Monte Carlo for a 10-sigma digital

The terminal price of an asset is normally distributed with mean $100$ and standard deviation $1$. You want to value a digital call that pays $1$ if the price ends above $110$. Why does straightforward Monte Carlo fail here, and how would you fix it?

The event is a 10-standard-deviation move, so essentially no paths hit it. Its probability is about $8\times10^{-24}$; plain sampling returns $0$ with an enormous relative error. Use importance sampling, e.g. draw from $N(110,1)$ and weight each payoff by the likelihood ratio $e^{-10(x-100)+50}$, or simply use the closed form $1-\Phi(10)$.