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What are the chances of rolling double 6s with 6 dice?

Depends how good your luck is my friend has miscast with 3 6s on 4 dice ended up not doing much and exploding.

Point being you can miscast on 2 dice or 6 depends how lucky you are.

If you cast with a high level caster 4 dice usually do it 5 tops unless this is a game changing spell then 6 is appropriate.

Just want to know the chance percentage man. thanks though

1 dice has a 16.6% chance of hitting 6. Spread across 6 dice the odds of getting any pair would be 8.3% if I'm not mistaken.

Realistically the statistics on dice only apply to casino grade dice which are perfectly balanced. Almost all gaming dice have something like a 29% chance to roll a 1 due to the indented pips screwing up the balance and thus causing the heaviest side(the one with the fewest indentations) to land facing up.

So basically the stats don't mean a thing. But there they are.

It depends if you mean at least two 6s or 2 and only 2 6s.

Each dice has 6 outcomes, which gives you 6^6 possible outcomes, or 46,656.
The probability of not rolling a 6 on the first 5 dice is 3,125 out of 7,776. Which equates to a 4,651 / 7,776 chance of rolling a 6. about 59.81%

The chance of definitely rolling a 6 on your last dice is 1/6.

If you add the two together it gives you a 9.96% chance of rolling at least two 6s (I think).

EDIT: Actually that's wrong... The chance is higher... ahh crap wait a sec... *goes to get piece of paper*

Okay the maths is kind of complicated. This explains how to do it.
http://answers.yahoo.com/question/index?qid=20100125181948AAzUwMU

And I think this is the answer.
http://www.wolframalpha.com/input/?i=1+-+%285%2F6%29^6+-+%285%2F6%29^5

So about 26% for at least 2 or more 6s

I'm confused as to how the chance for 2 6's across 6 dice is higher than the chance for 1 die to hit 6.

And again, using Chessex dice or the like, you have to factor in that 1 has a 29% chance of happening.

perhaps this helps.

http://www.dakkadakka.com/wiki/en/That%27s_How_I_Roll_-_A_Scientific_Analysis_of_Dice

The chance to roll a single six increases as you increase the number of dice thrown. The chance to roll any pair increases as the number of dice increase. So it's acceptable to think that rolling two sixes with six dice could be easier than rolling a single six on one die.

@aerathan - as Smacks says, it's a bit dependent on if syypher intended as JUST two 6's or AT LEAST two 6's, as there's a big difference.

In the case that it's JUST two 6's, (and for the purposes of this discussion, let us assume that the dice used are perfectly random and each side has equal probability of coming up, ie. all have 1/6 chance):

The probability equation (as suggested in the first link Smacks posted) is:

P = (1/6)^2 * (5/6)^4

Where in you two of the dice have 1/6 chance of rolling 6's and four dice have 5/6 chance of not rolling 6's. This gives you a probability of 0.013495. However, this is for only a single combination of a pair of 6's. (Ie. if you have dice A, B, C, D, E, F, you're only looking for dice A and B rolling 6's). In this way, there're 14 different combinations of a pair of 6's that you can come up with 6 dice, and as such, the probability is weighted accordingly. So the total probability for just two 6's occuring would be:

P = 14 * (1/6)^2 * (5/6)^4 = 0.18754, or 18.75%. Already higher than the 1/6 chance of simply rolling a 6 on a single die.

If you factor in the second case of rolling six dice and wanting AT LEAST two 6's, you repeat the process to include the probability of situations where you roll three 6's, four 6's, five 6's and all 6's to the equation. So basically, as you add more dice, while the individual probability gets a bit smaller, you're also increasing the number of times the event can occur by the added number of combinations that are possible to achieve the event.

See now your math I understood.

I still say that statistics for dice rolling are a waste of time to worry about as you are likely using Chessex dice. A full set of 30 or 40 casino dice would set you back a pretty penny.

Yes, the "real" probabilities skew these numbers a bit, but I imagine it doesn't do so to such a degree that you can't get a reasonable ball-park estimate from "ideal" probabilities.

well the 29% for a 1 on chessex dice is a far way off from the 16.6% it should be. It's almost double.

But if you're more concerned about the odd's of the 6's, the probability that 1's are rolled are accounted for in the (5/6) parameter of the probability equation (assuming the 6's are somewhat close to 1/6 probability). Even keeping in mind the non-idealities of regular chessex dice, you can at least use the ideal probabilities to get a feel for an "upper bound" of the chances of getting something.

It's not a completely worthless exercise, though I personally don't tend to run through numbers like this myself.

My google-fu produced this:

Chances of rollin 2+ sixes wrote:2D6 = 1/36 = 2.7%
3D6 = 16/216 = 7.04%
4D6 = 171/1296 = 13.9%
5D6 = 1526/7776 =19.6%
6D6 = 12281/46656 = 26.3%
7D6 = 92436/279936 = 33.%
8D6 = 663991/1679616 = 39.5%
9D6 = 4608946/10077696 = 45.7%
10D6 = 31169301/60466176 = 51.5%
11D6 = 206547056/362797056 = 56.9%
12D6 = 1346704211/2176782336 = 61.9%

As you can see it takes even DE into account.

HoverBoy wrote:My google-fu produced this:

Chances of rollin 2+ sixes wrote:2D6 = 1/36 = 2.7%
3D6 = 16/216 = 7.04%
4D6 = 171/1296 = 13.9%
5D6 = 1526/7776 =19.6%
6D6 = 12281/46656 = 26.3%
7D6 = 92436/279936 = 33.%
8D6 = 663991/1679616 = 39.5%
9D6 = 4608946/10077696 = 45.7%
10D6 = 31169301/60466176 = 51.5%
11D6 = 206547056/362797056 = 56.9%
12D6 = 1346704211/2176782336 = 61.9%

As you can see it takes even DE into account.

Tell that to my DE friend that used 15 dice to cast enchanted blades of Aiban and got only 1 6......

Krellnus wrote:

HoverBoy wrote:My google-fu produced this:

Chances of rollin 2+ sixes wrote:2D6 = 1/36 = 2.7%
3D6 = 16/216 = 7.04%
4D6 = 171/1296 = 13.9%
5D6 = 1526/7776 =19.6%
6D6 = 12281/46656 = 26.3%
7D6 = 92436/279936 = 33.%
8D6 = 663991/1679616 = 39.5%
9D6 = 4608946/10077696 = 45.7%
10D6 = 31169301/60466176 = 51.5%
11D6 = 206547056/362797056 = 56.9%
12D6 = 1346704211/2176782336 = 61.9%

As you can see it takes even DE into account.

Tell that to my DE friend that used 15 dice to cast enchanted blades of Aiban and got only 1 6......

I assume that was storm of magic as the max in regular games is 12 PD at a time.

Couldn't you roll 12 dice then sac an elf for a 13th die though?

frenrik wrote:Couldn't you roll 12 dice then sac an elf for a 13th die though?

The sacrifice would have to happen after the spell was resolved as far as I know. Then again throwing 12 dice at anything is a stupid idea.