Good work re-deriving the general form of the Kelly Criterion. I am glad to see a more accessible example derivation available on the web thanks to you.

I am a fan of the formula you are calling "correct." I too struggled to find this version when I first started looking into the KC and ended up deriving it myself, but I also later found a PDF of Kelly's original derivation, which matches this "correct" version.

I'm here because I am looking at modifying it to maximize expected utility rather than maximizing growth rate (and wondering if it will be any different, since I use ln to model my personal utility function, lol). Anyway, keep up the good work.