Monte Carlo for estimating small

Question

Suppose that I have two samples $x_1,\cdots,x_n$ and $y_1,\cdots, y_m$ of two random variables $X$ and $Y$, with $m$ and $n$ very large. I want to estimate the probability $P(Y>X)$ which I know is small, something like $0.0001456$. If I use traditional montecarlo taking $N$ pairs $(x_i,y_i)$ and counting how many of them satisfy $y_i>x_i$ to estimate this probability I would need many simulations to aproximate it accurately, with enough decimal places. I would like to know if there are better monte carlo methods to estimate this probability with less simulations than this approach, maybe using aditional information from somewhere.