The expected value calculator tells you how much a bet is worth on average, every time you place it. Put £10 on odds of 2.20 when you think it’s a 50% chance and the expected value is +£1.00 per bet: a 10% edge. Over 100 bets that’s +£100 on average. It’s free, and you can also enter your own list of outcomes for bets that don’t fit a simple win or lose.
Expected value: the formula
EV = (chance of winning × profit if it wins) − (chance of losing × stake).
At 2.20, a £10 win pays £12 profit. So EV = 0.5 × £12 − 0.5 × £10 = £6 − £5 = +£1. The odds you need to break even are 2.00, a 50% chance. The price on offer is higher, which is where the edge comes from.
Change the chance to 40% and the same bet is −£1.20 every time. That’s the whole problem: EV is only as good as the probability you put in.
Where your probability comes from
- A sharper price. Many bettors use a low-margin exchange or bookmaker as the “true” chance and look for higher odds elsewhere. If the fair price is 2.00 and someone offers 2.20, that’s +10%.
- Your own model. Fine, as long as you check it against results over hundreds of bets, not ten.
- Casino games. Here the chances are known exactly. A £10 straight-up bet on European roulette pays 35 to 1 and wins 1 time in 37: EV = −£0.27. Every bet on that wheel has the same −2.7%.
Why positive EV can still lose
EV is an average. The calculator also shows the range where about 95% of results land after your chosen number of bets. For the 2.20 example, that’s roughly −£120 to +£320 after 100 bets. So even a real 10% edge loses money over 100 bets more often than people expect. Stake sizing helps here: the Kelly criterion calculator works out how much of your bank a given edge is worth.
Use “my own list of outcomes” for things like a bonus with several possible results, a cash-out decision or an each-way bet. Give each outcome a chance and an amount won (+) or lost (−), and make sure the chances add up to 100%.
Positive EV is a long-run idea. Only bet what you can afford to lose in the short run. BeGambleAware.org is free and confidential if it stops being fun.