The problem with this analysis is that with the "choose the same as your flip strategy", the case where A is right and B is wrong do not occur. Likewise when A is wrong and B is right does not occur. The results of each coin flip are independent, however the strategy produces a non-independent result.

  A, B, GuessA, GuessB, Winner, AmountC, Chance, EV
  H, H, H,      H,      AB,     -3,      0.25,   -0.75
  H, T, H,      T,      C,      +1,      0.25,   +0.25
  T, H, T,      H,      C ,     +1,      0.25,   +0.25
  T, T, T,      T,      AB,     -3,      0.25,   -0.75

Sum(EV)=-1 per round So C should not play