There are two numbers behind every bet: the price the bookmaker gives you (the odds) and the true chance the thing actually happens. Expected value — EV — is just the gap between them, turned into a profit-or-loss-per-stake figure. Get it positive often enough and you win long term. Get it negative and no amount of luck saves you.
Reading the odds: implied probability
Decimal odds are a disguised probability. Flip them over and you get the chance the market is pricing in:
implied probability = 1 / odds
Odds of 2.10 imply 1 / 2.10 = 47.6%. There's a
catch: add up the implied probabilities of every outcome in a market and
they sum to more than 100%. That overround is the bookmaker's
margin — the built-in fee you're paying. It means the odds already lie
slightly against you, so "the market thinks 47.6%" is really "the market is
charging you as if it were a bit higher than that."
The EV formula
Stake one unit. If the bet wins you collect odds − 1 in profit;
if it loses you're down your one unit. Weight each by how likely it is and
you get expected value per unit staked:
EV = p × odds − 1
Where p is your probability the bet wins. The bet
is +EV exactly when p > 1 / odds — i.e. when
your probability beats the market's implied probability. That difference is
your edge, and it is the entire game.
A worked example
Say a match is priced at 2.10 for "over 2.5 goals," and your
model puts the real chance at 52%.
- Implied probability =
1 / 2.10 = 47.6% - Your edge =
52% − 47.6% = +4.4 percentage points - EV =
0.52 × 2.10 − 1 = +0.092→ +9.2% per unit staked
Over many bets like this, you'd expect to make about 9 cents for every euro
you stake. Flip your probability to 45% — below the implied 47.6% — and the
same odds give 0.45 × 2.10 − 1 = −0.055: a −5.5% bet, no matter
how good it feels.
Edge is the whole game — and it's hard
EV is only as honest as your p. Pull it out of thin air and you'll talk yourself into negative bets all day. The hard part isn't the arithmetic — it's producing a probability that is genuinely better calibrated than a sharp market. That's why GSS derives p from a backtested probability model rather than gut feel, and surfaces only the bets where the edge clears a threshold as live +EV value bets.
One +EV bet means almost nothing
Expected value is a long-run average. A +9.2% bet still loses 48% of the time. The number only shows up in your bankroll over volume — which is why the two companion questions matter just as much: how much to stake on a given edge (the Kelly criterion), and whether your edge was real in the first place (closing line value). Find the +EV, size it sanely, and verify it against the close — that loop is the entire job.