Tools / Markets
Odds calculator: implied probability and expected value
Enter a price in any format and your own probability. The conversions, the edge, and the expected value update as you type.
Your estimate 50.0% vs the 40.0% the price implies: +10.0 pts of edge
Assumes a binary contract settling at $1 or $0, no fees or spread. Expected value uses your probability estimate, which can be wrong; the market's is the break-even line.
| Line | Decimal odds | Probability | Payout on $100 |
|---|---|---|---|
| Offered | 2.50 | 40.0% | $250.00 |
| Fair at your estimate | 2.00 | 50.0% | $200.00 |
$41.67 = 4.2% of bankroll (quarter Kelly; full Kelly is 16.7%)
Caution: Kelly assumes your probability is exactly right and that you can repeat the bet many times. Estimates are noisy, and full Kelly overbets badly on noise, which is why the default here is quarter Kelly.
What implied probability is
Every price is a probability wearing a costume. A prediction-market contract that costs 40¢ and settles at $1 implies a 40% chance, because 40¢ is what a 40% chance of $1 is worth. American, decimal, and fractional odds encode the same thing differently: decimal odds are the total payout per $1 staked, so implied probability is 1 divided by the decimal odds. A 40¢ contract is decimal 2.50, American +150, and roughly 3/2 in fractional form. All four describe one number, and this calculator translates between them so you can compare a sportsbook line to a Kalshi price directly.
Expected value, worked through
The price only becomes a bet when you disagree with it. Say the contract costs 40¢ and you believe the true chance is 50%. Staking $100 buys 250 contracts, which pay $250 if the event happens. Half the time you collect $250, half the time you collect nothing, so the average outcome is $125 against $100 staked: an expected profit of +$25 per $100. The general formula is stake times (your probability times decimal odds, minus one). If your estimate matches the market's 40%, the same arithmetic returns exactly zero.
Break-even probability is the market's opinion
The break-even probability equals the implied probability: the event frequency at which the bet returns exactly your stake over many repeats. That makes the comparison honest in both directions. You are not asking whether the bet can win; you are asking whether the event happens more often than the price says. Betting a 40¢ contract is a claim that the true chance exceeds 40%, and if you cannot say why the market is wrong, the safest assumption is that it is not.
Kelly sizing, and why the default is a quarter
The Kelly criterion sizes a bet to maximize long-run bankroll growth: the fraction is (p times b minus q) over b, where b is the net decimal odds, p your probability, and q the complement. In the example above that is 16.7% of the bankroll, which is a lot. Full Kelly assumes your probability is exactly right; real estimates are noisy, and Kelly overbets badly on noise, with drawdowns most people abandon. The selector defaults to quarter Kelly, about 4.2% here, which keeps most of the growth with a fraction of the swings. Treat any Kelly output as a ceiling, not a target.
Combining bets multiplies the vig Parlay calculator: payout vs true probability 
Why a 62¢ contract is not a 62% chance What actually moves a prediction market price