  The Adaptive Multilevel Splitting algorithm is a very powerful and versatile
method to estimate rare events probabilities. It is an iterative procedure on
an interacting particle system, where at each step, the $k$ less well-adapted
particles among $n$ are killed while $k$ new better adapted particles are
resampled according to a conditional law. We analyze the algorithm in the
idealized setting of an exact resampling and prove that the estimator of the
rare event probability is unbiased whatever $k$. We also obtain a precise
asymptotic expansion for the variance of the estimator and the cost of the
algorithm in the large $n$ limit, for a fixed $k$.

Probability