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OP really makes me wonder what they teach people in schools in the US and the UK...

Im gona invoke the holy law. Merphys law.

That is, if something can go wrong, it most likey will. especilly if you state it.

example. 'Im goning to fail this Ld roll.' and behold as he rolls dubble six.

And then theirs jinxing. If some else says that you will role badly, and they have some phykic power, they might indead role badly. That haw orcs work too, but on a far bigger scale.

Maths tells us the chance of something happening is 1/6 give or take some unnaturaly small number for the chance of it landing on it edge or something. in this way we can say that if we roled an ifinate number of times, then 1/6 roles would be 1,2,3,4,5 or 6.

in real life, there is no way you can roll a dice ininate number of times and in truth, you never roll anything but 6 on a fair dice.

Ledabot wrote:Maths tells us the chance of something happening is 1/6 give or take some unnaturaly small number for the chance of it landing on it edge or something. in this way we can say that if we roled an ifinate number of times, then 1/6 roles would be 1,2,3,4,5 or 6.

No, it doesn't. Probability will show that over time the expected standard distribution of the rolls will shrink relative to the total number of dice rolled. This is due to vagaries of improbable outcomes such as high streaks and low streaks offsetting each other the more dice you roll, the actual numbers rolled on each dice roll are not impacted by the total number of dice rolled.

in real life, there is no way you can roll a dice ininate number of times and in truth, you never roll anything but 6 on a fair dice.

It doesn't matter how many dice you've rolled or what those dice managed to roll. It doesn't matter how many dice you will roll in the future. What matters is that on the next roll the odds of rolling each number is 1/6.

Now, you can get streaks of high and low rolling. You will roll three 6s in a row every so often, in fact, you'll see it once every 216 rolls. Thinking about the number of times you roll three dice for attacks or armour saves or anything like that, you can expect to see it reasonably often if you play enough. All of this is true regardless of the number of dice rolled.

I have no idea why you said you'd never roll anything but 6 on fair dice. What do you mean by that?

Psyker_9er wrote:
If luck (or what ever you may want to call it) can be identified as a force of will, then the game is no longer a game of odds. It becomes a battle of minds. And therefore, still not cheating...

It would also be measurable which, as I recall, is something that you don't want luck to be.

Psyker_9er wrote:
We still have hope, and have plenty of room to grow. Those who stick to the laws of others have already given up, and bound by those laws they shall go no further.

Still sticking to the laws of the Beat Generation I see.

sebster wrote:

Ledabot wrote:Maths tells us the chance of something happening is 1/6 give or take some unnaturaly small number for the chance of it landing on it edge or something. in this way we can say that if we roled an ifinate number of times, then 1/6 roles would be 1,2,3,4,5 or 6.

No, it doesn't. Probability will show that over time the expected standard distribution of the rolls will shrink relative to the total number of dice rolled. This is due to vagaries of improbable outcomes such as high streaks and low streaks offsetting each other the more dice you roll, the actual numbers rolled on each dice roll are not impacted by the total number of dice rolled.

in real life, there is no way you can roll a dice ininate number of times and in truth, you never roll anything but 6 on a fair dice.

It doesn't matter how many dice you've rolled or what those dice managed to roll. It doesn't matter how many dice you will roll in the future. What matters is that on the next roll the odds of rolling each number is 1/6.

Now, you can get streaks of high and low rolling. You will roll three 6s in a row every so often, in fact, you'll see it once every 216 rolls. Thinking about the number of times you roll three dice for attacks or armour saves or anything like that, you can expect to see it reasonably often if you play enough. All of this is true regardless of the number of dice rolled.

I have no idea why you said you'd never roll anything but 6 on fair dice. What do you mean by that?

i think my fingers worked slower than my brain. I ment that you could find that you could never roll a dice ininate number of times and so might roll a dice every day of your life and you might mot roll anything but 6s.

Da Butcha wrote:
I totally agree that perfectly random dice are going to produce independent, random results when thrown in a manner which doesn't bias their results. However, it is hard for people in the real world to come up with a priori knowledge that their dice have been produced perfectly random.

Randomness is the absence of intent, but not the absence of causality, at least in the context of this conversation. The sort of randomness that constitutes the absence of causality is probably impossible.

You are correct that attempting to influence the dice by throwing them in a way that made them land on 6 more often would deny randomness.

However, the parallel point that dice are not all unbiased does not indicate that they are not random. Something can be random and have weighted probabilities. The alternative is that nothing that has any probability can be random, as probability represent a determination, or signal, that can be perceived.

I know in my graduate physics days we had a rule of thumb that while nothing is strictly impossible we called things impossible and discounted them if they were likely not to happen once in the age of the universe (14 billion years). Throwing a fair dice every day of your life and having it always come up 6 I think falls into this category.


