This happens because Sample tries to use evalhf to determine the probabilities for all numbers in a reasonable range. What ends up happening is, roughly:
r := RandomVariable(NegativeBinomial(3, 0.1));
p := MakeProcedure(ProbabilityFunction, r, numeric);
numbers := Array(0 .. 169, i -> i, datatype=float);
This requires evaluating evalhf(p(169)), which doesn't work: there's an overflow, because GAMMA(172) cannot be stored in an IEEE double variable. In theory, you could simplify GAMMA(3+t)/t! to a polynomial and just evaluate that instead, but that won't work for cases where the first parameter is not an integer (which we allow). Instead, I'm testing a fix that tests whether the sum of the resulting probabilities in the Array 'numbers' is close to 1, and if it isn't, retry without 'evalhf'. Unfortunately, it looks like it may be a while until this fix is in a released version of the product.
I will add that another workaround is using the option 'method = custom' in the sample call: Sample(r, 10000, method=custom). (The default for the negative binomial distribution is the discrete method.) For more details, see the help page for Statistics[Sample].
Math group manager, Maplesoft.