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Does randomization imply possible failure?

No.

Roughly speaking, there are two types of randomized algorithms. Las vegas and Monte carlo, which, if I recall correctly, are algorithms that are guaranteed to succeed eventually and that are guaranteed to terminate within a certain interval respectively.

So a Las vegas algorithm will always provide a correct answer, but if you're unlucky it may take a long(er) time.

But can you PROVE that k>37 ?

Pfft. Real consultants can create a program where the user can determine the constant K at will.

The probability of failure is 1-(1/(2^k)) where k is my fee in thousands of dollars. Get the best result you can!