Positive EV Betting: How to Calculate Your Edge

A positive EV bet isn’t a hunch that hits. It’s a price mistake: a number on the board that pays you more than the outcome is actually worth. Expected value betting is the whole discipline of finding those prices — and it rests on a single honest estimate of fair probability. Get that right and everything after it is arithmetic.

How to calculate expected value in betting

One bet, two futures. It wins with probability and pays decimal profit per dollar risked, or it loses and takes your dollar. Weight each outcome by its chance and you have the expected value per dollar staked:

Positive means the price is tilted in your favor. Negative means the book’s. That’s the entire scoreboard — and the whole difficulty of +EV betting hides in one variable: getting honest.

Where fair probability comes from

Here’s the trap. You can’t use a book’s own price as your estimate of . That price already bakes in the vig, and it’s the exact number you’re trying to beat — circular by construction. The fix is to de-vig a sharp book’s line, stripping out the hold to recover a clean fair probability, and treat that as your benchmark. When a softer book prices the same outcome below that benchmark, the gap is your edge.

That’s why de-vigging and +EV are two halves of one move: de-vig the sharp line to get , then test a soft price against it.

How big is a real edge?

Small. Genuine +EV edges run about 1% to 4% per dollar, and that number governs everything. Two consequences follow. First, an edge that faint needs a huge sample before it surfaces in your win rate, so short-run results tell you essentially nothing. Second, a 1–4% edge is the same size as ordinary line movement — so a +EV price goes stale in minutes. An accurate benchmark and speed aren’t nice-to-haves; they’re the job. Finding the price is only half of it: the Kelly criterion decides how much to stake on the edge once you’ve found it.

Expected value, derived from a posted price

Every step, from a moneyline on a screen to “this price pays a few cents per dollar above fair” — implied probability, the vig, the de-vig, the sharp benchmark, and EV itself. No leaps, no vibes.

Watch it work: same games, same wins, three prices

Three bettors stake a flat $25 on the exact same coin-flip games and win the exact same bets. The only difference is the price each accepted: the standard −110 (the book’s fee baked in), +100 (perfectly fair), and +105 (an above-fair price found by comparing books). Nobody here beats the game — the game is a coin flip. Watch who beats the price.

Advanced: EV rewritten, break-even, and the suspect band

The formula is the workhorse, but the same number wears several outfits, and each one makes a different fact obvious. Start with decimal odds. Since is just net profit plus the returned stake, , the loss term collapses into the stake:

That’s the fastest mental version when a book quotes decimal odds directly: multiply the fair probability by the payout multiplier, subtract one, done.

Now substitute , the price’s own implied probability, and the same expression becomes a ratio of probabilities:

Two facts fall straight out of this form. EV and edge always share a sign — one is positive exactly when the other is. And a fixed edge in probability points is worth more EV per dollar on an underdog than on a heavy favorite, because you divide by a smaller .

Next, set EV to zero and solve for . The probability at which a price pays exactly its worth turns out to be a number you already know:

That identity is why this article keeps comparing against : “implied probability” isn’t a metaphor. It is, by construction, the win rate at which the price returns nothing on average — so any fair above it is +EV and any below it is −EV. De-vig, compare, done.

Finally, the Live Board applies a sanity ceiling before it flags anything:

Real market-vs-market edges run about 1% to 4% per dollar. A price showing +15% or more against the fair line almost always means something else: a book that hasn’t repriced after news, a feed hiccup, or a mis-keyed number. Books routinely void obvious-error bets, so the board reads “too good” as a data-quality warning, not a bigger edge.

Every formula here lives on the Formula Sheet for quick reference.