Dumoulin and Thouin's idea is to use the distribution of shotgun pellets rather than sand or rice (which would presumably be in short supply in the post-apocalyptic world). So these guys set up an experiment consisting of a 28-inch barrel Mossberg 500 pump-action shotgun aimed at a sheet of aluminium foil some 20 metres away.
Of their 30,000 pellet holes, they chose 10,000 at random to perform this estimation trick. They then use the remaining 20,000 pellet holes to get an estimate of π, safe in the knowledge that importance sampling allows the calculation to proceed as if the distribution of pellets had been random.
The result? Their value of π is 3.131, which is just 0.33 per cent off the true value. "We feel confident that ballistic Monte Carlo methods constitute reliable ways of computing mathematical constants should a tremendous civilization collapse occur," they conclude.