Step-by-step: how to calculate expected value on a hedged sports bet. The formula, a worked example, and why hedge EV is easier to calculate than single bet EV.
Calculating expected value on a hedge is simpler than calculating EV on a single bet — because you don't need to know the true probability of each outcome. Here's the formula and a step-by-step example.
For any bet or decision:
EV = (Probability of winning × Amount won) − (Probability of losing × Amount lost)
For a single bet, the challenge is "probability of winning" — you're estimating it, and your estimate might be wrong.
For a properly structured hedge where both outcomes pay a profit, the EV is positive regardless of the true probability. You don't need to estimate anything.
For a two-outcome hedge, calculate the profit on each possible outcome, then find the expected value:
EV = (P₁ × Profit₁) + (P₂ × Profit₂)
Where P₁ + P₂ = 100% (exactly one outcome will happen).
Since you profit on either outcome, EV is positive for all possible values of P₁ and P₂.
The minimum EV = the lesser of Profit₁ and Profit₂ (locked in even in the worst case)
The maximum EV = the greater of Profit₁ and Profit₂ (achieved in the best case)
The actual EV falls between those two numbers.
Setup:
Step 1: Calculate winning payout of the bonus bet
$300 bonus bet at +240: profit = $300 × 2.40 = $720
Step 2: Find the optimal cash bet size
You want to find a cash bet on the Celtics where both outcomes are roughly equal.
Let's say you bet $550 on Celtics -290.
Step 3: Calculate profit on each outcome
Step 4: Calculate EV
EV = (P_warriors × $170) + (P_celtics × $190)
Since both profit numbers are positive, EV is positive for any probability split. If the game is 50/50: EV = (50% × $170) + (50% × $190) = $85 + $95 = $180
If the Celtics are 70% likely to win: EV = (30% × $170) + (70% × $190) = $51 + $133 = $184
The EV barely changes between probability scenarios because both outcomes are profitable. This is the power of a properly structured hedge.
For any hedge, the minimum locked-in profit = min(Profit₁, Profit₂).
In the example above: min($170, $190) = $170 locked in, no matter what.
This is the floor. The actual result will be either $170 or $190 — you just don't know which in advance.
Contrast this with a single +EV bet: a bet you estimate has +$20 EV might actually return -$100 in any given result. The variance is high. The hedge has zero variance on the positive side — both outcomes pay.
Bet-and-get bonuses (on win): The bonus only appears in one outcome. The EV calculation needs to account for the bonus value multiplied by the probability of the qualifying bet winning.
No sweat bets: Bonus only appears if the qualifying bet loses. Similar complexity.
Early payout bonuses: Add a probability-weighted "both sides win" scenario where your early payout triggers and the cash bet also wins.
The Ungambled app handles all of these calculations automatically, including the complex two-stage bonus structures.
EV on a standard hedge is straightforward: calculate profit on each outcome, confirm both are positive, then the EV is somewhere between the two (and always positive). Minimum EV equals your lower profit outcome — that's your locked-in floor. No probability estimate needed.
For the full framework on expected value in sports betting, read our guide to expected value.
Want the full picture?
The Ungambled guide covers this in depth — with screenshots from the app, worked numbers, and a step-by-step walkthrough of putting it all together.
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