Probability: Does order matter when rolling groups of dice?

[Lord kanarik]

What really bugs me about probability is that can be completely different if order matters vs. if it doesnt. If order is taken into account when rolling 1 dice 10 times, does it matter when rolling 10 dice once? My common sense says no, but probability often ignores rules of common sense.

[Zakath the slaughterer]

Hehe, of course it doesn't. How could it?

[Dalamar]

Whatever other disbelievers tell you, it matters if you believe it!
(I know a person who *never* rolls a 1 when rolling single dice... only when rolling more than one... guess how he saves his terminators? (40k player luckily ) )

[Arquinsiel]

Order is different from rolling together and in batches.

Imagine rolling to wound for every attack a model has and then rolling to hit. How do you then decide which wound rolls hit and which miised? Or taking armour saves before rolling to wound. Same deal.

[Lord kanarik]

Well, i figured it out, and actually, (at least for figuring out the probability of rolling at least 2 ones for any number of dice) it does. Dont ask me why though.

and if anyone wants it, the formula for finding the probability of rolling 2 or more 1s is :

((5/6)^x) + x((1/6)((5/6)^(x-1)))

where x is the number of dice rolled. Multiply by 100 and you got your percent.

[Dalamar]

no, it doesn't. you math is flawed at the thesis level
it doesn't matter if you roll 2 dice together
or
roll 1 dice and then roll another dice after it.
the chances of rolling double anything in both situations are exactly 1:36
your formula is overcomplicated for basic dice rolls, and that might be why you get different results.

[Lord kanarik]

I dont think so. Check it. It works.

for 2 dice, there is only 1 possible way to roll snake eyes. 36 possible combos.

for 3 dice, there are 16 possible ways, and 216 possible combos.

for 4 dice there are 171 possible ways, and 1296 possible combos.


It works.

oh, and I am counting 3 1's, 4 1's and so on, since these would count as miscasts.

[Archdukechocula]

oh, and I am counting 3 1's, 4 1's and so on, since these would count as miscasts.

It doesn't matter, it just creates the perception of mattering because statistics are based upon the odds of results based on imperfect knowledge. If you roll a group of dice, you go from zero knowledge of the dice to total knowledge. If you roll dice sequentially, then your knowledge of the outcome is gradually revealed. Practically speaking, what this means is, if you roll sequentially, the odds change after each dice roll, only because you have increasing knowledge of the dice rolls. After the first roll, you know what that first dice is, which means you have to recalculate the probability to reflect that roll, because probability is really just the science of prediction based on odds. Naturally, your predictions get better the more information you have. From the start your odds are the exact same. As your rolling progresses, they change only because you have new information that allows you to refine the calculation with increasing accuracy. Statistically though, at the starting point, your odds are exactly the same. You still end up with 10 dice face up on the table that all had the same chance of rolling a given number. Physically speaking, what you are going to roll is what you are going to roll no matter what the statistics, because reality follows physical laws. Statistics are just a way to predict the odds of any given outcome with the information at hand.

[Lord kanarik]

Well I wasn't actually calculating on the go, I was looking at the odds of rolling 2 or more 1's with x number of dice. I thought that, since they were all being rolled at exactly the same time.

But you are right, the two are exactly the same. And so, for either one, a roll of 2,1 is different from a roll of 1,2. And that is what I was stuck on at first. But I got it after a while, and the formula works.

Physically speaking, what you are going to roll is what you are going to roll no matter what the statistics, because reality follows physical laws. Statistics are just a way to predict the odds of any given outcome with the information at hand.

True, but the physical world also follows statistics. It helps to know the odds so that you can pick the best option for the situation.

MODERATOR EDIT: If you have more to say then EDIT, don't post again. This is the second post I merged from you in this thread. Linda

[Archdukechocula]

Well I wasn't actually calculating on the go, I was looking at the odds of rolling 2 or more 1's with x number of dice. I thought that, since they were all being rolled at exactly the same time.

But you are right, the two are exactly the same. And so, for either one, a roll of 2,1 is different from a roll of 1,2. And that is what I was stuck on at first. But I got it after a while, and the formula works.

That was always the thing that I had trouble with when I took statistics classes.

Physically speaking, what you are going to roll is what you are going to roll no matter what the statistics, because reality follows physical laws. Statistics are just a way to predict the odds of any given outcome with the information at hand.

True, but the physical world also follows statistics. It helps to know the odds so that you can pick the best option for the situation.

Oh, I agree fully. I was just commenting on the purpose of statistics. it is an attempt to anticipate the outcomes of physical law based on the information we do have (the likelyhood of a result), because we can't actually see into the future. If we understood physics well enough, our statistical models would get better, and you could theoretically anticipate results to an ever higher degree of accuracy. The foundation of statistics, unlike physics, is using math to determine the most likely results about what is unknown rather than what is known.

[The_everchosen]

Surely it doesn't matter, as however many dice you roll you still have a 1/6 chance of rolling any particular number. For every 6 dice rolled together you should roll roughly one 1, for every 6 you roll seperately you should also get roughly one 1.

