Question for Don: Adjusting kelly for expenses

[MJ1]

MathProf once said that if your hourly expenses are half of your hourly earnings, a counter playing at 0.5 kelly is effectively playing to 1.0 kelly.

I am wondering what is the formula or method to determine "adjusted kelly" which is the kelly factor after taking expenses into account.

Suppose a counter plays at 1/3 kelly and the ratio of his hourly expenses to his hourly EV is 1/4. What is his adjusted kelly factor? I was playing around with this and guessed it is (1/3)/(1-1/4) = 4/9. Is that correct?

What about a counter who plays with 2/3 kelly and his expenses for each trip are roughly 2/5 of his EV per trip. Does his adjusted kelly factor become 10/9 (2/3 * 5/3)?

MJ

[DSchles]

Have seen your question but am going to be very busy for the next couple of days and will do my best to get to it as soon as I can. In the meantime, if anyone wants to take a shot, be my guest.

The problem with the calculation is that while the e.v. has a variance associated with it, the expenses do not; they are fixed. So, they are a certain "loss" with no variance attached to them, and that changes the calculation. As Kelly is a function of e.v. divided by variance, you have to take that fact into account.

Don

[Unknown]

Is this two people roleplaying a 15 year old post from another forum? That would be most excellent.

https://bj21.com/boards/free/sub_boa...cis-salmon-etf

[MJ1]

Unknown, I thought I posed a similar question a long time ago on some forum but wasn't sure where or when. Thanks for digging it up.

Nevermind Don, you already answered my question. :-) Based on your answer from 15 years ago, I seem to have arrived at the correct answers.

MJ

[21forme]

Don't you hate when that happens?