Kelly Betting: Spread vs. Moneyline

[hedgie43]

Let's say I have 2 bets that are on the same game and are correlated. One is ATS and one is SU. The ATS is -110 and has an edge of 2% and the other is +450 and has an edge of 8%. Betting full kelly on both does not seem optimal as the bets are correlated. My gut instinct is that you should bet both, at somewhere near between 1/2 and 3/4 kelly but I would prefer a more exact answer here. Is there some type of way to calculate this based on the degree of correlation?

[crockpot]

if you're willing to go to the trouble, you could make a spreadsheet outlining the three possibilities (win outright, cover but lose, fail to cover), with the respective probabilities and odds for each, then test some bet amounts to maximize the geometric mean of your expected bankroll.

[rjp]

Excel is supposed to have a solver to figure this out for you (I have no idea how to use it, however), as long as you construct the growth function properly.

[rush66]

I know how to use solver in excel. If you need help with how to use solver let me know, besides that I can't help.

[Thremp]

Despite taking optimal college class scheduling (easiest classes as possible) sadly it does me no good now since I can't do any of this stuff :/


Somewhere on my reading list I need to include a stats/prob text. Suggestions?

[Austiger]

[ QUOTE ]
I can't do any of this stuff :/


Somewhere on my reading list I need to include a stats/prob text. Suggestions?

[/ QUOTE ]

[mogwai316]

http://www.amazon.com/Probability-St.../dp/0131464132

Used an older version of this book when I was in school. It's good if you're interested in really learning the material and not just being spoon-fed. People that are bad at math and/or lazy tended to dislike it, as with most good textbooks; take the negative reviews with a grain of salt.

[rjp]

The DeGroot book is very good. I've seen it suggested in the Probability forum, yet it took me forever to drink the kool-aid and finally buy it.

http://www.amazon.com/dp/0201524880/

[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.

[rjp]

[ QUOTE ]
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).

[/ QUOTE ]

The Kelly criterion maximizes the geometric mean of your bankroll, which can be calculated using the natural log, so that is why. [img]/images/graemlins/smile.gif[/img]

As for simultaneous bets, checkout Ganchrow's stuff at SBRForum:

http://www.sbrforum.com/Betting+Tool...alculator.aspx