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For Monte Carlo eg in finance, you’d definitely take the speed improvement. This thing passes Big Crush and PractRand - it’s going to compute the approximate value of your three factor Power Reverse Dual note just fine.

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> This thing passes Big Crush and PractRand

... for the seeds that were tested.

In theory, you can get unlucky and end up in a short cycle, and it will not pass these tests.

That's why I'm not comfortable with it, when there are generators with a known, guaranteed period. They simply do not have this failure mode.

The probability of the problem occurring is vanishingly small - much smaller than a bit flip due to a cosmic ray in the machine computing it, leading to a wrong answer or a crash. And even that doesn’t matter, because the computations are repeated so often.

Again, the application determines what the most suitable PRNG is.

That's why I pointed out that the probability of a too-short cycle or sequence-overlap is no higher than that of randomly selecting one snowflake out of all snowflakes in Earth's history. Also, the paper has a graph and accompanying discussion of what happens with the shorter cycles.

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