Why is the 2/3-1/3 ratio optimal? HoPs also make it more complicated.

I tried to do out the math on it, you can say something like:

Start with M cards, M constant, let X be the number of Silver and M-X the number of Banks.

Then you have 2X+(M(M+1)-X(X+1))/2 money, 2X^2+X*((M(M+1)-X(X+1))/2) gains (or -(X^3)/2+(3/2)X^2+(M^2*X)/2 when you eliminate the 1 for being too small)

Derivative of that is -3/2*X^2+3X+M^2/2, set it equal to 0, and you get X~=M/sqrt(3), or .58 M

Hmmm, when I did that before, it came out to 2/3. Looks like I flipped a sign before

Anyway, you can do the same math with HoP Rocks, just have M-(X/2) be the number of Banks and account for an extra X HoP treasures when figuring the Bank value. Did it out and got something like X=(8+2sqrt(31))/15 M (where the number of HoPs is X/2), or 63% HoP, 37% Banks