The Dice - Explained

[Woodruff]

And so on. See what I'm saying?

Well, if you want to prove that the dice number distribution is not uniform, that should be easy: record 10000 rolls on dice analyzer. With that sample size, if there's a significant distortion in the distribution between the dice numbers, then you have a case.

No, dice analyzer will not catch what Haggis is referring to. He is correct in what he is saying. The higher likelihood of any single number appearing DOES help the defense, thanks to the "ties rule". However, as Metsfanmax says, the distortion is so minimal over the course of the 50,000 selection possibilities as to make it essentially irrelevant.

[natty dread]

No, dice analyzer will not catch what Haggis is referring to. He is correct in what he is saying. The higher likelihood of any single number appearing DOES help the defense, thanks to the "ties rule". However, as Metsfanmax says, the distortion is so minimal over the course of the 50,000 selection possibilities as to make it essentially irrelevant.

Dice analyzer also records wins and losses. If this were true, there should be a distortion in the ratios of wins and losses.

Also, the 5 numbers when you roll 5 dice are not picked individually. They are picked in 5 number strings...

[jimboston]

Blah, blah, blah... random, wah... dice suck... hurts me. Blah. Defender's favor. Blah, blab, blab, blah... I want to BITCH some more... blah.

[Haggis_McMutton]

Also, the 5 numbers when you roll 5 dice are not picked individually. They are picked in 5 number strings...

I don't think that matters.

Dice analyzer also records wins and losses. If this were true, there should be a distortion in the ratios of wins and losses.

Would be interesting, though I have to agree the difference is probably negligible.

Blah, blah, blah... random, wah... dice suck... hurts me. Blah. Defender's favor. Blah, blab, blab, blah... I want to BITCH some more... blah.

blah,blah, attempt trolling, blah,blah,blah,fail,blah,blah,leave.

[Woodruff]

Blah, blah, blah... random, wah... dice suck... hurts me. Blah. Defender's favor. Blah, blab, blab, blah... I want to BITCH some more... blah.

Actually, I don't believe this particular thread has the dice-bitchers in it. Or was there a different reason you're trolling here?

[TheForgivenOne]

Blah, blah, blah... random, wah... dice suck... hurts me. Blah. Defender's favor. Blah, blab, blab, blah... I want to BITCH some more... blah.

Good argument. +1 [/sarcasm]

[bedub1]

No, it absolutely is NOT the "definition of random".

Okay, it's not the DEFINITION, but it's definitely the first requirement. Picking a random number between 1 and 3 from this list: 1,2,3,3,3,3 will NEVER result in a random number because 3 is listed so many times. The "pool" isn't uniform.

The non-uniformity is tiny for a sample of 50,000 numbers. This effect is almost entirely irrelevant even if it does exist (which it does not). Besides, as long as it's consistent for all players there's no bias towards anyone.

Close only counts in horseshoes and hand grenades. Something either IS perfectly random, or it's not. This is black and white. 50,000 might seem like alot, until you consider this:

as of June 2010 Conquer Club processes 1,000,000 assaults each day

1 million assaults would be "approximately" 5 dice each time (assuming all the attacks are 3v2). 5 million a day. 50,000 isn't very "big" anymore.

As for the method for dealing with this potential problem, always having equal numbers of 1s through 6s in each document and just randomly generating their position in the document should work.

That would work for picking the 1st number. But what about the 2nd number? Now the pool is no longer uniform, because the 1st number you picked has been excluded from the list.

The way things are done now, the first number picked is definitely not truly random. But what about the 2nd? and 3rd? I think they might be....because all we are doing is reading a list of randomly selected number sequentially...which is how you are supposed to read those documents. It's the Pseudo random number generator picking the first number from a list without proper uniformity that spoils it.

Anyway, this is why I put the poll in. Given that they aren't perfectly random, does anybody care? Do people think that "close" is "good enough"? Or do they demand perfection? Seems to me with all the people bitching they might demand perfection. And claiming something that is "close" is perfect is incorrect.

[Metsfanmax]

Close only counts in horseshoes and hand grenades. Something either IS perfectly random, or it's not. This is black and white. 50,000 might seem like alot, until you consider this:

as of June 2010 Conquer Club processes 1,000,000 assaults each day

1 million assaults would be "approximately" 5 dice each time (assuming all the attacks are 3v2). 5 million a day. 50,000 isn't very "big" anymore.

The number of assaults per day is irrelevant for this argument. We're discussing the "error" created by picking a number for one roll from a finite, non-uniformly-distributed list. For one given roll, 50,000 is indeed a large sample size.

Anyway, this is why I put the poll in. Given that they aren't perfectly random, does anybody care? Do people think that "close" is "good enough"? Or do they demand perfection? Seems to me with all the people bitching they might demand perfection. And claiming something that is "close" is perfect is incorrect.

Even if we accept your argument, the only logical conclusion is that we have to intentionally fix the files so that they're uniformly distributed. That doesn't sound very random to me.

