# 64 events occurring in the flipping of a die

Hi there,

I am trying to figure out the 64 events occurring in the flipping of a die. Can someone help me with this?

regards
kautilya

## Answers and Replies

DaveC426913
Gold Member
Can you elaborate? Do you mean 64 outcomes of the die roll, or do you mean 64 muscle movements that go into throwing the die?

Is this an ordinary six-sided die? An eight-sided die (e.g. shaped like an octahedron) could lead to 64 possible outcomes if you rolled it twice.

Thanks a lot Dave and belliott.

Yes, i meant the 64 outcomes of the die roll of a six-sided die. Can you help me obtain this using the laws of probability?

regards
kautilya

CRGreathouse
Science Advisor
Homework Helper
We don't know what you mean. You'll have to tell us more if you want a sensible answer. To me, a die roll is an abstract event with exactly six equiprobable outcomes.

DaveC426913
Gold Member
Thanks a lot Dave and belliott.

Yes, i meant the 64 outcomes of the die roll of a six-sided die. Can you help me obtain this using the laws of probability?

regards
kautilya

Yes, as CRG points out, a single roll of a 6-sided die results in one of only six outcomes, all of which are equally probable.

If you roll two D6, then the number of possible outcomes rises to 36.
3 dice gets you 216.

I don't know any way of getting 64.

Sure it was 6-siders?
Rolling 2 8-siders would get you 64, as would rolling 3 4-siders...

Of course, none of this has to do with probability - it's just basic combinatorics, i.e. counting the number of possible outcomes. Probability enters only when you start to ask about the liklihood of a given outcome, that is, the fraction of all possible outcomes that will produce the given outcome, e.g. the number of ways to roll at least one "three" in four rolls of the die.

CRGreathouse
Science Advisor
Homework Helper
I don't know any way of getting 64.

Even/odd sequence after 6 rolls?

Edit: Turning that to a serious response, I can generate 64 equiprobable outcomes in 760/243 ≈ 3.13 fair die rolls on average. Is a better result possible? It can't be done with two rolls, since 6^2 = 36 < 64. It can't always be done in 3 rolls, since 6^3 = 216 is not divisible by 64 so some outcomes would be more likely than others.

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