A New Interpretation of Information Rate
John L. Kelly Jr. · Bell System Technical Journal
Main finding
Maximising the expected logarithm of wealth gives the fastest long-run exponential growth; with fair odds that maximum growth rate equals the channel's information rate. The staking rule derived here became known as the Kelly criterion.
Limitations
Assumes the probabilities are known exactly and the horizon is long. It says nothing about estimation error, short-run drawdowns or execution limits.
Study details
- Authors
- John L. Kelly Jr.
- Published
- 1956
- Venue
- Bell System Technical Journal 35(4), 917–926
- Status
- Published
- Evidence type
- Peer-reviewed theory
- Evidence strength
- Strong (our assessment of how much weight the finding can bear)
- Sport
- None (general gambling and communication theory)
- Markets
- Theoretical bets at fair and unfair odds
- Method
- Information-theoretic derivation of how fast a gambler's capital can grow when bets are placed on information received over a noisy channel.
- Sample
- Not applicable (mathematical result).
- Replication
- A mathematical result rather than an empirical claim; it has been extended and reinterpreted extensively.
Read the original
doi:10.1002/j.1538-7305.1956.tb03809.x (opens in a new tab) · Free version (opens in a new tab)
Our summary is an original paraphrase for education. Verification: Bibliographic record checked against publisher, index or author listings. Checked 2026-10-25.