A comprehensive theoretical analysis of the development of passive mode-locking in a giant pulse laser is presented. After a review of previous work, a rate equation approach is used to obtain a simple mathematical condition defining the "second threshold" of the system, close to which the best mode-locking occurs. In addition, a computer model enables the influence on the mode-locking quality of the statistical properties of the primordial noise patterns from which the signal evolves to be studied in detail for the first time. The results indicate that the shot-to-shot behavior is controlled by just two parameters characterizing the noise patterns, and the distribution functions for the two critical random variables are obtained. Although this work does not reveal any novel technique for designing a completely reliable laser system of this type, it does enable a systematic prescription for minimizing the reproducibility problems to be drawn up. This should greatly facilitate the optimization of present and future lasers of this type.