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Hey,

Just wanted to ask around, and get some opinions on something that led to a little argument during a Game.

The chap I was playing noticed I was being a little picky about Dice I would and wouldn't pick up, and asked why - I suppose he assumed I was in some way superstitious.

I'm not. I was picking Dice that had rolled low, because, although technically it's still a simple D6, I think it's more likely to roll high than one which just rolled a 6.

My Argument

Think of it this way; if I roll a 6, would you expect me to roll another 6? If I did, would you expect me to roll yet another consecutive 6? Of course you wouldn't. It defies what's probable.

His Argument

It's still a D6, so it has exactly the same odds of rolling a 6, no matter how many times you do so consecutively.

What side are you on?

Have at it, Dakka.

Martin

Have a read of this: http://en.wikipedia.org/wiki/Gambler's_fallacy

The dice rolls are not related.

On the other hand, some people who pick up dice with a particular facing showing do so to enable practised rolling.

Chances of rolling a six on a D6 is 1/6

No matter how many times you have rolled a 6 before the chance of you rolling another 6 is always 1/6

So I'm on his side

Everything Scott said above, with the addition of this:

If you *honestly* believe that by picking up certain dice, you will be more likely to roll a number you want, you are attempting to cheat. That is your intent, clear and simple, regardless of the fact that unless you have loaded or misbalanced die, it won't matter a bit.

However, if I were making Saves, say I had 20 Saves on a Tactical Squad, and I failed every single one, you'd say, 'That's unlucky/unusual'. Similarly, if I were to pick up a D6 and roll 1 20 times, consecutively, you'd say 'That's unlucky/unusual' because you'd expect that 'Surely I'll roll 2+ this time!'.

I'll put it another way. I pick up a D6, and I say to you, 'What am I going to roll?'. It could be anything. You say 2.

It isn't. It's a 5. I say 'What am I going to roll now?'. 5 is the last thing you'd guess, surely?

In response to Jokorey: I'm cheating because I pick up one die over another? Really?

The sequence overall would be unusual. Each specific roll is not. That's the difference.

ETA, and the sequence only exists after the roll is made. It can't reach into the future and affect the up-coming dice roll.

Also, those sequences are utterly artificial. You can roll 20 6's and say "that's unusual" but what is the die's average over every roll it's ever done and every roll it will ever do? Those 20 rolls may be utterly insignificant. By extracting the set which is anomalous you imply meaning which is not, in fact, there.

Popsicle wrote:I was picking Dice that had rolled low, because, although technically it's still a simple D6, I think it's more likely to roll high than one which just rolled a 6.

You are *attempting* to cheat because you are trying to generate a non random result.

You *aren't* cheating because the way in which you are artificially trying to alter the random result does not work.

I'm talking about it in a sequence, since, in a game, you roll sequence of D6s to determine various things. The fact that I've rolled it, and am now rolling it again, makes it a sequence of two rolls, surely?

I don't see your point.
The chance of rolling a 6 is ALWAYS 1/6 regardless of the dice (if you throw it in a decent manner of course), but as dice are somewhat erratic...funny things can happen.
Personally I don't care what dice I use, even if it's normally a pile of 10-12 while the rest is spread out as wound markers or terrain markers.

And of late I've started to care less about super-bad or super-good rolls. Sure, I react when it happens but I don't go around saying "OMFG, MY TERMIES FAILED 3/5 2+ SAVES!!!" stuff happens and that's that.

And I agree with your friend if that's not clear.

I feel the same as youabout it if the dice rooled low it has a chance to roll higher this time around just like if a dice has just rolled a 6 its more likely to roll low. its just how it seems to work.

Finally, someone in agreement with me.

The chances of rolling a 6 followed by a 6 is 1/36.

The chances of rolling a 6 followed by a 5 is 1/36

The chances of rolling a 6 followed by a 4 is 1/36.

The chances of rolling a 6 followed by a 3 is 1/36

The chances of rolling a 6 followed by a 2 is 1/36.

The chances of rolling a 6 followed by a 1 is 1/36

The chances of rolling a 5 followed by a 6 is 1/36.

The chances of rolling a 5 followed by a 5 is 1/36

The chances of rolling a 5 followed by a 4 is 1/36.

