Poker Stack Exchange is a question and answer site for serious players and enthusiasts of poker. It only takes a minute to sign up.
Sign up to join this community
This paper has the correct formula for the Kelly criterion for SNG's where there are multiple outcomes. It stated it is more correct than the one given on sitandgoplanet.
The problem is I do not know how to do the maths. Can someone give a clear step-by-step calculation on how that x value is derived?
If you have a little background in calculus, you'll notice that the dg(x)/dx line is the derivative of g(x) and then is set equal to 0 to find the critical point which in this case will be a maximum point and thus the optimal fraction of the bankroll to bet. Here is a little background/refresher on performing derivatives with log functions.
Whether or not you understand how to arrive at the derivative of log functions yourself, these particular ones boil down to a simple formula: the derivative of a*log(b+cx) = ac/(b+cx), where a, b, and c are constants.
With this example, you have three terms with their respective a, b, and c values being: (0.62, 1, -1); (0.24, 1, 1); (0.14, 1, 3). Plugging these into the above formula gets you to the dg(x)/dx line and from there you'll use some algebra to combine terms and solving for x.