[Lord kanarik]

Surely it doesn't matter, as however many dice you roll you still have a 1/6 chance of rolling any particular number. For every 6 dice rolled together you should roll roughly one 1, for every 6 you roll seperately you should also get roughly one 1.

No, although that is a common mistake for probability. You actually have to look at your desired outcomes divided by your possible outcomes.

For six dice, as in your example, you actually have a 6.6 percent chance to get exactly one 1, and almost a 25% chance of getting 2 or more 1s.

Think about it, for 6 dice, how many ways are there to get exactly one 1?

(if N is any number except for 1)

you could get:
1,N,N,N,N,N
N,1,N,N,N,N
N,N,1,N,N,N
N,N,N,1,N,N
N,N,N,N,1,N
N,N,N,N,N,1

so in each case there is 1/6 chance of 1 and a 5/6 chance of N.

Simplified, that is 6((1/6)(5/6)^5)

if order did not matter for this, we would get a ridiculously small chance of getting exactly one 1.

[Nathan mcduck]

Okay, maybe I'm misinterpreting what you're saying. (I'm not a native speaker)

But, is your thesis that the odds to get a double 1 (for example) are different when you roll one dice and then a second as opposed to rolling two dice at once?

If so, you're wrong.

What changes is, as Archdukechocula pointed out, the probability to role double ones if you know you already rolled a single one:

for all those mathematicians out there
P(A=1 and B=1 given A=1) = P(A=1 given A=1) * P(B=1 given A=1) = 1 * P(B=1) = 1/6
P(A=1 and B=1) = P(A=1) * P(B=1) = P(B = 1)^2 = 1/36
if A and B are independant and identical Experiments (which is the case when rolling dice that are not in some way magically connected :-) )

Oh and btw, you're formula is absolutely correct, but in no way implies a difference between rolling x dice simultaneously or sequentialy.

[Lord kanarik]

Sorry, I'm sure my writing looks convoluted, because I was thinking this through as I wrote this. I know the odds for both are the same.

What I was talking about is that the order of the dice in each case matters, as

1,N,N,N, .... is different from

N,1,N,N, ....

I dont really know how to say it in a different way. I was confused as to whether, for the purposes of calculating probability, the two cases above would count as 1 case, or whether you would count them as different cases.

That is what I meant by order. Sorry if I didn't clarify.

And by the way, your English is impeccable. Better than most native speakers I know, actually.

[Nathan mcduck]

ahh ok

[Arquinsiel]

You are forgetting that the dice don't know or care what order they are being rolled in or what the other dice have already rolled.

IE: they are independant of each other.

Given how long you are dragging this out I suspect you either fundamentally misunderstand the very basics of probability or are trolling.

[Darc]

I think I know what you're asking. When considering all possible combinations of a set number of dice and to keep this simple lets just make it two dice: A and B

In order to calculate the number of possible outcomes..

A rolling a 2 and B rolling a 5 is a completely seperate outcome from A rolling a 5 and B rolling a 2

Is that what you were asking about?

[Lord kanarik]

@ Arq.

No, you dont understand. I'm not sure if its my explanation or what.

What I'm SAYING, is that for the purposes of CALCULATING probability, the order of the dice in each case matters. (see my previous post.)

I know that it doesn't actually matter in the real world, which was what was confusting me to start. But let's get one or two things straight. My math is NOT wrong, and I do NOT troll. The only reason I'm dragging this out is because people refuse to understand what I am trying to say.

If you don't believe me, then that's your problem.

and @ Darc, yes. that is what I was saying.

For my purposes, at least, this topic is done.

[Arquinsiel]

Thing is, you're just talking about permutations of the set of results. In probability the number of possible permutations leading to a result is the important number not the actual permutation itself. I'll come up with a clearer explaination after some sleep.

In the meantime, if you *really* want to get pissed off at probability look into calculating the probability of rolling an edge. I hope you enjoy recursion.

[EDIT]
Okay, look at it this way:

You have a space marine commander with artificer armour and no invulnerable save. Thanks to shitty luck he gets pasted with six krak missiles in one turn. Any one of those crack missiles will insta-kill him, but he has a 2+ save. The chances of him dying are one in six on each roll, or (1/6)^6 (1/6*1/6*1/6*1/6*1/6*1/6) overall. This is unaffected by rolling the dice as a batch or singly, as either way a single one kills him. If you're looking for the chances of him only failing one save then you take, essentially, the inverse chance of him failing and add instead of multiply resulting in 1/6+5/6+5/6+5/6+5/6+5/6 (5/6 = 1-1/6 etc). Again the order does not matter, the marine is equally dead if the failed save is the first or last rolled or if the entire lot are rolled as a batch.

The only difference it makes is if you roll one dice and then, after it's result, examine the probability for the marine surviving the entire set of rolls (ie: removing one dice's worth of randomosity).
[/EDIT]