The chances of rolling a 5 followed by a 3 is 1/36

The chances of rolling a 5 followed by a 2 is 1/36.

The chances of rolling a 5 followed by a 1 is 1/36

And so on.

Any combination of one number followed by another number is 1/36.

However, once you have rolled the first dice, the odds for the second dice become 1/6 for any number.

A new six on a dice that just rolled a 6 is just as likely as a new 6 on a dice that just rolled a 5, or 2, or a 3.

A 3 followed by a 6 is equally likely as a 6 followed by a 6.

Dice have no memory. They do not even themselves out intentionally.

Automatically Appended Next Post:

templeorks wrote:I feel the same as youabout it if the dice rooled low it has a chance to roll higher this time around just like if a dice has just rolled a 6 its more likely to roll low. its just how it seems to work.

Just because you feel the same, it does not mean you are right.

You aren't. You are wrong.

There are no opinions on this topic. You are simply WRONG.

Of course, dice isn't completly random, with a "weak" (as we call it here) roll it might seem like they aren't...

But it isn't. Sure rolling a 6, and then a 6 seems unlikely, but it has the same odds at happining as rolling a 1 followed by a 6.

Edit: How did I get ninja'd by that megapost?

Popsicle wrote:I'm talking about it in a sequence, since, in a game, you roll sequence of D6s to determine various things. The fact that I've rolled it, and am now rolling it again, makes it a sequence of two rolls, surely?

Yes, but is there anything about those two rolls that is more or less significant than any other rolls the die will make or has made? No, absolutely nothing.

The thing is, all the results are equally likely.

Rolling 20 6's and then a 1 is just as likely as rolling 20 6's and then another 6.

The problem is you are trying to apply what you consider logic to a probability. You always have a 1 in 6 chance for any number, regardless of what rolled before. The odds of rolling 6 6's in a roll are the same as rolling a 6,5,5,3,3,1. Your brain is trying to make sense and find a pattern. Picking up a low number does not give you any benefit at all.

Fifty wrote:There are no opinions on this topic. You are simply WRONG.

Unless, of course, you believe in either karma or destiny.

But then talk of probability is utterly redundant.


Automatically Appended Next Post:

Oscarius wrote: Sure rolling a 6, and then a 6 seems unlikely, but it has the same odds at happining as rolling a 1 followed by a 6.

Melchiour wrote:The problem is you are trying to apply what you consider logic to a probability. You always have a 1 in 6 chance for any number, regardless of what rolled before. The odds of rolling 6 6's in a roll are the same as rolling a 6,5,5,3,3,1. Your brain is trying to make sense and find a pattern. Picking up a low number does not give you any benefit at all.

Absolutely.

6,6,6,6,6,6 is exactly as likely a sequence as 1,2,3,4,5,6 or 1,1,1,1,1,1

By focusing on the 6 as being more significant than the other results you are skewing your perception of the result.

Scott-S6 wrote:

Fifty wrote:There are no opinions on this topic. You are simply WRONG.

Unless, of course, you believe in either karma or destiny.

But then talk of probability is utterly redundant.

Well, if it is his destiny to roll a 6 on his second dice, it won't matter what he rolled on his first dice either, will it?

Unless his destiny is actually to NOT roll the same number twice in a row on the same dice. As destinies or fates go, however, that seems like an oddly quirky one. I can't see anyone making a movie about a guy who is fated to NOT roll the same number on a dice twice in a row...

Gee, that got quite serious, quite quickly.

I didn't intend it to become such a serious debate. I simply wanted to gauge the response.

I think I get the general gist of people's opinions on this.

Popsicle wrote:Gee, that got quite serious, quite quickly.

I didn't intend it to become such a serious debate. I simply wanted to gauge the response.

I think I get the general gist of people's opinions on this.

(I am a Physics and Maths teacher. I take this stuff seriously )

They aren't opinions, its statistical fact. Take this from someone who has had to take more Stats classes than i would like to admit.

Fifty wrote:

Scott-S6 wrote:

Fifty wrote:There are no opinions on this topic. You are simply WRONG.

Unless, of course, you believe in either karma or destiny.

But then talk of probability is utterly redundant.

