Based on the mixed strategy Nash equilibrium of the game theory, the probability theory and numerical analysis theory are used to study the optimal bidding for the random composite base method. Using the quadratic polynomial equivalent nonlinear function, the analytic formula for the optimal bidding under continuous random complex base method is given. For the discrete random complex base method, it can be solved by the continuous equivalent composite base or by the enumeration method combining with MATLAB programming solver. Through bidding case of practical project, the excellent practical engineering value of the proposed theory is validated.