Polymarket Kelly Criterion Calculator

What Is the Kelly Criterion and Why It Matters for Polymarket

The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. at Bell Labs in 1956. It was originally designed for optimizing bets in information theory, but traders and gamblers quickly realized its power: it tells you exactly what fraction of your bankroll to wager on any bet where you believe you have an edge, in order to maximize the long-term growth rate of your capital.

On Polymarket, you are buying and selling shares in binary outcome markets. A YES share priced at $0.60 implies a 60% market probability that the event occurs. If you believe the true probability is actually 70%, you have a 10 percentage point edge. But knowing you have an edge is only half the battle. The critical question is how much to bet. Bet too little and you leave money on the table. Bet too much and a string of losses can devastate your bankroll, even when you have a genuine edge.

The Kelly formula answers this question precisely. For a binary bet where you pay the market price and receive $1 if your side wins, the formula is: f* = (b * p - q) / b, where b is the net odds you receive (calculated as (1 - marketPrice) / marketPrice), p is your estimated true probability of winning, and q is 1 - p. The result f* is the fraction of your bankroll you should bet. If f* is zero or negative, you have no edge and should not bet at all.

Why Half Kelly Is Usually the Better Choice

Full Kelly sizing is mathematically optimal for maximizing long-term growth, but it comes with a brutal trade-off: extreme volatility. Under full Kelly, it is perfectly normal to experience drawdowns of 50% or more of your bankroll before recovering. Most people, even experienced traders, find this psychologically unbearable and end up abandoning their strategy at exactly the wrong time.

Half Kelly, which simply means betting half of what the full Kelly formula suggests, offers a compelling alternative. You sacrifice only about 25% of the theoretical maximum growth rate, but you cut the variance roughly in half. Your drawdowns become far more manageable, your equity curve is smoother, and you are much less likely to blow up from estimation errors. In practice, many professional bettors and traders consider half Kelly to be the true sweet spot between growth and survival.

There is another critical reason to use fractional Kelly on Polymarket specifically. The Kelly formula assumes you know the true probability exactly. In reality, your probability estimate is just that, an estimate. If you think an event has a 70% chance of occurring, the real probability might be 65% or 75%. Full Kelly is extremely sensitive to these estimation errors. Overestimating your edge by even a small amount can turn what should be a profitable strategy into a losing one. Fractional Kelly provides a natural buffer against this uncertainty.

How to Estimate Your Edge Accurately

The entire Kelly system depends on having a genuine edge, which means your probability estimate needs to be better than the market consensus. This is harder than most people think. Polymarket prices aggregate the views of thousands of participants, many of whom are sophisticated. Consistently beating this collective wisdom requires either superior information, superior analysis, or faster reaction to new information.

One practical approach is to build a base rate from historical data. If you are betting on whether a political candidate will win, look at polling averages, prediction model outputs, and historical accuracy of similar polls. If you are betting on a corporate event, examine precedent from similar situations. The key is to ground your estimate in data rather than gut feeling. Gut feelings are systematically overconfident, which leads to overestimating your edge, which leads to overbetting.

A useful discipline is to ask yourself: if the market price is 60% and I think it should be 70%, what do I know that the market does not? If you cannot articulate a specific, concrete reason for your disagreement with the market, you probably do not have a real edge. Markets are not always right, but they are right often enough that the burden of proof should be on you to justify why you are smarter than the consensus in this particular case.

Common Mistakes with Kelly Sizing

The most dangerous mistake is overestimating your edge. If you think you have a 15% edge but your real edge is only 5%, full Kelly will have you betting three times too much. Over many bets, this does not just reduce your returns. It can actually cause your bankroll to shrink. The math is unforgiving: overbetting by a factor of two relative to the true Kelly fraction produces zero expected growth, and overbetting by more than that produces negative expected growth. This is why fractional Kelly is so important as insurance against estimation error.

Another common mistake is ignoring correlated bets. If you have positions in five different markets that all depend on the same underlying event, such as several markets related to the outcome of a single election, you are effectively making one large bet, not five independent ones. Kelly sizing should be applied to your total exposure to correlated outcomes, not to each market individually. Failing to account for correlation leads to dramatically oversized positions.

A third mistake is applying Kelly to markets where you have no genuine informational edge. If you are simply looking at a market priced at 50% and guessing it should be 60% based on a hunch, the Kelly formula will happily tell you to bet 20% of your bankroll. But the formula is only as good as its inputs. Garbage probability estimates produce garbage bet sizes. Kelly does not create edge; it only helps you size bets optimally when you already have one.

Finally, many people forget that Kelly assumes you can make the same bet repeatedly. A single Polymarket position resolving once is not quite the same as the repeated-bet scenario Kelly was designed for. For one-off bets with no opportunity to learn and adjust, even more conservative sizing (quarter Kelly or less) makes sense, because you have no chance to recover from the variance of a single outcome.