Well, if it is his destiny to roll a 6 on his second dice, it won't matter what he rolled on his first dice either, will it?

Unless his destiny is actually to NOT roll the same number twice in a row on the same dice. As destinies or fates go, however, that seems like an oddly quirky one. I can't see anyone making a movie about a guy who is fated to NOT roll the same number on a dice twice in a row...

(had to edit the comic as it had a naughty word)

templeorks wrote:I feel the same as youabout it if the dice rooled low it has a chance to roll higher this time around just like if a dice has just rolled a 6 its more likely to roll low. its just how it seems to work.

funny thing, you are right, if you look only to this dice, you have 1/6 possibility of another 6 and 5/6 to roll under.

The thing is, the odds are always 1/6 to any result. you may pick the dice that rolled a 1 and get another one.

Where the problem comes in figuring this out is that some people in the thread are failing to look at the issue from two sides.
Yes. He has a 1/36 probability of rolling 6,6. This is the same as his probability of rolling 6,1.
The thing is, he doesn't want to roll a 6,1.

So, he has a 1/36 chance to roll 6,6 and a 35/36 chance NOT TO.
The odds of rolling 6,6 are FAR worse than rolling something that is not 6,6 (in general, not any specific combination).

When you continue to play it out, the odds become increasingly worse.

Therefore, though it's possible, probability dictates that he will NOT roll 6 twenty times in a row without a skewed die.

Eric

SCYTHE9 wrote:

templeorks wrote:I feel the same as youabout it if the dice rooled low it has a chance to roll higher this time around just like if a dice has just rolled a 6 its more likely to roll low. its just how it seems to work.

funny thing, you are right, if you look only to this dice, you have 1/6 possibility of another 6 and 5/6 to roll under.

The thing is, the odds are always 1/6 to any result. you may pick the dice that rolled a 1 and get another one.

And if it just rolled a 1 then there's a 1/6 of getting a 6 and 5/6 of getting under.


Automatically Appended Next Post:

MagickalMemories wrote:Where the problem comes in figuring this out is that some people in the thread are failing to look at the issue from two sides.
Yes. He has a 1/36 probability of rolling 6,6. This is the same as his probability of rolling 6,1.
The thing is, he doesn't want to roll a 6,1.

So, he has a 1/36 chance to roll 6,6 and a 35/36 chance NOT TO.
The odds of rolling 6,6 are FAR worse than rolling something that is not 6,6 (in general, not any specific combination).

When you continue to play it out, the odds become increasingly worse.

Therefore, though it's possible, probability dictates that he will NOT roll 6 twenty times in a row without a skewed die.

Eric

Yes, but that sequence only exists after the dice have been rolled. What's the probability of getting another 6 on the 21st die?

In statistics, this is known as an independant event, a simple model is a coin toss, each toss is independant of the others, so N number of heads flips in no way influence the next flip. This is opposed to a non independant event like say a hand of cards, once you have gotten 5 cards from a deck, the probability the next card will be a specific card is not the same as it was at each point the first 5 were dealt because they are all coming from a fixed size deck and each draw changes the ods.

Dice are like coin flips they are independant events.

If we make the assumption the dice are fair (including the rolling mechanism as well as geometry) then it doesn't matter what was previously rolled.

Also the probability of rolling continuous N sixes in sequence is 1/(6^N).

For example rolling one 6 is:

1/(6^1) = 1/6 or 1:6

Two sixes is:

1/ (6^2) = 1/36

Three sixes:

1/(6^3) = 1/216

Actually, given that the dice we're all using are less than perfect, you could make the argument that it would be best to use those that already came up with a 6...

Aaaaaaaand here's the assumption that quite a lot of people are making:

Augustus wrote:
If we make the assumption the dice are fair (including the rolling mechanism as well as geometry) then it doesn't matter what was previously rolled.

If you already KNOW that the dice (and rolling method) are fair and truly random, then the next die roll is just as likely to be a 6 as anything else.

On the other hand, short of rigorous physical analysis of the die, rolling surface, and rolling technique, how does one justify the assumption that the die is random?

Well, you might eyeball it and see that it isn't obviously misshapen. You might buy them from some well-regarded manufacturer.

