[Spete]

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The probability of getting s or fewer sets is exactly what you want (anyway there isn't much more to infer from it than that you've been unlucky in terms of flopping sets). Any statistical test with a fancy name would be just an approximative method for calculating Pr(s<=s_observed) and if you can calculate it exactly from the binomial distribution an approximation is not needed.

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I'm not sure I understand. If I take one coinflip and get tails, then use binomial distribution to calculate the probability of hitting 0 heads in 1 trials, I'll get - surprise surprise - 0.5. Now I'm having a hard time interpreting 0.5 as the probability of my coin being random. Any reasonable statistical significance indicator should give me a number very close to 1, shouldn't it?