The performance of fingerprinting codes has been studied under the well-known marking assumption. If colluders get to know the binary sequence of their codewords, they will be able to employ more active collusion strategies. In this study, we analyze the balance between the number of "0" and "1" symbols in a pirated codeword and propose an equalizer to cancel the bias by giving weights on the calculation of correlation score. From our simulation results, it is revealed that the proposed detector can trace more colluders when the number of "0" and "1" symbols becomes imbalanced.