Or, you just might roll the die and see if it "seems random" to you. If that die rolls a wide variety of numbers, and doesn't noticeably favor one or two numbers, you might treat your assumption of randomness as reasonably justified. If that die proceeds to roll seventeen '1's in a row, you might be reasonably justified in assuming that it is NOT random. If you roll it seven million times, and it always rolls a '1', you would seem to be more than a bit obtuse in insisting it was random.

While it is possible for a truly random die to roll seventeen '1's in a row, or even seven million '1's in a row, you have to know that the die is truly random through some other means. Otherwise, that huge series of '1's is your testing to verify the assumption of randomness.

Now, my two questions:

For all of the people who keep telling someone "The chance of rolling any number on the die is the same", how are you arriving at your knowledge of the genuine randomness of the die? If you don't know that the die is random, then you don't know that the chance of each side being rolled is the same, right?

For anyone (especially math geeks), statistically, how many rolls of a single die would you need to track in order to establish that die was random? Feel free to provide an answer with a degree of accuracy, if you would like ("With x number of rolls, I can say with 99% certainty that this die is random).


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Now to be fair, none of this directly solves the OPs question. If his rolling is of a die whose randomness is not already conclusively established, then he might expect very slightly fewer ones in the series of rolls that he is making given the initial roll of a '1'. After all, in a series of say, 3600 test rolls, he would expect roughly 600 of each side, '1' through '6'. Since his initial roll is a '1', he might expect roughly 599 more '1's, and ONE more of ANY other number. Note that in a sample size of so few rolls, the actual statistical variation would swamp this effect (a genuinely random die might roll 590 '1's, 580 '2's, 605 '3's, 595 '4's , 620 '5's, and 610 '6's in a sample of 3600 rolls.

There's no real reason for the OP to expect a 6 after rolling a one, any more than he should expect a 2 or a 5.

Da Butcha wrote:Aaaaaaaand here's the assumption that quite a lot of people are making:

Augustus wrote:
If we make the assumption the dice are fair (including the rolling mechanism as well as geometry) then it doesn't matter what was previously rolled.

...
Now, my two questions:

For all of the people who keep telling someone "The chance of rolling any number on the die is the same", how are you arriving at your knowledge of the genuine randomness of the die? If you don't know that the die is random, then you don't know that the chance of each side being rolled is the same, right?

For anyone (especially math geeks), statistically, how many rolls of a single die would you need to track in order to establish that die was random? Feel free to provide an answer with a degree of accuracy, if you would like ("With x number of rolls, I can say with 99% certainty that this die is random).

Oh my, how do you arrive at your knowledge that a die is fair? In all honesty you just guess or leave it to fate, right? No one really knows. If that's your point I concede it, but I don't think its beyond the pale to generally use game store bought dice and make these assumptions, do you?

On a more technical note, I would say I only use clear, square ended, numbered (not pip) dice when I play because one can verify no internal tampering or imperfections and the mass loss per side is better for numeric indicatiors than pips and square ended dice roll truer than tumbled curved dice.

To the other point, how many die rolls do you need to 'verify' a claim of a true dice, to determine that you need a sample size and to perform an experiment and test it with a degree of certainty in a p distribution, where you essentially calculate the ods that a die is rolling true based on set size versus a predicted pattern.

Here's the page for this method:

http://en.wikipedia.org/wiki/Negative_binomial_distribution

There's no way I am actually going to do that, but I would say generally a larger set size makes for a higher degree of confidence, as is intuitive. I've never even heard of a dice manufacturer for gaming even publishing this kind of an analysis for any of their dice though.

Interesting reading for the math nerds. I know there exists a game manufacturer of dice called game science, maybe they have...?

Game on!

EDIT: Scott-S6, that was a hilarious comic, I loved it, thx!

Sorry, but there's no way around it, it doesn't matter in what order or what group you roll it, a d6 will always have a 1/6 theoretical chance to roll any value.
Any differing from the 1/6 probability is not due to other dice, but to the particular d6 being faulty, or you rolling it in a non-random way (such as dropping it directly onto the value you want)

Also please don't try to "what you would expect" math. It really doesn't work that way. You should take a statistics class.

The other guy, when it comes to rolling the dice individually.

It's only when you batch roll, looking for a specific result that probability changes.