Kelly criterion

Also called Kelly · full Kelly

The stake fraction that maximises long-run bankroll growth, computed from your edge and the net payout multiple.

With a one-dollar contract at an all-in cost c, the net payout multiple b is (1 − c) / c: the profit each staked dollar returns if the contract pays. Full Kelly is then the larger of zero and (b·p − (1 − p)) / b, where p is your probability. Below zero the answer is not a small position, it is no position.

What Kelly maximises is the expected logarithm of bankroll, which is the right objective when you intend to keep trading with the same money. Maximising expected dollars instead would tell you to stake everything on any positive edge, which goes bankrupt with probability approaching one. Kelly is the sizing that survives, and that is the whole claim — it is not a profit guarantee and nothing about it makes a negative-edge trade positive.

It is also aggressive, because it assumes your probability is exactly right and yours is an estimate. The calculator here therefore applies a fraction of the full number and then a hard per-market exposure cap, and flags when the cap bound before the Kelly math did. Note also that the fee enters through c before any of this runs; sizing off a fee-free price systematically oversizes every position you take.

Where this shows up

Related terms

Definitions describe how Polymarket and Kalshi behave and how WhaleTracks models them; venue rules and fee schedules can change, so confirm anything you size a position on with the venue itself. WhaleTracks is informational analytics, not financial advice. Past performance does not guarantee future results.