The Math Behind the Market
Expected value as a mathematical concept
8 min · The long-run average of a repeated situation — a weighted average of outcomes.
- Expected value
- Probability
The stat
The long-run average of a repeated situation — a weighted average of outcomes.
Learn the number
Expected value (EV) is what a repeated situation averages out to. Multiply each outcome by its probability, then add the results.
It is a weighted average, and the weights are probabilities. Outcomes that happen more often count more.
EV is a long-run statement. A single event lands on one actual outcome, which is often nowhere near the expected value.
A fair game has an EV of zero. A game with a built-in margin has a negative EV for the customer — that is what the margin means in EV terms.
Read the stat
A fictional-credit simulation: risk 100 credits at a true 50% chance, priced at 52% by the platform.
- A correct call returns about 92 credits of profit (100 ÷ 0.52 ≈ 192 back, minus the 100 risked).
- An incorrect call loses the 100 credits.
- EV = (0.50 × +92) + (0.50 × −100).
- EV = 46 − 50 = −4 credits.
Each repetition averages −4 fictional credits — 4% of the 100 risked, matching the overround exactly.
Your turn
A fictional scenario pays +150 credits when right and −100 when wrong, and you judge the true probability to be 45%. What is the EV?
Explain what it means
EV explains why the margin matters so much. Even a customer who is right exactly as often as they claim has a negative expected value once the price includes the overround.
Make a prediction
Take any published pair of percentages, convert to implied probabilities, and predict whether a customer with perfectly accurate probabilities would have positive or negative EV. With an overround, it is negative.
Review what happened
Notice how far single results sit from EV. A −4 EV can win five in a row; that is variance, not evidence the EV was wrong.
Check your understanding
0 of 4 correct
Every question has to be right for this lesson to count as complete. Miss one and you can try it again.