I rolled 17 normal dice and got 9 deuces. Seemed the most lopsided role I've ever made. Maybe not that extreme: about 3 times the expectation. So what are the odds of getting 9 or more of any one of the six possibilities in a roll of 17 dice?

* Got a change it little. I was actually going for deuces. So what are the odds of getting 9 out of 17 of one specific of the possibilities?

(Game involves 40 dice yahtzee type game, and I already had 23 deuces on five rolls, then had a 9 deuce roll with 17 left.)

Given enough trials, the probability approaches 100%.

There are 17!/(k!(17 - k)!) ways to choose k dice from 17 dice. The probability that each of these dice is a deuce is (1/6)^k. The probability that each of the other dice is not a deuce is (5/6)^(n - k). Then the probability of rolling exactly k deuces is:

P(k) = (17!/(k!(17 - k)!))*((1/6)^k)*((5/6)^(n - k))

The probability of rolling at least k deuces is:

P(k) + P(k + 1) + ... + P(17).

I got .00398 or 0.398%

Since you have 17 and need 9 or better the probabilities of either 1-6 getting such extreme result are disjoint and purely added up leads to

6*Sum[17!/k!/(17-k)!*(1/6)^k*(5/6)^(17-k),{k,9,17}]

https://www.wolframalpha.com/input/?...2C9%2C17%7D%5D

or indeed 0.00398062

Getting 12/17 or worse 1or 2 rolls is about half that.

Just 4 out of a 1000 then? ... thought it might be much more. Thx.

the deuce took up half the rolls.............. the other 5 numbers took up the other half..

17 rolls....... i thought it would have been lower probability than that...

there are 2 things people confuse.........


1) these are the odds of this happening with just 17 rolls of the dye, looking forward ...... this is not the same as rolling the dice a million times and looking back seeing that this happened as sequence during all those million rolls of the dice.

2) this is pretty minor.......... to get those odds, you'd have to specify beforehand that it has to be the 2 that is rolled so often. not one of the 6 dye faces.

all kinds of weird things happen in life...... but it's not predictable beforehand what they will be.