How do you calculate expected value in betting?

EV = (P_win × Profit) − (P_loss × Stake). Example at odds 3.00 with 40% true probability on a £100 bet: EV = (0.40 × £200) − (0.60 × £100) = £80 − £60 = +£20.

What is a positive EV bet?

A positive EV (expected value) bet is one where the available odds are greater than the true probability warrants. Over a large sample, positive EV bets will generate profit. Short-term results can still be negative due to variance.

Can you consistently find positive EV bets?

Yes, but it requires a reliable probability model, access to low-margin markets (Pinnacle, exchanges), and the discipline to only bet when genuine edge exists. The closing line value (CLV) metric is the strongest available indicator that you are finding +EV.

Expected Value (EV) in Betting Explained

The Formula

EV = (P(Win) × Profit if Win) − (P(Loss) × Stake)

Where P(Win) is your estimated true probability of the outcome occurring (not the bookmaker's implied probability).

Worked Example: Positive EV

Decimal odds of 3.00 (implied 33.3%) on a $50 stake. You believe the true probability is 40%.

Profit if win = $50 × (3.00 − 1) = $100
EV = (0.40 × $100) − (0.60 × $50) = $40 − $30 = +$10

Positive EV means this bet, repeated many times under identical conditions, profits on average — even though it will still lose 60% of the time.

Worked Example: Negative EV

Same odds (3.00), but your true probability estimate is only 28% — below the bookmaker's 33.3% implied probability.

EV = (0.28 × $100) − (0.72 × $50) = $28 − $36 = −$8

This is a losing proposition in the long run, even if it happens to win this time.

Why EV Is Theoretical, Not Guaranteed

EV calculations are only as good as your probability estimate. If your estimate of 40% in the first example was actually wrong — and the true probability was really 30% — you'd have a negative EV bet that merely looked profitable on paper. This is why accurate probability modelling (not the EV formula itself) is the hard part of profitable betting.

EV and Variance Are Different Things

A single +EV bet can still lose. A single −EV bet can still win. EV only describes the average outcome across a large number of repetitions. This is precisely why disciplined bankroll management matters — surviving the variance long enough for a real edge to play out requires careful stake sizing, not just identifying +EV opportunities.

Practical EV Checklist

Convert the offered odds to implied probability.
Form an independent probability estimate using research, statistics, or modelling — never just "gut feel."
Calculate EV using the formula above.
Only bet when EV is clearly positive, with margin for estimation error.
Track results over a large enough sample (100+ bets minimum) to assess whether your edge is real.