A key parameter of GNSS receiver performance is the sensitivity, meaning how weak signals the receiver can acquire and track. For acquisition, this is typically measured by the minimum signal strength that can be detected with a certain probability. In this paper, a novel method of computing the probability of detection is presented. In contrast with prevailing techniques, it takes receiver parameters such as correlator and doppler spacing into account when computing the probability distribution function. The likelihood of data bit switches inside the correlation window is also considered in a similar fashion. The method is demonstrated both on a traditional correlator architecture, and on two different FFT based acquisition algorithms, coherent and non-coherent. Further, the computational complexity of the different algorithms is evaluated for a general computing platform. The combination of these two methods provide valuable insight into the problem of minimizing power consumption while maximizing sensitivity for software based GNSS receivers.