The Kelly Criterion Explains Exactly How Much to Bet. Are You Listening?
Most people who bet on prediction markets or sports have a process for picking their positions. Very few have a process for sizing them. They find an edge, they think it is good, and they put in some amount of money that feels right. That feeling is costing them money.
The Kelly Criterion is a formula developed in 1956 by Bell Labs scientist John Kelly to solve this exact problem; given a known edge and known odds, what fraction of your bankroll should you bet to maximize long-run growth. The answer is not "whatever feels right." It is a specific number, and if you bet more than that number you are actually destroying expected long-run value even when you keep winning in the short term.
The FatNarwhal Kelly tool takes your edge, the odds on offer, and your bankroll, and tells you exactly what Kelly recommends. It also shows you half-Kelly and quarter-Kelly, because full Kelly is mathematically optimal but psychologically brutal and most real-world bettors run a fraction of it.
How to Use It
Go to fatnarwhal.com/kelly and put in three things; your estimated probability that the event happens, the market odds (in decimal or implied probability form), and your bankroll size.
Let's say you think a candidate wins an election with 60% probability, but the market on Polymarket has them at 52%. You have an edge. The question is how much to put in.
Enter your probability (0.60), the market implied probability (0.52), and your bankroll (say $1,000). The tool calculates your edge, runs the Kelly formula, and tells you the recommended bet size. It also shows you what happens at half-Kelly and quarter-Kelly, which most serious bettors prefer because full Kelly drawdowns are stomach-turning even when your edge is real.
Play with the numbers. Shrink your estimated edge down toward the market price and watch the recommended bet size collapse toward zero. That is the model telling you the less certain you are of your edge, the smaller you should go.
The Math Behind It
Kelly's formula is surprisingly clean:
Where f* is the fraction of bankroll to bet, b is the net odds (what you win per dollar risked; decimal odds minus 1), p is your probability the bet wins, and q is your probability it loses (just 1 − p).
If the numbers do not give you a positive f*, Kelly is telling you not to bet at all. The edge is not there, or the payout is not good enough for the risk.
The deeper insight is what Kelly is actually maximizing; not expected value per bet, but the expected value of the logarithm of your bankroll over time. That distinction matters enormously. Two bettors can face the same bet with positive expected value, and if one of them bets too large they will systematically underperform the one who sized correctly, because variance compounds against you when you overbet. Kelly found the exact threshold where growth is maximized.
When to Use It and When Not To
Use it any time you have a quantified edge in a prediction market, sports bet, or financial position and you want a principled answer on size rather than a gut call. It is particularly useful for prediction markets where you can directly observe the implied probability and compare it against your own estimate.
Do not treat the output as gospel in a few specific situations. Kelly assumes you know your true edge with confidence; if your probability estimate is soft, the recommended bet will be too aggressive. It also assumes you are going to make many bets over time and can withstand drawdowns along the way. If this is a one-off bet or you cannot stomach variance, run quarter-Kelly or less.
One genuine limitation is that Kelly optimizes for a single bet at a time and gets complicated fast when you are sizing a portfolio of correlated positions simultaneously. For that you want the multi-asset Kelly extension, which is a whole other level of math. For single bets it is the right tool.
Try It
Go to fatnarwhal.com/kelly, find a market where you think you have an edge on the consensus, plug in your numbers, and see what Kelly says. The result might surprise you; either your edge is smaller than you thought, or you have been dramatically undersizing.
Gut feel is a fine starting point. Kelly is the finishing point.