Kelly Criterion Modification

Hi,

I have been very interested in the Kelly Criterion lately, but I'm no able to do math at the level of some of you. I would like to modify the Kelly criterion to include another factor, but I am not sure how.

For those who don't know what the Kelly criterion is here a link:

Kelly criterion - Wikipedia, the free encyclopedia

Basically if you have a set amount of money it will tell you how much to bet on a given bet to maximize your earnings while minimizing the chances of going broke.

Now I've been thinking about this for some time and I believe this changes when a "fee" is added.

Basic Kelly Criterion example:

Say for example we have 1000 dollars and we can place a bet once a month. Our bet has a 60% chance of being successful and is even money. According to Kelly Criterion we would want to bet 20% of our money or 200 dollars.

Now the problem I am having is that naturally it seems if we have some thing that is decreasing out total amount of money every month ( say bills or investment fees ), then we would want to bet less of our money. But this doesnt seem to be true. See the next example:

Say we again have 1000 dollars, but now we have a fee that we pay on that money of 500 per month. Let's say now that instead of 60% chance of winning we have a 30% chance of winning. According to Kelly Criterion we shouldn't even take a 30% bet, but once a fee is add it may be better to take a "bad" bet. If we don't take the bet our money is gauranteed to be gone in 2 months. 1000-500-500 = 0. If we don't bet the first month and bet the second month we will have an expected value of (500 x .3) - (0 x .7) = 150 as opposed to 0.

(now I haven' done a whole lot of math for years, so correct me if my math or logic is wrong)

It seems that if there is a fee per bet that we would need to adjust our bet amount. Does anyone smarter than me know how we can modify the Kelly Criterion formula to account for this?

Re: Kelly Criterion Modification