Practice question · Fill in the blanks
Complete the statement about convergence.
Doubling the number of Monte Carlo samples reduces the error by a factor of about ______.
Word bank: 2 · 4 · the square root of 2 · 10
Hints
- Error goes like 1 over the square root of N, not 1 over N.
- Take the square root of the factor 2.
Show the answer
Doubling the number of Monte Carlo samples reduces the error by a factor of about the square root of 2.
Why
Doubling N divides the error by the square root of 2, roughly 1.4, not by 2. Expecting the error to halve is the standard misreading of the convergence rate, and it makes Monte Carlo look far cheaper than it is.
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