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A 6 Sided Dice's average roll is 3.5.

I want to roll three 6 Sided Dice and meet or beat an arbitrary number 30% of the time. How do I figure out what that arbitrary number needs to be to meet or beat it 30% of the time?

And how do I figure out what the arbitrary number should be if I want to meet or beat it 60% of the time?

Thank you for your help.

user3570952
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  • You probably want to try this on stats.stackexchange.com for help with statistics. – Jeff Feb 24 '15 at 00:44
  • Thanks Jeff. I hope to get an answer here and don't want to double post so I will wait a little while and see. Thanks for looking. – user3570952 Feb 24 '15 at 00:50
  • You need to look at cumulative binomial distribution. Calculate the probability of rolling a 3 $(\frac{1}{216})$, probability of rolling a 4 $(\frac{3}{216})$, etc. Then calculate the cumulative probability by adding them up as you go, stopping when you get past the percentage you are interested in. – turkeyhundt Feb 24 '15 at 00:53
  • Turkeyhundt, I am not familiar with cumulative binomial distribution but I am not apprehensive to learning. Could you please point me in the right direction for some easy-to-understand methods of cumulative binomial distribution? – user3570952 Feb 24 '15 at 00:57
  • I was a little bit off in my explanation. It's not exactly a binomial distribution. I don't have too much time now, and somebody smarter might jump in, but if you google binomial three dice 216 you can see some methods (or get an actual chart of the values you're after). I will have some time later to jump in. But there are 216 total possible outcomes (666) and you just need to figure out how many will have a sum of 3,4,...,18. – turkeyhundt Feb 24 '15 at 01:10
  • Thank you Turkey. I am not great with Math and don't know binominal distribution well at all. Is there any way you could give me a crash course as if you were giving it to a younger audience? Thank you so much for your time. – user3570952 Feb 24 '15 at 18:20

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