Hedge and cash-out calculator

You are on at one price and the market has moved. This solves the stake that pays the same whichever way it settles, the stake that maximises expected value, and the stake that maximises bankroll growth, then shows what the first one costs.

Worked example — Hedge that pays the same either way, on this page's own example: $181.82. $100 at 4.00, now 1.80 / 2.20

Price the hedge, not just the equal-profit number

Enter the stake you already have on, the price you took it at, and both sides of the market now. This returns the stake that locks a flat outcome, the stake that maximises expected value, and the stake that maximises bankroll growth, then prices what the first one costs against the second two.

Try:

Odds format

Stake already on$Price you tookYour side nowOther side now, the hedgeBankroll, including this bet$

Fair-price method and custom stake 2

Fair probability from

Try any hedge stake$

Current resultHedge that pays the same either wayHedge that pays the same either way: $181.82. locks $118.18

Your open bet is still worth +0.5 points, hedging trades that away.

The hedge price of 2.20 implies your side wins 54.5% of the time. The de-vigged market says 55.0%.

Taking the full hedge gives up $1.82 of expected value, which is 1.8% of the original stake. That is the price of the flat outcome. It is not automatically a mistake: the growth-optimal row below often beats standing pat on a bankroll this size, and it does it with a smaller stake than the equal-profit hedge.

Fair probability used55.0%

Hedge price implies54.5%

Cost of certainty$1.82

Growth-optimal hedge$172.50

Value-maximising hedgeNone

Hedge the bankroll allows$900

Why expected value cannot pick an interior hedge

Expected value is a straight line in the hedge stake: each extra dollar changes it by (1-p)(h-1) - p, which does not depend on how much is already hedged. A straight line is maximised at an end point, so the value-maximising answer is always all or nothing, and it flips at the moment the fair probability crosses the hedge price.

Why the growth-optimal hedge is interior

Score the two branches in log wealth instead, which is what sizing a bankroll to survive actually means, and the objective becomes curved. It lands between doing nothing and levelling the outcomes whenever the bet still has an edge, and it moves toward the full hedge as the edge disappears.

Where the fair probability comes from

Both current prices are de-vigged before anything is compared, because the hedge price on its own contains the book's margin and would make every hedge look cheaper than it is. Override it with your own number if you have one: on a live position, you often do.

Prices are the ones you typed; this page reads no venue and holds no market data. The hedge is assumed to be the exact opposite side of the same event, settled at the same time, with no commission and no partial fill.

Hedge stake by price move, on a $100 bet

The equal-profit hedge, x = stake times original price divided by hedge price, on a $100 bet at each original price against a grid of current hedge prices. Each cell is the stake that pays the same amount whichever way the bet settles, and the locked amount underneath it.

Equal-profit hedge stake and the amount it locks, per $100 originally staked
Original price	Hedge at 1.50	Hedge at 1.80	Hedge at 2.20	Hedge at 3.00
2.00	$133.33locks -$33.33	$111.11locks -$11.11	$90.91locks $9.09	$66.67locks $33.33
3.00	$200.00locks $0.00	$166.67locks $33.33	$136.36locks $63.64	$100.00locks $100.00
4.00	$266.67locks $33.33	$222.22locks $77.78	$181.82locks $118.18	$133.33locks $166.67
5.00	$333.33locks $66.67	$277.78locks $122.22	$227.27locks $172.73	$166.67locks $233.33
10.00	$666.67locks $233.33	$555.56locks $344.44	$454.55locks $445.45	$333.33locks $566.67

The stake needed scales directly with the original price and inversely with the hedge price, so a long shot that came all the way in (original 10.00, hedge down near 1.50) needs a hedge stake several times the original bet to level the outcome. That is capital most bankrolls do not have free, which is exactly why the calculator above also solves the largest hedge an actual bankroll can fund.

Does hedging always cost you expected value?

No, only when the de-vigged fair probability still favours your original side. The break-even rule is exact: hedging is EV-positive once the fair probability drops below the hedge price's own implied probability, (h - 1) / h. On this page's own default position, $100 at 4.00 with the market now 1.80 against 2.20, that boundary is 54.5% and the de-vigged market says 55.0%, so the open bet is still worth +0.5 points against the hedge and the full hedge gives up $1.82 of expected value. That is what the certainty costs, stated in dollars rather than implied.

Hedging vs cashing out, the actual difference

A cash-out button is not a hedge at the posted two-way price. Books quote cash-out at a worse number than the current market, and that gap is the point of the feature: it is priced to be a convenience the book profits from, not a neutral settlement. Hedging manually at the other side's actual current price, the way this calculator prices it, captures the full two-way market instead of the discounted number a cash-out button offers. If the book's cash-out price and the manual hedge price are ever the same, manual hedging cannot do worse; in practice it is usually better.

What each of the four numbers is

Standing pat is the original bet, untouched. The equal-profit hedge is the stake that pays the same whichever way it settles, which is a statement about your preferences, not the arithmetic. Expected value is linear in the hedge stake, so the value-maximising answer is always all or nothing, flipping the moment the fair probability crosses the hedge price's implied probability. The growth-optimal hedge scores both branches in log wealth instead, which curves the objective and gives an interior answer: on the default position it is $172.50, a little under the equal-profit stake, because sizing a bankroll you intend to keep using is a different question than levelling one bet's two outcomes.

What this does not model, and what I would actually do

Exchange commission on the hedge, partial fills, and the price moving while you place it are not modelled. The bankroll is treated as a single number available now, and log utility is an assumption about you, not a fact about the bet. My own rule: hedge when the position has grown large against the bankroll, not when the price has moved a lot, those are not the same trigger. If the open bet still carries an edge against the de-vigged market, take the growth-optimal stake rather than the flat one, it costs less expected value and gives up almost none of the risk reduction. If the edge has gone, the full hedge is not a compromise, it is the correct trade. The case I would refuse is hedging a still-good bet down to a flat number because the amount on the screen got uncomfortable; that discomfort is real information about stake size, and the fix belongs at the sizing decision, not here.

The next question after this one

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