How many dice rolls until 2 consecutive sixes?

MANIFOLD

resolved Apr 19

1-6

7-12

31-36

37-42

19-24

13-18

25-30

43-48

49-54

55-60

61-66

67-72

73-78

>=79

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Answer based on your intuition, not any calculations. On average how many times will you need to roll a 6-sided dice until you roll sixes two consecutive (back to back) times?

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@traders thanks for participating! The answer is 42

# ∈ {1, 2, 3, 4, 5, 6}

x ≠ a

#ₓ ≠ #ₐ

#####6 <-- selection set 1

####6#

###6##

##6###

#6####

6##### <-- selection set 2

total: 6

The selection set size is 5! = 120, it doesn't matter.

this pair is needed: #####6 6#####

pair count: 6 * 6 = 36

frequency: 1 in 36

7 cuz you have a 1/6 chance to get a consecutive roll starting on the 2nd roll

@MaxE Shoot my intuition is terrible confirmed

@Qoiuoiuoiu That's what happens when you're more familiar with d20s than d6s lol

@MaxE Sorry I mean until you roll a one and then a one, specifically, not any consecutive faces no matter what faces they are. I changed it to sixes to clear up any confusion.

@spiderduckpig what?? then it should be 20-25

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