Automatically Appended Next Post:
so doing some quick math the age of the universe in days is 5.1 x 10 ^12. Even rolling a 6 for 30 day in a row is 1 in 4.5 x 10 ^24 chance of happening. So if 10 billion people rolled dice every day for as long as the universe has existed you would have a 1 in 100 chance for one of those people to have rolled 30 6's in a row. In other words it isn't going to happen.

Maybe the OP has a point... If you pick up a dice that has just rolled a 1 then you can be about 83% sure it won't roll a 1 a second time. :p

You're making this way to complicated. It's a 50/50 chance every time. You either roll a 1 or you don't.

asmith wrote:I know in my graduate physics days we had a rule of thumb that while nothing is strictly impossible we called things impossible and discounted them if they were likely not to happen once in the age of the universe (14 billion years). Throwing a fair dice every day of your life and having it always come up 6 I think falls into this category.


Automatically Appended Next Post:
so doing some quick math the age of the universe in days is 5.1 x 10 ^12. Even rolling a 6 for 30 day in a row is 1 in 4.5 x 10 ^24 chance of happening. So if 10 billion people rolled dice every day for as long as the universe has existed you would have a 1 in 100 chance for one of those people to have rolled 30 6's in a row. In other words it isn't going to happen.

What im saying is that the porbility never reaches 0. only a realy little number. There is always chance that it will happen, but dont count on it.

Ledabot wrote:

asmith wrote:I know in my graduate physics days we had a rule of thumb that while nothing is strictly impossible we called things impossible and discounted them if they were likely not to happen once in the age of the universe (14 billion years). Throwing a fair dice every day of your life and having it always come up 6 I think falls into this category.


Automatically Appended Next Post:
so doing some quick math the age of the universe in days is 5.1 x 10 ^12. Even rolling a 6 for 30 day in a row is 1 in 4.5 x 10 ^24 chance of happening. So if 10 billion people rolled dice every day for as long as the universe has existed you would have a 1 in 100 chance for one of those people to have rolled 30 6's in a row. In other words it isn't going to happen.

What im saying is that the porbility never reaches 0. only a realy little number. There is always chance that it will happen, but dont count on it.

There is a chance that you will turn into an-appropriatly sized pink unicorn. There is a chance that your models could begin to duke it out in your living room, firing cannons and bolters. The odds of this are such that if you began writing .000... at the beginning of the universe you still wouldn't have hit any other numbers.

I'm not sure where this is all going, however the chance of rolling 6,6,6,6,6,6 is exactly the same as the chance of rolling any other pre-defined series of numbers, for example 4,1,3,5,5,6, or 1,3,4,2,6.4, or 1,2,3,4,5,6.

I think this is terning into an argument about probility vs (what the frazzle are you guys on?)

Ledabot wrote:i think my fingers worked slower than my brain. I ment that you could find that you could never roll a dice ininate number of times and so might roll a dice every day of your life and you might mot roll anything but 6s.

Sure, it's possible. But the point is that having just rolled 12 6s in a row, the odds of the next die coming up a 6 is 1/6. This remains true no matter how many dice you have rolled, or how many you will roll.

You know what would be awesome? If the people that had these crazy failed ideas about how they will win if they pick up all the dice that rolled 3's and 5's and reroll them or whatever just spent that time and effort making army lists that didn't fail so bad that they required said voodoo magic to actually win a match.

sebster wrote:

Ledabot wrote:i think my fingers worked slower than my brain. I ment that you could find that you could never roll a dice ininate number of times and so might roll a dice every day of your life and you might mot roll anything but 6s.

Sure, it's possible. But the point is that having just rolled 12 6s in a row, the odds of the next die coming up a 6 is 1/6. This remains true no matter how many dice you have rolled, or how many you will roll.

but the probability of rolling 12 6's in a row is FAR less than 1/6, actually i think its around 1/2176782336... (my maths might be off, but that seems about right to me)... thats where the notion of "luck" comes from, beating the odds so profoundly that it seems impossible
edit: poor english :rollseyes:

jordanis wrote:

sebster wrote:

Ledabot wrote:i think my fingers worked slower than my brain. I ment that you could find that you could never roll a dice ininate number of times and so might roll a dice every day of your life and you might mot roll anything but 6s.

