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@Greenbank
FWIW, with a Monte Carlo simulation (each experiment is run 10,000 times) I get:-
(My test is to simply to see whether the 1/18 outcome occurs more times than the 1/36 outcome.)
50% confidence: ~19 rolls
75% confidence: ~80 rolls
90% confidence: ~200 rolls
95% confidence: ~310 rolls
98% confidence: ~475 rolls
99% confidence: ~600 rolls
With 1000 rolls there are still 0.1% (about 10 times) where the 1/36 outcome occurs more times than the 1/18 outcome. (I've not bothered to check how good the PRNG I'm using is or determine if I've exhausted the entropy pool.)