Kelly Criterion Calculator: Size Your Bets Optimally

Welcome to this video on sizing your edge scientifically using the Kelly Criterion Optimization. This framework, originating from Bell Labs in 1956, focuses on maximizing long-term geometric growth while effectively managing risk. The universal dilemma of position sizing lies in finding the optimal peak, or the Goldilocks Continuum. Betting too little underutilizes capital, while betting too much risks catastrophic drawdowns and ruin.

The Kelly formula originated in telecommunications to optimize signal-to-noise ratios. It was later applied to capital allocation, where optimizing capital-to-risk ratios uses the same mathematical structure to maximize geometric wealth. The mathematical anatomy of an edge is defined by the Kelly formula. K equals P minus Q over B.

K is the optimal percentage to risk. P is the probability of winning. Q is the probability of losing. And B is the win-slash-loss ratio.

Calculating the win-slash-loss ratio, or quote, varies across domains. In sports betting, B equals the decimal odds minus 1. In financial trading, B is the average winning trade divided by the average losing trade. A mathematical red light occurs when the Kelly value K is negative.

This means your expected value is negative, and you have no mathematical edge. The formula's absolute command is to not bet, as it guarantees a loss of capital over time. The Kelly workflow involves three steps. First, assess the edge with win probability and the win-slash-loss ratio.

Second, calculate K, which gives the full Kelly recommendation. Third, apply a bankroll constraint to determine maximum exposure. Remember, the formula assumes each bet is independent. The fatal flaw of the theoretical maximum, or full Kelly, is that it assumes perfect knowledge of your win probability.

Overestimating the edge can lead to severe drawdowns, demonstrating the risk of theoretical maximum growth in reality. Due to the concave nature of growth, reducing the bet size from the optimal peak creates a massive asymmetric advantage. Betting half the recommendation, or half Kelly, retains approximately 75% of the growth rate, while significantly slashing risk. Half Kelly is the professional standard, because variance scales with the square of your bet size.

Reducing your position size in half reduces your variance by 75%, providing a massive mathematical safety margin against estimation errors. The fractional optimization matrix shows various strategies. Half Kelly is the gold standard, offering a high growth rate with much lower volatility. Lower fractions like third and quarter Kelly offer increased safety for more volatile or conservative applications.

Kelly is deployed differently across market environments. Quarter Kelly is suggested for high volatility markets like cryptocurrency. Half Kelly is typically used for poker, sports betting, and conservative stock and options trading. The system directives are rule 01, be conservative, and always round down your win probability when in doubt.

Rule 02, optimize for survival, using fractional Kelly for resilience against drawdowns. Rule 03, no edge, no exposure, as a negative Kelly output means stay out of the market.