Dutch book question

I’m following Jack’s Dutch book discussion with interest and would like to know about the computational complexity of constructing a Dutch book. If I give you a finite table of probabilities, is there a polynomial time algorithm that will verify that it is or is not Dutch bookable? Or: help me make this question better-posed.

It reminds me of Boolean satisfiability, which is known to be NP complete, but maybe the similarity is superficial.

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