If you throw six fair dice, what are the odds that at least three dice make a straight (i.e. 123, 234, 345, or 456) I am certain that I am making a mistake in calculating it?
What are the odds of rolling a 3 number straight throwing 6d6
6
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probability
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0what's your current calculation? – 2011-10-01
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3should be moved to SE mathematics – 2011-10-01
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0It's pretty high, pretty near one. But I'd have to think of how to get the exact probability... – 2011-10-01
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0I went through a long and nasty inclusion-exclusion argument, watched lots of stuff cancel, and in the end got $6^6 - 6 \cdot 4^6 + 8 \cdot 3^6 - 3 \cdot 2^6$, which agrees with Ed Pegg's calculations. I imagine there's a simple way to explain this formula, but I don't see it. I'm offering my results here in the hope that someone else can. – 2011-10-02
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0@Mike Sounds like I did the same calculation as you. If you have time, why don't you post your solution? We can also try to think of a shortcut. – 2011-10-02
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0@Byron: I've added my argument. Do you see a shorter explanation? – 2011-10-03