Calculator

Hedge Calculator

About this calculator

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

You already have a bet. Here is the stake on the other side that makes both outcomes pay the same, and what that certainty costs you. When the line has moved far enough, the two prices sum under 100% and the result says so: that is an arbitrage on the position you already hold, and this page sizes it directly.

See both sides of the market as they move: open the app →

A hedge calculator sizes a bet on the other side of one you already hold so both outcomes pay the same amount. It removes the sweat, and at any price with vig in it, it costs a little expected value.

The cost nobody prints

The equal-payout stake is your first bet's total return divided by the decimal odds on the other side. Total return, not profit. That is the step most calculators get wrong.

Hedging removes the swing. It does not remove the price. Both bets carry margin, so locking the outcome almost always costs you expected value, and this page prints that number instead of hiding it.

Sometimes paying it is obviously right. A number you cannot afford to lose is worth giving something up for. That is a decision about your life rather than about the math, and the math should still be on screen while you make it.

Want more math?the Nerd Corner

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:

$S$ : stake at risk on the original bet, in dollars.
$d_1$ : decimal odds of the bet you hold. +250 is $d_1 = 3.50$ .
$d_2$ : decimal odds on the other side now. +150 is $d_2 = 2.50$ .
$H$ : the equal-profit hedge stake, in dollars. It 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 hedge whose profit exactly covers the original stake.
$p_2$ : the de-vigged fair probability that the hedge side wins, 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 at current fair prices. The $5.75 gap is what the certainty costs: 4.11¢ per dollar hedged.

Break-even and partial hedges

The form also prices break even only ($66.67 here, whose profit cancels the original $100 loss while the original side still pays $183.33) and any partial fraction of the equal-profit stake, which leaves the outcomes unequal and scales the cost with the fraction.

What the hedge costs

The number the rest of the category omits. A hedge is a bet at a posted price, and posted prices carry margin. Per dollar staked the hedge leg is worth

\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 $q_2 = 40.00\%$ against a fair $p_2 = 38.36\%$ , so every hedged dollar is worth $0.3836/0.40 - 1 = -4.11\%$ : −$5.75 on the $140 hedge. That rate is the market’s margin on the side being bought, which is why a tighter market is cheaper to hedge into. On an exchange it arrives as a fee instead.

When the hedge side is priced above fair the expected cost is negative, and the calculator prints $0.00 rather than dressing a favourable price up as a saving. Two prices that far apart are arbitrage, not a hedge: an arb needs both prices live at once, a hedge only the second.

The locked $110 depends only on the two prices and does not move. The cost depends on the fair probability, which is an estimate: $5.75 proportional, $7.50 Shin, $8.39 power. The sign never changes, which is why the calculator names the method it used (how to de-vig odds).

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 stake trades $5.75 of expected value for the removal of a $350 swing, and no formula ranks those for a particular bankroll. What it does settle is the price of that trade and its direction: against a market carrying margin, hedging always lowers expected value and always lowers variance.

Common mistakes

Hedging off the profit instead of the return. The hedge stake divides $S d_1$ , the total return, by $d_2$ . Dividing the profit $S(d_1-1)$ instead under-hedges by $S/d_2$ : $40 short here. The original price is otherwise sunk: every figure uses the current market.
Using the hedge price alone for the fair probability. One side of a two-way market cannot be de-vigged alone, hence the field for your side’s price now.
Assuming both legs fill. A hedge quoted and not filled is not a hedge; a partial fill is a partial hedge at a worse price.

Check this number yourself

One division for the stake, one de-vig and one multiplication for the cost, both in the MIT-licensed teachersbettextbook package.

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. What is open and what is not.

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.

How do you calculate a hedge stake?

H = S × d₁ / d₂. A $100 bet at +250 returns $350 in total; hedging at +150 takes $350 / 2.50 = $140, which leaves $110 whichever side wins.

Does a hedge remove the risk?

It makes both outcomes pay the same number, but only the two prices decide whether that number is positive. If the market has moved against the original bet, the equal figure is an equal loss.

How much does hedging cost?

The hedge leg gives up H × (1 − p₂d₂), where p₂ is the de-vigged fair probability that the hedge side wins: the margin on the side being bought, 4.11¢ per dollar or $5.75 on a $140 hedge.

Can you hedge a free bet?

The arithmetic differs, because a stake-not-returned token pays profit only: its return is F × (d − 1) rather than F × d, so the hedge stake is smaller. The free bet calculator handles it.