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In a 40K game today I rolled seven 6s on a roll of eight saves (eight dice).

At first that roll seemed incredible, but after running the numbers, doesn't seem all that unbelievable.

Can someone give me the probability, and explain how they did it?

I came up with around 1/2099, which doesn't seem as impressive.

Mez

Whoops - meant to post this to Dakka Discussions - can a mod move?

Wow, that is the most interesting development in the miniatures hobby today. : ) Just teasing.

To start with, you find the total number of unique rolls possible. In this case it's 6 (sides) to the power of 8 (dice): 1,679,616.

Then you find the number of combinations in which you'd make exactly seven 6+ rolls on 8 dice. That's eight different batches of combinations where one dice failed (has a number between 1 and 5), and the other seven dice passed (rolled exactly 6), for a total of 40 combinations (1,6,6,6,6,6,6,6 ; 2,6,6,6,6,6,6,6 ; 3,6,6,6,6,6,6,6... 6,6,6,6,6,6,6,4 ; 6,6,6,6,6,6,6,5).

Then the probability is the second number divided by the first: 40 / 1,679,616 = 1 / 41,990.4

,The probability of two answers being the same is... low...

I make it 1/335,923.

I get there by:
Chance of a 6 = 1/6
Chance of not 6 = 5/6
8 dice so 1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 5/6
= 5/1,679,616 = 1/335,923

stroller wrote:
,The probability of two answers being the same is... low...

I make it 1/335,923.

I get there by:
Chance of a 6 = 1/6
Chance of not 6 = 5/6
8 dice so 1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 5/6
= 5/1,679,616 = 1/335,923

You have to treat the dice distinctly, which you aren't doing.

There are 5 cases where die #1 isn't a 6, but all else are.
There are 5 cases where die #2 isn't a 6, but all else are.
Etc, etc.
There are 40 (5 for die #1 + 5 for die #2 + ...) cases where one die isn't a 6, but all else are.

There are 1,679,616 possible cases. That's 6^8 or 6*6*6*6*6*6*6*6.

40 interesting cases out of 1,679,616 possible cases is the same as 1 out of 41,990.4. You had a roughly 1 in 42k chance of rolling what you rolled.

OK. I follow that logic.