A Simple Kelly Problem I Can't Solve

[Stephen H]

Yea, it seems I didn't explicitly give the relation of r1 and r2 to f1 and f2 and the whole function declaration looks dumb.

I think I really meant something like:

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

As you actually have to account for the fact that you lose the f2 bet when you win the f1 bet, and you lose the f1 bet when you win the f2 bet. That way, if you bet 0 on the arb, it simplifies back to:

G(f1,0)=p*log(1+f1*b1)+q*log(1-f1)

which is the initial formula. (b1 & b2 = dec odds -1 for respective bets, just easier to write in the formula)