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.

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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?

  • I do not know the answer. I suggest that you ask this on the math section of this site. I am sure they can help. – Raymond Timmermans Aug 11 '17 at 7:58
  • I am not saying this section is wrong, since it is about poker, but on the math section you will likely get a better answer – Raymond Timmermans Aug 11 '17 at 7:58

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.

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