Simulating random points to approximate pi

Describe a simulation method for estimating $\pi$, and say how accurate it is.

Throw uniform points in a square and count those inside the inscribed circle. For $(U,V)$ uniform on $[0,1]^2$, $P(U^2+V^2\le1)=\pi/4$, so $4\times$ the hit fraction estimates $\pi$. The standard error is $\sqrt{\pi(4-\pi)/n}\approx1.64/\sqrt n$, so each extra digit costs about $100\times$ more points; quasi-random points or integrating $4\sqrt{1-x^2}$ with variance reduction converge faster.