What is expected value in betting?
Expected value, or EV, is the average amount you would win or lose per bet if the same bet were placed many times, calculated from the odds and the true probability of winning.
One bet tells you nothing. It wins or it loses. EV asks a better question: if I made this exact bet a thousand times, would I end up ahead or behind?
A bet with positive expected value is “+EV” (say “plus EV”). A negative one is “−EV”. The shorthand is most common in US betting talk and poker. UK bettors usually say “value” for the same idea.
Example
The formula:
EV = (chance of winning × profit if it wins) − (chance of losing × stake)
You stake $10 at odds of 2.50, so a win brings $15 profit. You believe the true chance of winning is 45%.
- EV = (0.45 × $15) − (0.55 × $10)
- EV = $6.75 − $5.50 = +$1.25
On average each of these bets earns $1.25, or 12.5% of the stake. Now say you were too optimistic and the true chance is 35%:
- EV = (0.35 × $15) − (0.65 × $10)
- EV = $5.25 − $6.50 = −$1.25
Same bet, same odds, and now it costs you $1.25 a time. The break-even point is the implied probability: 1 ÷ 2.50 = 40%. Above 40% the bet is +EV. Below, it isn’t.
Watch out
- EV is an average, not a promise. A +EV bet at 2.50 still loses more often than it wins. You need a big sample and a bankroll that survives the bad runs.
- Your probability is a guess. The formula is only as good as the number you feed it. Bookies employ people and models to make that number hard to beat.
- Most bets are −EV by design, because of the bookie’s margin.
I go deeper on finding +EV prices in my value betting guide.