Power in Monte Carlo permutation tests is non-monotonic and can decrease with more sampled permutations, with such decreases occurring infinitely often due to distributional discreteness.
On the number of replications in resampling tests and Monte Carlo simulation studies
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More Permutations Do Not Always Increase Power: Non-monotonicity in Monte Carlo Permutation Tests
Power in Monte Carlo permutation tests is non-monotonic and can decrease with more sampled permutations, with such decreases occurring infinitely often due to distributional discreteness.