Expected value, and what it does not tell you

Chance of winning multiplied by profit, minus chance of losing multiplied by stake. A 55 per cent chance at +100 on a 100 stake is 0.55 × 100 − 0.45 × 100, which is +10.

It is the average outcome across every possible repetition of the same bet, which makes it the only number that answers 'should I take this' without reference to how the last one went. Everything else — confidence, form, feel — is a story about one instance.

It depends entirely on the probability you fed it, and you do not know the probability. The de-vigged market price is usually the best estimate available, which means most honest EV calculations end up asking whether you can beat the market rather than whether you can beat the game.

Which is where it goes wrong. It says nothing whatever about the next bet. A positive-EV wager that loses is not evidence the calculation was wrong, and treating each result as a verdict on the process is how people abandon something that was working.

What to do with it. Compute it before betting, not after. An EV calculated once the result is known is not a calculation, it is a justification.

Work it out. The expected value calculator turns a price and your own probability estimate into EV per bet and the break-even probability.