Sure, it's possible. But the point is that having just rolled 12 6s in a row, the odds of the next die coming up a 6 is 1/6. This remains true no matter how many dice you have rolled, or how many you will roll.

but the probability of rolling 12 6's in a row is FAR less than 1/6, actually i think its around 1/2176782336... (my maths might be off, but that seems about right to me)... thats where the notion of "luck" comes from, beating the odds so profoundly that it seems impossible
edit: poor english :rollseyes:

Thats my point. you could say that i believe in it. stuff works fo me sometimes like red cars do for orks, but not quite on the same scale. It can come in handy like correctly reading the side a coin landed by reading the thorghts of the person that looks at it 20 times in a row.

jordanis wrote:but the probability of rolling 12 6's in a row is FAR less than 1/6, actually i think its around 1/2176782336... (my maths might be off, but that seems about right to me)... thats where the notion of "luck" comes from, beating the odds so profoundly that it seems impossible

Well, yeah, when you have unlikely events happen in your favour a lot you'd lucky. No-one is arguing that luck doesn't happen, improbable events occur, I've rolled plenty of improbable things in my time. But I've rolled a crapload of dice, so you will expect to see unlikely results from time to time.

The big point is that each roll is independant from every other roll. The odds of rolling 12 6s in a row is one about 2 billion, as you noted, and if you failed and rolled again the odds would still be 1 in 2 billion. If you actually managed it, then picked up the dice to roll again the odds would still be 1 in 2 billion. If you then handed the dice to someone else to roll them, the odds would still be 1 in 2 billion.

The only way you can think that it matters who rolls the dice, or that hot streaks and cold streaks influence the rolls on future dice, is if you believe in magic.

I have a loosely related thought problem for you math guys.
It's related to probability, independant events, and luck.

Assume there is a betting game that you can only play once ever. You bet $1 at the beginning, if you roll a 1 on a d6 you lose your money, anything else and you double your money. You have to let your money ride or stop playing. When should you stop playing?

asmith wrote:Assume there is a betting game that you can only play once ever. You bet $1 at the beginning, if you roll a 1 on a d6 you lose your money, anything else and you double your money. You have to let your money ride or stop playing. When should you stop playing?

Interesting problem.

You need to have a plan from the start. If you just calculate your odds after each roll, there's always a positive expected value, so rolling again always makes sense. Obviously, that's not a good strategy, as you'll keep going until you roll a 1 and end up with nothing.

So, what's your expected value if you decide to do N rolls? Well, it's the chance that you wont roll a 1 in those N rolls multiplied by your value if you do make those rolls (plus the chance that you do roll a 1 multiplied by your winnings if you roll a 1, but that's zero, so can be ignored)

Value = (5/6)^N * 2^N

But, even this doesn't have a maximum for N. Making a billion rolls will have a higher expected return that a billion minus 1, or any other number less than a billion. So, mathmatically, I'd say keep rolling forever.

This is really an economics question, dealing with risk and investments and all that. If it were me, I'd keep rolling up to 32 times. That way, I'd have a 0.3% chance of walking away with $4.3 billion (that's American billion, with 9 zeros). That's more money than I can imagine ever needing, so rolling again doesn't actually get me a benefit.

asmith wrote:I have a loosely related thought problem for you math guys.
It's related to probability, independant events, and luck.

Assume there is a betting game that you can only play once ever. You bet $1 at the beginning, if you roll a 1 on a d6 you lose your money, anything else and you double your money. You have to let your money ride or stop playing. When should you stop playing?

Interesting question. Each time you roll you have 5/6 chance of winning, for which you double your money. That's a pretty good bet.

You winnings would increase -2-4-8-16-32-64...

Your rough (because I've been rounding up decimals) accumulated odds of achieving this would be 83% - 69% - 47% - 23% - 5% - >0%

I think that's about right, because at 3 rolls you are at about 50%, which would be the odds of rolling a 1 with three dice. Once you get to 6 rolls you've in 1:1 odds.

Obviously you have only a 1 in 6 chance of failing each time, and as we've said on this thread previous throws do not affect future throws. However, you can't keep throwing forever, I would say it's best to plan beforehand to throw only three dice and stop there, because that's where you hit even odds of getting away with it, probability is on your side, but you only have £8 to show for it. hardly worth the effort. Beyond that is a real gamble, but the payoff could be very good if you are fortunate. I suppose if it's a one off chance you should keep going until you get an amount of money you are happy with.

@ grakmar: I'd have a hard time rolling the dice once it got to $500,000, and I'm pretty sure I would definately stop at $1mil. You are a braver man than me that's for sure.
@ howard treesong: You'd really walk away from a game like this with only $8?

Howard A Treesong wrote:
Your rough (because I've been rounding up decimals) accumulated odds of achieving this would be 83% - 69% - 47% - 23% - 5% - >0%

Your odds are way off. It's more like 83.3% - 69.4% - 57.9% - 48.2% - 40.2% - 33.5%

Your early calculations were correct, but they fell apart when you did (5/6)^3 and it just snowballed from there.



Automatically Appended Next Post:

asmith wrote:@ grakmar: I'd have a hard time rolling the dice once it got to $500,000, and I'm pretty sure I would definately stop at $1mil. You are a braver man than me that's for sure.

