[HDB 2008-06-04] This text is lifted from some website and I can't remember where.
For those who are interested in the theory, here are the mathematical steps I used to generalize the above problem.
Let's define some variables:
F = % of your bankroll that you invest in A W1 = ROI of Product 1 = 30% W2 = ROI of Product 2 = 10% W3 = ROI of Product 3 = 12% W4 = ROI of No Products Launching = -15% P1 = Probability of Product 1 Launching P2 = Probability of Product 2 Launching P3 = Probability of Product 3 Launching P4 = Probability of No Product Launching B = Initial Bankroll B' = Future Bankroll after N such investments M = The Geometric Mean of N such investments
Using the above infomation, we can formulate:
B' = B * (1 + W1*F)^(P1*N) *
(1 + W2*F)^(P2*N) *
(1 + W3*F)^(P3*N) *
(1 + W4*F)^(P4*N)
M^N = B'/B = (1 + W1*F)^(P1*N) *
(1 + W2*F)^(P2*N) *
(1 + W3*F)^(P3*N) *
(1 + W4*F)^(P4*N)
M = [(1 + W1*F)^(P1*N) *
(1 + W2 * F)^(P2*N) *
(1 + W3*F)^(P3*N) *
(1 + W4*F)^(P4*N)]^(1/N)
M = (1 + W1*F)^(P1) *
(1 + W2*F)^(P2) *
(1 + W3*F)^(P3) *
(1 + W4*F)^(P4)
Therefore, to maximize the geometric return M, we need to find F such that the Product Sum of (1+Wi*F)^Pi for all i is maximized. Unfortunately, there is no simple formula that can compute the Kelly Criterion for multiple possible outcomes. Fortunately, with the aid of computer, I constructed an optimization model that will find the Kelly Criterion for you.
The 
