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?