m=1: closed form matches truth table: True
     q=9/20: P_g = 0.719019, 2p^2 = 0.605000, P_g < 2p^2: False
     q=2/5: P_g = 0.764800, 2p^2 = 0.720000, P_g < 2p^2: False
     q=3/8: P_g = 0.793701, 2p^2 = 0.781250, P_g < 2p^2: False
m=2: closed form matches truth table: True
     q=9/20: P_g = 0.628242, 2p^2 = 0.605000, P_g < 2p^2: False
     q=2/5: P_g = 0.713344, 2p^2 = 0.720000, P_g < 2p^2: True
     q=3/8: P_g = 0.763260, 2p^2 = 0.781250, P_g < 2p^2: True
m=3: closed form matches truth table: True
     q=9/20: P_g = 0.606705, 2p^2 = 0.605000, P_g < 2p^2: False
     q=2/5: P_g = 0.711194, 2p^2 = 0.720000, P_g < 2p^2: True
     q=3/8: P_g = 0.769507, 2p^2 = 0.781250, P_g < 2p^2: True
m=4: closed form matches truth table: True
     q=9/20: P_g = 0.603373, 2p^2 = 0.605000, P_g < 2p^2: True
     q=2/5: P_g = 0.715141, 2p^2 = 0.720000, P_g < 2p^2: True
     q=3/8: P_g = 0.775889, 2p^2 = 0.781250, P_g < 2p^2: True
m=1 bracket 2p(1-2q) - q(q^2+2p^2): real roots [0.364975775044] ; value at q2: 0.267766952966 ; sign changes in (0, q2]: 0
closed forms OK: True
