Skip to content

Expected value calculator

What a bet makes on average, given its chance, and how far one run of bets can stray from it.

%
Expected value per bet+1.00
Edge+10.00%
Fair odds2.50
Break-even chance36.36%
Expected over 100 bets+100.00
Typical swing (one standard deviation)±134.72
EV needs an honest probability

A BAI8 assessment gives you a researched probability for any match and the edge against the best price, so the EV has something real behind it.

Free plan: 5 assessments a month, no card needed.

Assess a match free

How it works

A bet’s expected value is what it makes on average if you placed it many times: the chance it wins times what it pays, minus the chance it loses times the stake. With decimal odds that is the stake times (probability × odds − 1). A positive EV means the odds are longer than the chance deserves.

EV is an average, not a forecast. Over a few dozen bets the result can sit far from it either way, so the calculator shows the typical swing beside the expected profit.

The formula

  • EV = stake × (probability × decimal odds − 1)
  • Edge = probability × decimal odds − 1
  • Fair odds = 1 ÷ probability, and break-even probability = 1 ÷ decimal odds
  • Swing over n bets = stake × decimal odds × √(n × p × (1 − p))

A worked football example

You rate an away win at 40% and it is priced 2.75. A stake of 10.00 has an EV of +1.00, an edge of 10%. Over 100 such bets you would expect +100.00, but one standard deviation either side is ±134.72: a run of 100 can easily end behind.

What it does not tell you

EV is only as honest as the probability. If your chance is too high, so is the EV. It also treats every bet as independent and says nothing about how much of your bankroll to stake: the Kelly calculator does that.

Common questions

How do you calculate expected value in betting?

Multiply your probability by the decimal odds, subtract 1 and multiply by the stake. A bet of 10 at 2.75 on a 40% chance: 10 × (0.40 × 2.75 − 1) = +1.00.

What is a positive EV bet?

One whose odds are longer than its real chance deserves, so it makes money on average. It still loses often: a 40% chance at 2.75 loses six times in ten.

What is the break-even probability?

The chance a price needs to break even: 1 divided by the decimal odds. At 2.75 it is 36.4%, so any real chance above that is positive EV.

Why can a positive EV bettor still lose?

Because over a short run the swing dwarfs the edge. With a 10% edge on 100 bets of 10 at 2.75, the expected profit is 100, but one standard deviation is about 135.

Where does the probability come from?

From your own model or research. The odds’ implied probability includes the margin, so EV on it is always negative. Comparing your prices with the closing price is a common check on whether your probabilities hold up.

Read more

Expected value in betting, in plain numbersBlogWhat a positive edge actually meansBlogWhat variance does to a good betBlogWhy the closing line is a useful scoreboardBlogExpected value (EV)GlossaryEdge (value bet)GlossaryVarianceGlossaryClosing line value (CLV)Glossary

More calculators

Kelly criterion calculatorThe stake that grows a bankroll fastest, at full, half or quarter Kelly.Implied probability calculatorThe chance each price implies, the bookmaker’s margin and the fair odds without it.Odds converterDecimal, fractional, American and the Asian formats, with the chance each price implies.Every calculator

Put this calculator on your site

Free to use on any site. The calculator sizes itself to its content, follows the theme you pick and sets no cookies. Paste the code where it should appear.

<iframe src="https://bai8.app/tools/expected-value-calculator/embed/" title="Expected value calculator · BAI8" loading="lazy" style="display:block;width:100%;max-width:760px;height:620px;border:0;border-radius:20px"></iframe>
<p style="margin:6px 0 0;font:13px/1.4 system-ui,sans-serif">Calculator by <a href="https://bai8.app/tools/expected-value-calculator/">BAI8</a></p>
<script>addEventListener("message",function(e){if(e.origin!=="https://bai8.app"||!e.data||e.data.type!=="bai8:height")return;document.querySelectorAll("iframe").forEach(function(f){if(f.contentWindow===e.source)f.style.height=e.data.height+"px"})})</script>