Probability to clear the board or win
Pyth, (67 bytes) / 2 = 33.5

L_,*lbJ*FeCbsm*hd/JedbM?&amp;hHstH?GymgtG-XdKH_1_!dlH,01,TT*100cFghQstQ


This qualifies for the bonus even though I had to manually implement arbitrary precision rationals.

(I wish Pyth5 was already a thing).

Input from STDIN in the format A, H, L

Demonstration.

Corrected to output percentage. Percentage is as acurate as possible, due to use of integer math until the last step.

At the high level, the first segment, L_,*lbJ*FeCbsm*hd/Jedb, is a helper function which takes a list of rationals in the form of 2 element lists, and outputs their average as an (unreduced) rational.

The second segment, M?&amp;hHstH?GymgtG-XdKH_1_!dlH,01,TT, recusively calculates the probability of victory.

The third segment, cFghQstQ formats the input to fit the function and performs the final division.

On the second example case, the final unreduced 2-tuple is too long to fit on the screen:

[83158592487544376524800000000000000000000, 1079462498636393349120000000000000000000000]


Fortunately, Pyth does have arbitrary precision integers.