A million would be nice, but your chances of getting that (20 rolls) are 2.61%. Getting a billion (1.7 billion with 24 rolls) is 1.26%. So, it basically equivalent to: "Flip a coin, if heads, get 1000 times your money, if tails, loose". That's the most awesome bet ever!

It's one thing to know the odds, and it's another to roll the dice with a million dollars sitting on the table. If I was already a millionaire I'm sure I would go higher.

Guess I'm not a good gambler.

Edit: Wait a minute 24 rolls is only $17 million not $1.7 billion! Your argument to go farther seemed a little to good to be true

asmith wrote:It's one thing to know the odds, and it's another to roll the dice with a million dollars sitting on the table. If I was already a millionaire I'm sure I would go higher.

Guess I'm not a good gambler.

Like I said, this can't be a purely mathematical problem. As the math answer is to keep rolling indefinitely.

There is no right or wrong answer in that sense. It all comes down to how risk averse each individual is. You need to add some "value" to each dollar beyond what you've already won. If you're saying "a million would make me really happy, but I don't really need more than that. So any additional money isn't as valuable to me as that first million", then you're totally making the logical decision.

I guess, I'm just a little greedy

Grakmar wrote:

Howard A Treesong wrote:
Your rough (because I've been rounding up decimals) accumulated odds of achieving this would be 83% - 69% - 47% - 23% - 5% - >0%

Your odds are way off. It's more like 83.3% - 69.4% - 57.9% - 48.2% - 40.2% - 33.5%

Your early calculations were correct, but they fell apart when you did (5/6)^3 and it just snowballed from there.

Oh yes I've ballsed that up. You're quite right of course, I fouled up the powers on the calculator. :p

@ grakmar: I ninja'd your post: it takes 10 more rolls to hit $1B not 4 that changes my outlook considerably.

asmith wrote:@ grakmar: I ninja'd your post: it takes 10 more rolls to hit $1B not 4 that changes my outlook considerably.

Damn! You're right. I fail at counting decimal places.

Howard A Treesong wrote:Interesting question. Each time you roll you have 5/6 chance of winning, for which you double your money. That's a pretty good bet.

You winnings would increase -2-4-8-16-32-64...

Your rough (because I've been rounding up decimals) accumulated odds of achieving this would be 83% - 69% - 47% - 23% - 5% - >0%

What a great question. I'm sure I must have heard a question like this before, not because it's familiar, it's just such a good way of illustrating some really important economic principles.

As people have pointed out, it isn't a purely mathematical question because the maths answer is to just keep going, as the expected return grows with every roll. But economics recognises that every dollar you get isn't equal to the one before it, because the first dollar is spent on the thing you most need, the second dollar on the thing you second most need, and so on, until dollar $314,524 is spent on some novelty hat you saw on e-bay that's kind of funny. It's called marginal utility.

So the question becomes 'at what point doubling your money not worth the risk of losing all the dollars that came before'. In my case, I look at what half a million dollars could do to set me up, and I really don't think another half a million after that would be worth the 1/6 risk of losing it all.

But it'd be different for everyone, because of how our needs and wants all differ. Excellent question.

dogma wrote:

Psyker_9er wrote:
We still have hope, and have plenty of room to grow. Those who stick to the laws of others have already given up, and bound by those laws they shall go no further.

Still sticking to the laws of the Beat Generation I see.

Gen-whY?, Beat Generation, Elvis Generation, James Dean, transcendentalism, or what ever you want to call it. The concept of thinking for yourself has been around for a very long time.

Bookwrack wrote:Because if luck was truly an applicable power, the casinos are where you'd see it manifest. If it's an application of will, of need or desire, given the incentives to get the dice to come up in your favor, that is where you'd see it happen, not over a wargame.

This is a good point, and it gave me a funny idea:
What if there has already been some one who studied his luck at casino dice? What if he wanted to publish a book, but the Mafia found out? Or any casino owning organized crime boss for that matter. I might want to be more careful with what I say

hemingway wrote:
so skepticism of scientific conclusions is neither stupid nor should it be ridiculed, because skepticism is precisely what the method is based on. make a claim, prove it, and bob is your uncle. however, when lab B says drug Y doesn't work in spite of what lab A says, and both have lab reports and conclusions supporting the theory, the Pfizer is going to go with lab A's report and publish their results in their ads in People magazine because IT WILL SELL DRUGS.

QFT

We got ourselves a Lab-A and a Lab-B situation here. So for the purpose of this thread, and the topic of this thread only, I will conclude with:
The Realistic Probability of Rolling 6s Continuously is a very low probability. Having said that, I can see and understand how the OP came up with the perceived conclusions that he did.