Jason A.

asked • 12/12/19

What is the probability of rolling any 5 straight with eight d8 dice?

How is this calculated? What about any 6 straight, 7 straight, and 8 straight?

Michael H.

Please explain the terms "straight" and "d8 dice"
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12/12/19

Jason A.

A straight is any sequential number set, for example, a 5 straight would be either a "1, 2, 3, 4, 5" or a "2, 3, 4, 5, 6" or a "3, 4, 5, 6, 7" or a "4, 5, 6, 7, 8." Also, "d8 dice" (singular "die") is an 8 sided die with a single number on each face consisting of the numbers 1 through 8; an octohedron.
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12/12/19

1 Expert Answer

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Stanton D. answered • 12/13/19

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Hi Jason A.,

Is 5, 4, 3, 2, 1 also a 5-straight? That doubles your odds. If not:

These are discrete permutations. You just have to write down your possible straights (there aren't many!); probability per is (1/8)^n for each n-straight. So the (single) 8-straight would be (1/8)^8. Pretty low; in any game of chance at that, the house will break you before you break even!

-- Cheers, -- Mr. d.

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Jason A.

Hey Stanton, Thank you so much for your help!! You are awesome! I would like to ask a follow-up question if I may. You asked if the numbers in reverse is also a straight. Yes, and actually, any combination of the dice that includes the 5 numbers (so in any order) would qualify for a straight. I suspect this would drastically affect the probability, because the equation you posted would only be for the 1 instance of the first 5 dice being that ordered set, correct? So my question is, do I have to use combinatorics to find all possible configurations (let's say its x), then multiply (1/8)^n by x? This would mean I have to account for every combination that all 8 dice can contain those 5 numbers, right?
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12/13/19

Stanton D.

Yes, Jason A., If that's the case (any order OK) you'd need the combinations. For the 1-5 straight that's 5 factorial, since 5 ways to pick the first roll #, 4 ways to pick the next, and so forth. You don't have to list them, just know how to calculate them, and multiply the permutation probability by that (that will include the 5-4-3-2-1 of course). That is for a specific straight, you have 4 possible 5-straights with a d8 die, starting with lowest # 1, 2, 3, and 4 respectively. Now for a bit of a romp: In how many different orders could you list all the combinations for a 1-5 straight? The combos are 120 (=5!); the permutations (possible listing orders of the combos) are 120!, which is ~6.7 x 10^198 . Well more than the protons in the universe (~10^77 if I recall). Better to stick with a 4 straight: only 6.2 x 10^23 permutations correspondingly. That's about 1 mole of atoms (6.022 x 10^23), by the way. -- Mr. d.
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12/15/19

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