If E(W,B) is the expected number of correct guesses when starting from a state of W white marbles and B black marbles:

If either B or W is zero, E(B,W) = the non-zero argument.

Otherwise:

If B>W then E(W,B) = (W/(W+B)) * E(W-1,B) + (B/W+B) * (E(W,B-1) + 1)

Otherwise:

      E(W,B) = (W/(W+B)) * (E(W-1,B) + 1) + (B/W+B) * E(W,B-1)

      

It looks like I could have avoided the more complex logic of checking for zeros each time by simply, in line 70, had Black > 0 rather than Black >= 0 in that IF statement, to avoid the bad subscript error, as I had already populated the (w,0) and (0,b) entries in lines 20 and 30, as represented in line 1 of the formula above.

BTW, in my recent foray into Project Euler (thanks to the mention on this site), one thing I picked up was the concept of "dynamic programming". Note that while the function is defined recursively, it was calculated from the small numbers first, and then the larger numbers, with the smaller results stored for future use. If starting with, say E(10,10), we'd need to calculate E(9,10) and E(10,9), but both of those use E(9,9), so those would be calculated twice when programmed strictly recursively from large to small values, rather than iteratively from small to large. (I hesitate to say top-down vs bottom-up, as the concepts are the reverse of how they are displayed on a table.)  Then as you get to smaller and smaller values, the number of times each would calculated would expand exponentially (powers of 2 in this case), though at some point the number of points needed would go down.