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So last night I played a game of Sisters vs Tau, but I took a small detachment of Grey Knights because I wanted to see how I like them what with the new codex being released soon and all.

So my Strike Squad attempted Smite 3 times, every time I rolled double 1.
My Brother Captain also attempted Smite 3 times and Perils'd on a double 1 as well.

Basically, out of the 7 psychic powers I attempted to manifest, 4 of them resulted in double 1s. My dreadnought was the only competent psyker in the army. I'm not a maths person so I was wondering if someone could figure out the odds of this? It's not the first time either, by tyranid broodlords are also pretty bad psykers and seem to roll a lot of double 1s.

Not a math person but I'd say the odds are pretty low for that to happen normally .
I would look into new dice pronto, your current set may be flawed.

Rare...or you're using the same two dice and they're badly manufactured.

I have seen a few games where my opponent has rolled perils 3-4 times in a game between a few psykers. It happens.

I played a game yesterday where my opponent's weirdboy caught perils both times he tried to cast on double 6's. It is what it is. The dice gods are cruel masters.

But yeah, go buy some better balanced dice.

Chance of double 1s is 1 in 36
1/36 = 0.0277
2.7% chance

It happening 4x is
(1/36)^4 = 0.000000595

or 0.0000595%

 Talamare wrote:
Chance of double 1s is 1 in 36
1/36 = 0.0277
2.7% chance

It happening 4x is
(1/36)^4 = 0.000000595

or 0.0000595%

Thanks. I'm wasn't angry at my dice or anything (they're pretty swingy to the other end of the spectrum as well), just curious. Though my terrible psychic rolls is making me rethink buying more into an all psyker army.

If an all psyker army is what you desire don't let the dice hold you back. Game Science makes perfectly balanced dice, so rolling snake eyes shouldn't be a thing very often.

 Talamare wrote:
Chance of double 1s is 1 in 36
1/36 = 0.0277
2.7% chance

It happening 4x is
(1/36)^4 = 0.000000595

or 0.0000595%

Happening 4 time out of 7 is not the same as happening 4 times out of 4 (which is what you calculated).

You have to work out the combinations (nCr).

No. of double 1s - combinations:
0 - 1
1 - 7
2 - 21
3 - 35
4 - 35
5 - 21
6 - 7
7 - 1

So, 4 double 1s out of 7 attempts happens 35 times out of 128 possibles.

Then you work out the odds of that specific result

1/35 x 1/35 x 1/35 x 1/35 x 35/36 x 35/36 x 35/36

and multiply it by the number of combinations (35) for a result of 0.0000191

If we work that out for all of the different results the distribution looks like this.

No. of double 1s - probability:
0 - 0.821
1 - 0.164
2 - 0.0141
3 - 0.000669
4 - 0.0000191
5 - 0.000000328
6 - 0.00000000132
7 - 0 (not really zero but so close, who cares? 1/(2.8x10^12) for those that do.)

(NB When you're making a probability distribution you check your work by adding up all of the results. They should add up to 1 (usually a fraction under due to the decimal places you couldn't be bothered putting in). If they don't then you've screwed up)

TL;DR
So that's a 1 in 50,000 chance of rolling 4x double 1s out of 7 attempts. (The odds of 4 or more are only slightly more likely)

Also, 82% of the time you'll make 7 tests without rolling any double 1s. Only 2% of the time will you roll double 1s more than once.

But again, all that mathhammer fails if you have bad dice (which we've learned in the industry is about...all of them). Almost no commercially available dice are properly weighted/cut/balanced to be genuine 1/6 chances per face.

Now if the player has two special dice he prefers to use for psychic tests (because they're a different colour or something fancy) this could easily lopside the math completely --- several of the large dice rolling tests people have done have discovered certain faces skewed to 21-25% of rolls on occasion.

While almost equally unlikely, if you happen to grab the same dice every time, you can be increasing your likelihood to fail quite a bit.

Or substantially decreasing it (depending on how the dice are biased).

But knowing the odds is important. In this case if you get 3+ double ones out of 7 attempts in three games in a row your dice are probably bad.