Expected value math (without the scary notation)

What EV actually means

Expected value (EV) is what you'd expect to make, on average, per bet, if you made the same bet infinitely many times.

If EV is positive, you make money long-term. If EV is negative, you lose money long-term.

The formula in plain English

EV = (chance of winning × amount won per win) - (chance of losing × amount lost per loss)

If you bet $100 on a coin flip at even money (+100): - 50% chance of winning $100 - 50% chance of losing $100 - EV = (0.5 × $100) - (0.5 × $100) = $0

Break-even.

Now bet $100 at +120 on that same coin flip: - 50% chance of winning $120 - 50% chance of losing $100 - EV = (0.5 × $120) - (0.5 × $100) = $60 - $50 = +$10 EV

Over many of those bets, you expect to make $10 per bet on average. +10% ROI.

Why this matters

Sharp bettors don't think "will this bet win?" They think "am I getting the right price for how likely it is to win?"

A 30% favorite at +250 is a +EV bet. A 70% favorite at -280 might be -EV. The price decides.

How to estimate true probability

1. Sharp consensus (easiest). Pinnacle is the sharpest sportsbook. If they have a game at -180, de-juice it to get the true implied probability (~63%).
2. Market average across books. Average 5-6 major books' odds, de-juice.
3. Your own model. Where real handicappers earn their edge.

The trap: small edges, big conviction

Most profitable bets have thin edges. A 2-3 point edge is real and bettable. A 10 point edge is rare and almost certainly means your model is wrong.

Variance vs edge

Even a +EV bet loses often. A 55% winner loses 45% of the time. If you can't separate edge from variance emotionally, you'll talk yourself out of good bets during downswings. Stay disciplined.

Action step

For your next five bets, calculate your estimate of true probability BEFORE looking at the line. Then compare. Which ones have edge?