How free flowing the gas supply is has as much influence as the geometry. Small tank, pipe, regulator and valve will restrict gas flow and you wont get full pressure. The flipper arm mass has a small effect too, as does where the opponent is on the arm. You could get from 30cm to 3m depending on the system efficiency.
Assuming a very light arm and perfect pnuematics:
H = P*(R^2)*T/10/M
H=flip height
P = pressure in pascals
R = cylinder radius in metres
T= cylinder throw in metres
M = opponent mass in kg.
but that will only tell you the upper limit. The pressure drop will be significant.