Kelly Criterion Implementation - AI

 Certainly! The Kelly Criterion is a mathematical formula that helps you determine the optimal bet size in situations where you have an edge and need to manage risk. To apply it to an either-or situation, like a binary choice, follow these steps:

1. Assign Probabilities: Estimate the probability of success for each option. Let's say you have two options, Option A and Option B, with estimated probabilities of winning of "pA" and "pB" respectively. Make sure that pA + pB = 1, as these are complementary probabilities.

2. Determine Payoffs: Define the potential payoffs for each option. Let "bA" and "bB" be the net odds received on the bets for Option A and Option B respectively. For instance, if you win, you receive bA times your wager for Option A, and similarly for Option B.

3. Calculate Optimal Wager Fraction: Use the formula f* = (bp - q) / b, where:

   - "b" is the net odds received on the bet (bA for Option A or bB for Option B).

   - "p" is the probability of winning (pA for Option A or pB for Option B).

   - "q" is the probability of losing (1 - p, so qA = 1 - pA for Option A or qB = 1 - pB for Option B).

   - "f*" is the optimal fraction of your bankroll to wager.

4. Implement the Fraction: Once you calculate f*, you can decide how much of your bankroll to wager on each option. It's important to note that the calculated fraction might sometimes exceed what you're comfortable with, so you can adjust it to a more conservative level if needed.

5. Monitor and Adjust: Continuously update your estimates of probabilities and payoffs, and recalculate the optimal wager fraction as the situation evolves.

Remember that while the Kelly Criterion can be powerful, it assumes you have accurate probability estimates and doesn't consider the possibility of losing your entire bankroll. To mitigate this risk, some investors and gamblers use a fraction of the calculated f*, known as "fractional Kelly," to balance potential gains and losses more conservatively.