  We present a way to analyze the distribution produced by a Monte Carlo
algorithm. We perform these analyses on several versions of the Sudakov veto
algorithm, adding a cutoff, a second variable and competition between emission
channels. The analysis allows us to prove that multiple, seemingly different
competition algorithms, including those that are currently implemented in most
parton showers, lead to the same result. Finally, we test their performance and
show that there are significantly faster alternatives to the commonly used
algorithms.
