A bet is +EV when the price pays more than the true probability deserves. That's the entire concept. Everything else in sharp betting is a method for finding those prices before they move.
The formula
Expected value = (decimal odds × true win probability) − 1.
Say a book posts +120 on a team that truly wins 48% of the time. Decimal odds are 2.20, so EV = 2.20 × 0.48 − 1 = +0.056. That bet earns 5.6 cents per dollar on average. You'll still lose it 52 times out of 100 — being +EV says nothing about tonight and everything about the next thousand bets.
Where the true probability comes from
The formula is trivial; the win probability is the whole game. Nobody knows the true number, but the market itself gets close: take a two-way market, strip each book's hold out of its prices, and the result is the market's honest opinion. When one book's posted price beats that consensus, the gap is measurable edge.
That's the exact process behind [The Edge board](/edge) on this site: de-vig every book, take the median, flag what's mispriced.
Why most bettors never see it
Books don't advertise probabilities, they advertise payouts. A +450 underdog feels like opportunity; whether it is depends entirely on whether the true chance beats the 18.2% the price implies. Without the conversion habit, every bet is vibes.
What to do with it
Bet only when you have a reason to believe the price is wrong, size it to the edge (see the [Kelly guide](/learn/kelly-criterion)), and grade yourself on closing line value, not wins. Short-term results are noise. The math is not.
