[Stephen H]

Mostly I've just read this forum, the Kelly Criterion page on wikipedia, and played in excel, and that seems to be enough to dig into these questions.

First, the Kelly formula is a maximum of a growth function for your bankroll. The main thing to remember is to use log() of your growth (no I can't explain why, but that's the function to maximize).

So for a single bet, the function is:

G(f) = p*log(1+bf) + q*log(1-f)

Where:
f=% of your bankroll bet
p=% of time wager wins
q=% of time wager loses, or 1-p
b=Odds you're getting on the bet; for 2-1 odds b=2, for an even money wager b=1.
Basically the stuff inside the log() will be what your bankroll looks like after the bet - either up bf or down f.

For a more complex scenario, you can expand out the growth formula. In this case, you have 2 wagers, and 3 outcomes. Since they're correlated, you'd need some info on how the correlation works (What % of the time do you win both, lose both, and win only 1). I'm the first to admit I have no idea how those might be correlated, but someone else may have done the work for you in other books.

Say you win both p %, win just one bet p1 %, and lose both q %:

G(f1,f2) = p*log(1 + b1*f1 + b2*f2) + p1*log(1 + b1*f1 - f2) + q*log(1 - f1 - f2)

So you could make a spreadsheet with cells for f1 and f2, and a cell with this formula in it (I'd make a bunch of intermediate cells, with the bet odds for each bet, win % of each bet, and so forth in seperate cells so you can change them for different scenarios), and then use solver to maximize the growth formula cell by changing f1 and f2. Put boundaries on f1 and f2 of 0-1 (it's a % of bankroll bet) and let 'er rip.
Solver in excel is a plug-in, so it requires having it installed. Once installed, it's tools->solver and there may even be some help in there, it's been a while since I looked.

If you want to actually get into how to figure out the correlation of the two bets, then you're going to want a lot of data and a stats book, and that gets beyond me. But Kelly questions should be able to be solved with formulas like that and excel solver (or Mathematica if you're feeling saucy).

One of these days I want to try out something like 8 uncorrelated bets or so to see what it says. I suspect that betting a full Kelly on each bet isn't optimal; it's probably a bit too high. I'm not sure if the difference is significant, though - a test with two uncorrelated bets seems to show that while you should be just under a full kelly bet, the difference is like 10% of bankroll vs 9.9998% of bankroll. 8+ bets might be a different story.