So, lets say that you have three outcomes: x_1, x_2, and x_3. Each as a probability and an expectation: e_1->p_1...e_3->p_3.
Now, I would like to know how to find the appropriate kelly bet relative to bankroll B. One way that is given is find the mean of the system:
mu = SIGMA e_i*p_1 //from k=1 to i.
This will find out mean, or "expected value"
Next, find variance:
(sigma)^2 = SIGMA (e_i*p_i - mu)^2 * p_i //from k=1 to i.
Once variance has been solved, use the following equation:
K = B*(mu)/((sigma)^2)
Which would be out kelly bet relative to our bankroll.
Is there another way of finding kelly on multiple outcomes, or is this it?
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