04 on average against a de-vigged 26.44% chance the original side still wins — so the hedge costs $14.18 of expected value while turning a −$200.00 / +$181.82 swing into a flat −$113.22. The calculator labels this cell “locked loss”, not “locked profit”.

What this calculator will not tell you

It will not tell you whether to place the hedge. That is a preference about variance, not an output of arithmetic: the equal-profit hedge trades $5.75 of expected value for the removal of a $350 swing, and no formula ranks those against each other for a particular bankroll. What the numbers do settle is the price of the trade, and the direction: against a market carrying margin, hedging always lowers expected value and always lowers variance. Kelly sizing is the other end of the same conversation — it prices variance in growth-rate terms rather than in dollars.

Common mistakes

Hedging off the profit instead of the return. The hedge stake divides $S d_1$ , the total return including the stake, by $d_2$ . Dividing the profit $S(d_1-1)$ instead under-hedges by $S/d_2$ — $40 short on the worked example. That single mistake is the most common wrong hedge number on the internet.
Reading the locked figure as a windfall. $110 either way is $110 either way. It came out of a position worth $115.75 on average, and the $5.75 difference is a real cost paid to the venue.
Using the hedge price to compute the fair probability. One side of a two-way market cannot be de-vigged on its own. The fair probability needs both current prices, which is why the form asks for your side’s price now as well.
Comparing to the price you took. The original price is sunk. Everything about the hedge decision is priced off the current market, and the calculator’s expected-value figures use the current market throughout.
Hedging a free bet with the cash formula. A stake-not-returned token returns $F(d-1)$ , not $F d$ , so it needs a smaller hedge. Use the free bet calculator for that case.
Assuming both legs fill. Between the two prices the market moves. A hedge quoted and not filled is not a hedge, and a partially filled one is a partial hedge at a worse price.

Check this number yourself

The hedge stake is one division; the cost is one de-vig plus one multiplication. Both run in the MIT-licensed teachersbettextbook package, which is the same math this page runs.

pip install teachersbettextbook

>>> from teachersbettextbook import decimal_odds, devig
>>> S, d1, d2 = 100.0, decimal_odds(250), decimal_odds(150)
>>> H = S * d1 / d2;  H
140.0
>>> S * d1 - S - H                      # locked either way
110.0
>>> p1, p2 = devig(-180, 150, 'proportional')
>>> H * (1 - p2 * d2)                    # what the hedge costs
5.7534246575...

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

A hedge is one price against another, so everything upstream of it lives on the neighbouring pages: the no-vig calculator for the fair line the hedge is priced against, bet payout for the return the hedge divides, arbitrage for the case where both prices are live, and free bet value for hedging a token instead of cash.

Frequently asked questions

What is a hedge calculator?

A hedge calculator finds the stake on the opposite side of a bet you already hold that makes both outcomes pay the same amount. It divides the original bet’s total return by the decimal odds now available on the other side, then reports what each outcome pays after the second stake is added.

How do you calculate a hedge stake?

The equal-profit hedge stake is H = S × d₁ / d₂, where S is the original stake, d₁ is the decimal price you took and d₂ is the decimal price on the other side now. A $100 bet at +250 returns $350 in total; hedging at +150 (decimal 2.50) takes $350 / 2.50 = $140, which leaves $110 whichever side wins.

Does a hedge remove the risk?

An equal-profit hedge makes both outcomes pay the same number, but that number is only positive if the two prices allow it. If the price on the other side has moved against the original bet, the equal figure is an equal loss. Hedging also replaces the position’s expected value with a smaller certain amount whenever the hedge price carries margin, which it almost always does.

How much does hedging cost?

The hedge leg gives up H × (1 − p₂d₂) in expected value, where p₂ is the de-vigged fair probability that the hedge side wins. Per dollar hedged that equals (q₂ − p₂) / q₂ — the margin on the side being bought. At the worked example’s prices it is 4.11¢ per dollar, or $5.75 on a $140 hedge.

What is a partial hedge?

A partial hedge is any stake between zero and the equal-profit stake. It leaves the two outcomes unequal and scales the cost proportionally: half the equal-profit stake gives up half the expected value and leaves half the swing in place. The calculator prints both outcomes and the expected value at any fraction you enter.

Can you hedge a free bet?

Yes, and the arithmetic differs because a stake-not-returned token pays profit only. The token’s return is F × (d − 1) rather than F × d, so the hedge stake is smaller than it would be for a cash bet of the same face value. The free bet calculator handles that case directly.