  Due to the chaotic nature of planetary dynamics, there is a non-zero
probability that Mercury's orbit will become unstable in the future. Previous
efforts have estimated the probability of this happening between 3 and 5
billion years in the future using a large number of direct numerical
simulations with an N-body code, but were not able to obtain accurate estimates
before 3 billion years in the future because Mercury instability events are too
rare. In this paper we use a new rare event sampling technique, Quantile
Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury
instability event in the next 2 billion years is approximately $10^{-4}$ in the
REBOUND N-body code. We show that QDMC provides unbiased probability estimates
at a computational cost of up to 100 times less than direct numerical
simulation. QDMC is easy to implement and could be applied to many problems in
planetary dynamics in which it is necessary to estimate the probability of a
rare event.
