Arbs › Guides › Expected value betting, with worked examples
Expected value (+EV) betting
Arbs research desk · Updated 2026-11-01 · Reviewed 2026-11-01 · 2 min read
The short answer: Expected value is a bet’s average result per dollar if you could repeat it many times: win probability × decimal odds − 1. A bet at +100 that wins 55% of the time is worth +10%.
The calculation
EV = p × d − 1
The bet breaks even when p equals one over the odds, so your edge in points is the gap between the two:
break-even = 1 ÷ d; edge = p − 1 ÷ d
| Bet | Win chance | Break-even | EV |
|---|---|---|---|
| +100 (2.00) | 55% | 50.0% | 0.55 × 2.00 − 1 = +10.0% |
| −150 (1.667) | 62% | 60.0% | 0.62 × 1.667 − 1 = +3.3% |
| Polymarket 45¢, 0.05 fee | 50% | 46.2% | 0.50 ÷ 0.4624 − 1 = +8.1% |
EV on Polymarket
On Polymarket the cost of $1 of payout is the price plus the taker fee, so the odds are one over that cost:
EV = p ÷ c − 1, where c = price + r × price × (1 − price)
Worked example: A 45¢ share you think wins 50% of the time
- Fee: 0.05 × 0.45 × 0.55 = 1.24¢
- Cost: 46.24¢ per $1 of payout
- EV = 0.50 ÷ 0.4624 − 1
+8.1%. Without the fee it would be +11.1%.
Where p comes from
Everything rests on the win probability. The usual sources are a sharp book’s no-vig line, a consensus of books, or a model. Arbs blends a devigged consensus of books and Kalshi with a team-records prior, calibrates it on graded games, and publishes every locked pick on the track record so you can see how its probabilities did.
Variance
A +10% bet at even money still loses 45% of the time. Results only settle down over many bets:
| Bets | Expected profit | Chance of being down |
|---|---|---|
| 10 | +1 unit | about 26% |
| 100 | +10 units | about 13% |
| 1,000 | +100 units | under 0.1% |
Sizing each bet with a fraction of the Kelly criterion keeps the swings survivable.
Checking yourself
Results take hundreds of bets to separate skill from luck. A faster check is closing line value: if you keep getting better prices than the market closes at, your probabilities are probably good.
Try it: EV calculator
Frequently asked questions
Can a +EV bet lose?
Often. EV is an average over many bets, not a promise about one.
What is a good EV percentage?
Long-run edges in liquid sports markets are small, often 1–5%. Claims of 20%+ on major markets usually mean the probability is wrong.
How do I calculate EV on Polymarket?
Use the price plus the taker fee as your cost. EV = probability ÷ (price + fee) − 1.