I don’t quite understand. Going with the worked out example in the post you link to:
To account for the compounding nature of losses, we can use the geometric expectation of total wealth instead of the arithmetic expectation of gains/losses when evaluating the alternatives. This is the mathematically correct thing to do, although I leave out the proof. If you want to dig into the gory details, see The Kelly Capital Growth Investment Criterion; MacLean, Thorp, & Ziemba; World Scientific Publishing; 2011. Yes, it’s that Thorp.
If we replace the worn out part for $5,000, we are guaranteed to end up with a reduced wealth of $45,000.
If we wait and see, there are two things that could happen:
With 90 % probability, our wealth will be unchanged at $50,000.
With 10 % probability, our wealth will be reduced to $10,000.
The geometric expectation of these two outcomes is
50,0000.9×10,0000.1≈43,000.50,0000.9×10,0000.1≈43,000.
Okay, so we’re optimizing for geometric expectation now.
Meanwhile, the same post:
[...] misconception 3: the Kelly criterion does not require logarithmic utility, it only requires trying to long-term maximise something that grows geometrically.
So we’re … not optimising for logarithmic utility. But isn’t optimizing the geometric expectation equivalent to optimizing the log of utility? Last time I checked, E[ln(X)] = ln(G(X)) where G(X) is the geometric expectation of X (mind you I only used chatgpt to confirm my intuition but it could be wrong)
Which is fine actually. I do care more about my geometric expected wealth than I do about my expected wealth, but that would have been a much shorter post
Just a side note: the “correct” way to deal with irrational thoughts is to find the feeling in your body that is creating that thought, and then sitting with that feeling nonreactively until it dissolves into insight.
I don’t necessarily have an argument, just years of practice and plenty of practitioners around me that would attest for this method. Go try it!