Competing Sudakov veto algorithms

We present a formalism 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 formal 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 in a semi-realistic setting and show that there are significantly faster alternatives to the commonly used algorithms.