A $100 bet at +120 profits $120 if it hits and loses the full $100 if it doesn’t. If the true chance of winning is 50%, that bet is worth $10 in expected value, a 10% edge over the book’s break-even line of 45.5%. That gap between the true odds and the posted price is what this calculator measures.
Expected value takes the odds offered and a bettor’s own probability estimate and turns them into a dollar figure and a percentage edge. A positive number means the price pays more than the real risk; a negative number means the opposite. Comparing that figure bet to bet is how a bettor tells a good price from a tempting one.
Enter the odds offered on the bet, in American format such as +120 or -150. Enter a win probability next, which is the bettor’s own estimate of how often the bet actually wins, entered as a percentage rather than the odds’ implied number. Enter the stake, the dollar amount being risked on that price.
The result shows expected value per bet in dollars and the edge as a percentage of the stake. It also shows the fair odds that match the entered probability, the book’s implied probability baked into the odds offered, and the break-even win rate needed at that price just to come out even.
Expected value equals win probability times the profit if the bet wins, minus loss probability times the stake. At +120 on a $100 stake, the profit if it wins is $120. With a 50% win probability and a 50% loss probability, EV works out to 0.50 times $120 minus 0.50 times $100, which is $60 minus $50, or $10.
Edge is that dollar figure divided by the stake, so $10 on $100 is a 10% edge. Fair odds at a 50% probability come from 1 divided by 0.50, which converts to +100 in American odds. The book’s implied probability at +120 is 100 divided by 220, or 45.5%, and that same 45.5% is the break-even win rate the bet needs to clear.
This math matters any time a bettor has a probability estimate that differs from what the market is pricing in. If the entered probability just matches the book’s implied number, the edge comes back at zero, and the bet is a coin flip dressed up as an opinion.
A common mistake is entering a win probability high enough to justify a bet that’s already been decided on for other reasons. Another is treating a single loss as proof the number was wrong, when a positive EV bet at 50% is still supposed to lose half the time.
A sharp bettor shops for the best price at the probability they actually trust, then checks whether that price clears the break-even line before the bet goes in. The dollar figure is tracked across many bets, not judged off one outcome, since expected value only shows up as an average over repetition.
What does a negative expected value mean? It means that, at the probability entered, the price pays less than the real risk, so making that bet repeatedly would lose money on average even though any single try could still win.
Why does a positive EV bet still lose sometimes? Because expected value is an average across many repeated tries at the same price and probability. A bet with a 10% edge at 50% true probability still loses half the time; the edge shows up over a long run of bets, not inside one ticket.
What’s the difference between edge and expected value? Expected value is a dollar amount tied to the size of the stake, while edge is that same result expressed as a percentage of stake. Edge is what makes bets of different sizes or different odds comparable side by side.
How does the break-even win rate help? It’s the minimum true win probability a bet needs at the given odds just to avoid a loss over time. If the bettor’s own probability estimate sits above that number, the bet carries positive expected value; if it sits below, the price isn’t worth taking.