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Not strictly related to 40k but it does crop up with psychic tests and so on.

My question is; What is the probability to roll more 1's than 6's on 4D6 (so either one 1 and 0 6's or two 1's and one 6's.. etc).

Thanks!

Razerous wrote:Not strictly related to 40k but it does crop up with psychic tests and so on.

My question is; What is the probability to roll more 1's than 6's on 4D6 (so either one 1 and 0 6's or two 1's and one 6's.. etc).

Thanks!

http://www.anwu.org/games/dice_calc.html

Hmm, That doesn't actually seem to help! xD

Well, I'm sure it's easy to work out when you know how, I'm just too lazy to work out how! :p

From a probability stand point the answer is there is no way to determine the outcome. Each die has the same odds of rolling a 1 as they do of rolling a 6. It doesn't matter how many dice you roll since the odds are the same with each die. So, as far as I understand statistics, the answer is indeterminant.

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

So it depends on the type of die/dice.

Leo_the_Rat wrote:From a probability stand point the answer is there is no way to determine the outcome. Each die has the same odds of rolling a 1 as they do of rolling a 6. It doesn't matter how many dice you roll since the odds are the same with each die. So, as far as I understand statistics, the answer is indeterminant.

Actually, there is I took a class of probability and statistics and we figured this kind of thing out all the time...

... Unfortunatly, that was 2 years ago, and I don't remember how

OK, time to be a geek about it.

I make the probability of more 6s than 1s to be 421/1296 = 0.32.

But I'm too embarrassed to tell you how I got there


Edited once so far...

Scientifically speaking, using GW dice, the probability of rolling more ones than sixes is OVER NINE THOUSAND!!!!!!!!

I'm not embarrassed so easily as doctorludo. I can confirm, through the magic of terrible spreadsheets, that 421 of the possible 1296 possible die rolls have more 6's than 1's.

I still don't see the relevance to psychic tests, though.

Yeah, I'm not seeing how there can ever be any difference in the end between rolling one number or another one on a D6. I suck at maths though!

Get some loaded dice and be done with it...

Kidding!

Not really...

No really...

It's not more likely - there are the exact same number of combinations with more 1's than 6's. What the question is about is how many of the possible outcomes satisfy our condition.

Every one of those outcomes is equally likely (as you noted, every number has the same chance to come up), but we can see how many of those outcomes give us what we want.

To give you a trivial example, if we need a 5 or more on one D6, there are six possible outcomes, all equally likely. 2 of those outcomes are what we want so we have a 2/6 chance of success.

Or, if we want to roll a double on 2D6, there are 36 outcomes and 6 of them satisfy our condition so the chance is 6/36=1/6

I'm new to the dice probability calc thing, but I'm very interested in learning more. Is there a formula, website, or application that gives you the odds for performing Multi-dice rolls when looking for a specific number or greater?


i.e. what are the odds of rolling XD6 where the result on each die is =>Y

So I have to roll 8D6 and need 4 or better


I know that on a single die that would be 3/6 (50%), but is this the same math for Multiple dice?

mrfantastical...


It sounds obvious, but you have to know exactly what question you want answering.

So, for your question, you are rolling 8 d6. Each dice has a 1/2 chance of rolling 4 or more.

If you roll two dice, the chance of getting four or more on both dice is 1/2 x 1/2 = 1/4.

If you roll X dice, the chance of getting all 4+ is 1/(2^X)

Where 2^X means multiply two by itself X times.

If you need to get Y+, it's a little more complicated.

First, write the probability of getting Y+.

Then multiply this whole probability by itself X times.

So, if you want to roll 5 dice, all of which are 5 or 6, the probability is (1/3)*(1/3)... 5 times = 1/243.

Apologies if this is patronising. People have different ideas of what probability means, so it's hard to assume what is known.

mrfantastical - I think what you need is a basic primer on probability.

http://en.wikibooks.org/wiki/Probability

Thank you guys...

this was extremely helpful

doctorludo wrote:OK, time to be a geek about it.

I make the probability of more 6s than 1s to be 421/1296 = 0.32.

But I'm too embarrassed to tell you how I got there


Edited once so far...

Those numbers are spot on, i get the same with my Python script:

def count(t,c): count = 0 for item in t: if item==c: count = count +1 return count counter = 0 sixes = 0 for a in range(1,7): for b in range(1,7): for c in range(1,7): for d in range(1,7): counter = counter +1 t = (a,b,c,d) if count(t,6)>count(t,1): sixes = sixes + 1 print("counter",counter) print("cases with more siwes than ones",sixes)

So just to confirm; That's a 32% chance to roll more 1's than 6's on four 6-sided die.

Right?

I know it doesn't help with psychic tests; it's to do with inquisitor role play & risky actions. I'm trying to let a friend know how lethal a plasmagun can be to ones inner bodily functions.