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're guaranteed to profit on either outcome, EV is positive for all possible values of P₁ and P₂.
The minimum EV = the lesser of Profit₁ and Profit₂ (guaranteed 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 guaranteed profit = min(Profit₁, Profit₂).
In the example above: min($170, $190) = $170 guaranteed, 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 guaranteed 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 course covers this in depth — with examples, calculations, and a step-by-step system for putting it all together. It's on Udemy.
Join the Ungambled community for step-by-step walkthroughs, live support, and a proven system.
Join the Ungambled Community →