Probability Calculator & Odds Converter
Convert between probability formats, calculate expected value, and find optimal bet sizes with the Kelly Criterion. Built for prediction market traders.
Odds Converter
Enter a value in any format and convert it to all other probability formats instantly.
Expected Value Calculator
Calculate whether a bet has positive expected value based on your estimated probability, bet size, and potential payout.
Kelly Criterion Calculator
Find the mathematically optimal bet size to maximize long-term bankroll growth. Enter your estimated win probability and the decimal odds offered.
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Use these calculations to find positive EV trades on Polymarket.
Trade on PolymarketUnderstanding Probability, Odds, and Expected Value in Prediction Markets
What Is Implied Probability?
Implied probability is the market's consensus estimate of how likely an event is to occur, derived directly from the current trading price. On Polymarket, if a Yes share is trading at $0.65, the implied probability is 65%. This is a critical concept because it transforms market prices into actionable information. Rather than simply looking at a dollar amount, you can compare the market's implied probability with your own estimate to identify potential trading opportunities. When your estimated probability significantly differs from the market's implied probability, you may have found an edge. The key word is "significantly" because small differences can be explained by trading fees, spread, and the inherent uncertainty in any estimate.
Understanding Odds Formats
Different regions and platforms use different odds formats, which can be confusing for new traders. Decimal odds (common in Europe and on most prediction markets) represent the total payout per dollar wagered. Decimal odds of 2.00 mean you double your money. Fractional odds (common in the UK) show the net profit relative to the stake. Odds of 3/1 mean you win $3 for every $1 bet, plus your stake back. American odds (common in US sports betting) use positive and negative numbers. Negative odds like -200 mean you must bet $200 to win $100. Positive odds like +150 mean a $100 bet wins you $150. All three formats convey the same information, just expressed differently. Our converter above lets you move seamlessly between these formats so you can always work in your preferred system.
Expected Value Explained
Expected value (EV) is the single most important concept for any serious prediction market trader. It represents the average amount you can expect to win or lose per bet if you made the same bet many times over. The formula is straightforward: EV = (probability of winning x payout) - (probability of losing x amount bet). A positive expected value means the bet is profitable in the long run. For example, if you believe an event has a 60% chance of occurring and you can buy Yes shares at $0.50 on Polymarket, the EV per share is (0.60 x $1.00) - (0.40 x $0.50) = $0.40, a strong positive EV. The challenge, of course, is accurately estimating probabilities, which is where research, calibration, and experience become invaluable. Professional traders focus almost exclusively on finding and exploiting positive EV opportunities.
The Kelly Criterion: Optimal Bet Sizing
Even with a positive expected value trade, betting too much can lead to ruin. The Kelly Criterion solves this problem by providing a mathematically optimal bet size that maximizes the long-term growth rate of your bankroll. The formula is: f = (bp - q) / b, where f is the fraction of your bankroll to bet, b is the net odds (decimal odds minus 1), p is your estimated win probability, and q is the loss probability (1 - p). In practice, most experienced traders use half-Kelly or quarter-Kelly, meaning they bet only 50% or 25% of the Kelly recommended amount. This reduces variance significantly while still capturing most of the long-term growth. For prediction market traders, the Kelly Criterion is especially useful because it naturally adjusts for the size of your edge. A small edge on a likely event produces a smaller recommended bet than a large edge on the same event. Many top Polymarket traders credit disciplined Kelly-based bankroll management as a key factor in their long-term success.
Applying These Concepts on Polymarket
Polymarket simplifies many of these calculations because shares are always priced between $0 and $1, making the implied probability immediately obvious. If you see a market where Yes is trading at $0.40 but your research suggests the true probability is 55%, you have a substantial edge. The expected value per share would be $0.55 - $0.40 = $0.15, or a 37.5% ROI if the event resolves Yes. You can then use the Kelly Criterion to determine exactly how much of your portfolio to allocate. Remember that prediction markets are efficient but not perfect. Edges exist, especially in newer markets, niche topics where you have domain expertise, or events where new information has not yet been fully priced in. The tools on this page help you quantify those edges and make informed decisions rather than guessing.
Common Mistakes to Avoid
The most common mistake new prediction market traders make is confusing a strong opinion with a quantified edge. Saying "I think this will happen" is not the same as saying "I estimate a 75% probability versus the market's 60%." Always think in terms of specific probabilities and expected values. Another frequent error is overbetting, putting too large a portion of your bankroll on a single position regardless of edge. Even with a genuine 10% edge, variance can wipe you out if you are overexposed. Use the Kelly Criterion as your guide. Finally, be honest about your calibration. Track your predictions over time using tools like Outcalled's Daily Game to build an accurate picture of your prediction accuracy before risking real money. Practice, track, improve, and only then trade with confidence.