Does it just happen?

From Stanford Wong's BJ21

Posted by ML on 15 Dec 1997, at 7:20 p.m., in response to Why Your f is optimal, posted by MathProf on 15 Dec 1997, at 4:47 a.m.

Mathprof said, "It happens that, in this case, the quantity that you want to amxiimize is essentially
your Expected Logarithm)."

What I do not understand is the fraction which maximizes the *expected* outcome is *always* the fraction which maximizes the logarithmic utility function. Is this a chicken and egg thing? To this layman's mind, saying one or the other is of equal significance. The calculation, however it is made or defined, ends up at the same place. And if each ends up at the same place, the same overall results accrue.

I understand the "optimal" bet leads to a nice compromise in win rate and certainty of win. Bet higher and the chances of getting to a goal is reduced while the goal is reached quicker when reached or bet lower and the chances of getting to a goal increases but the time to get there is slower.

But, and I feel sure the 35 year old, unused, undergraduate math degree is speaking here, I do not see what a logarithmic utility function has to do with the matter. There is a function and one takes a derivative and finds a maximum. There is the same function and one takes the log of the function and then takes the derivative of the log formulation of the original function and finds a maximum.

It seems to me the same thing happens either way.

I hope you understand this is not meant to be contentious in any way.

By the way, did you get the paper I sent you?

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