2

If there are two 6-sided dice, approximately how many rolls would it take to go through every possible combination at least once?

Both dice are separate, as in rolling (3, 4) is not the same as rolling (4, 3)

I managed to brute force an answer of 150 using a computer program that tested 1,000,000 times and averaged the number, but I can't seem to find a mathematical way to solve the problem.

This is not a duplicate of Throwing All Numbers From 2 to 12 With Two Dice because that problem sums the value of the two dice.

Jason Yuan
  • 76
  • HINT: since you treat (3,4) differently from (4,3), this is just like rolling a 36-sided die, with each side showing up with equal probability (1/36). Do you know how to solve that? – antkam Apr 19 '18 at 22:34
  • The answer to the problem you linked still applies, only now you have 36 probabilities, and $p_1=p_2=\cdots=p_{36}=1/36$, and $S={1,2,\cdots,36}.$ You should be able to make the same calculation made in that answer. – Plutoro Apr 19 '18 at 22:59
  • Are you perhaps asking for the expected number of rolls? There’s no absolute limit to the raw number since you might never get all 36 combinations. – amd Apr 19 '18 at 23:02
  • Thanks for the help guys. I followed the Wikipedia page for the Coupon Collector's Problem and I seem to understand it a little now. Using the formula they gave, I came to the answer of about 150.284. I'm really new to many of these concepts so it's still confusing, but I'll manage. – Jason Yuan Apr 20 '18 at 02:31

0 Answers0