One of the messages of this chapter is that while Monte Carlo is a clever method of calculation, it shouldn’t be used when some better method exists. The MC valuation of π in section 25.2, for example, converges very slowly. It’s a crummy way to compute π, since there are well-known methods for doing this. To see this, answer the following questions:

• Approximately how many runs does it require until you get 4-decimal accuracy for π using our MC simulation?

• Approximately how many runs does it require until you get 8-decimal accuracy for π using our MC simulation?

• Approximately how many runs does it require until you get 16-decimal accuracy for π using our MC simulation?

Note on exercises 5 and 6: We show you two alternative ways to compute the value of π. Both are substantially better than Monte Carlo!