[bedub1]

Anyway, this is why I put the poll in. Given that they aren't perfectly random, does anybody care? Do people think that "close" is "good enough"? Or do they demand perfection? Seems to me with all the people bitching they might demand perfection. And claiming something that is "close" is perfect is incorrect.

Even if we accept your argument, the only logical conclusion is that we have to intentionally fix the files so that they're uniformly distributed. That doesn't sound very random to me.

If the file is uniformly distributed, then the first dice will be truly random. But the 2nd dice won't be. Imagine 12 numbers in the file. The odds would be 2/12 for each number being picked the first time. But after the first number, then the odds for it fall to 1/12 because that number because it is in there twice and ONLY twice. That's where the 2nd requirement of random numbers comes in:

When discussing a sequence of random numbers, each number drawn must be statistically independent of the others.

Seems to me we can use a list of 60,000 numbers with perfectly uniform distribution that has been randomized by random.org, and replace it each hour, and use a Pseudo random number generator to pick a number from 1 to 60k each time we want a dice, and NEVER read anything sequentially.

I don't necessarily have a solution, because it's hard to prove something IS random. It's much easier to prove it's NOT.

[Woodruff]

No, it absolutely is NOT the "definition of random".

Okay, it's not the DEFINITION, but it's definitely the first requirement. Picking a random number between 1 and 3 from this list: 1,2,3,3,3,3 will NEVER result in a random number because 3 is listed so many times. The "pool" isn't uniform.

You are wrong. Absolutely WRONG. As I previously stated, ALL OF THE NUMBERS on a six-sided die could be 1's, and the roll of the die would still pull up a random 1. The idea that there is some requirement for uniformity in order for something to be random is thoroughly non-sensical. In fact, you seem to be the only one making this particular argument. Everyone else has moved on from that to discuss how the non-uniformity ACTUALLY DOES impact things.

Close only counts in horseshoes and hand grenades. Something either IS perfectly random, or it's not. This is black and white.

There is no such thing as "perfectly random" if a computer is making a decision along the process. Computers are not capable of "random", they are only capable of "pseudo-random".

Anyway, this is why I put the poll in. Given that they aren't perfectly random, does anybody care? Do people think that "close" is "good enough"? Or do they demand perfection? Seems to me with all the people bitching they might demand perfection. And claiming something that is "close" is perfect is incorrect.

Even if we accept your argument, the only logical conclusion is that we have to intentionally fix the files so that they're uniformly distributed. That doesn't sound very random to me.

If the file is uniformly distributed, then the first dice will be truly random.

No, it will not be truly random. Because a computer has to pseudo-randomly pick the starting point within the uniformly-distributed file.

When discussing a sequence of random numbers, each number drawn must be statistically independent of the others.

Seems to me we can use a list of 60,000 numbers with perfectly uniform distribution that has been randomized by random.org, and replace it each hour, and use a Pseudo random number generator to pick a number from 1 to 60k each time we want a dice, and NEVER read anything sequentially.

And it still wouldn't be truly random, if that is your goal.

[natty dread]

No, it will not be truly random. Because a computer has to pseudo-randomly pick the starting point within the uniformly-distributed file.

I dispute this.

Just because the starting point is chosen pseudo-randomly, doesn't mean that the numbers actually chosen are not truly random. It doesn't matter which location you read the numbers from a string of truly random numbers, they will be random whether you start from 1 or 50000 or anywhere in between.

[Metsfanmax]

natty_dread is correct: the fact that a PRNG chooses where to start on the list does not alter the randomness of the result. As long as one step in the process is truly random, the entire process is truly random, since it is not possible to predict what the outcome will be from the start.

[bedub1]

No, it absolutely is NOT the "definition of random".

Okay, it's not the DEFINITION, but it's definitely the first requirement. Picking a random number between 1 and 3 from this list: 1,2,3,3,3,3 will NEVER result in a random number because 3 is listed so many times. The "pool" isn't uniform.

You are wrong. Absolutely WRONG. As I previously stated, ALL OF THE NUMBERS on a six-sided die could be 1's, and the roll of the die would still pull up a random 1. The idea that there is some requirement for uniformity in order for something to be random is thoroughly non-sensical. In fact, you seem to be the only one making this particular argument. Everyone else has moved on from that to discuss how the non-uniformity ACTUALLY DOES impact things.

It might be a random "1" but it's not a random number between 1 and 6.

[natty dread]

Actually, yes it is, by definition. 1 is between 1 and 6, therefore a random 1 is a random number between 1 and 6.

[bedub1]

Actually, yes it is, by definition. 1 is between 1 and 6, therefore a random 1 is a random number between 1 and 6.

Then lets play a game. I'll use a 6 sided dice with 6's on each side, and you guys can use a 6 sided dice with 1's on each side.

the word "random" usually means "random with a uniform distribution."

Thus, when I use the word RANDOM, I mean it is random and follows the uniform and perfect distribution of a 6 sided 6-numbered die that is used in the real world.

[natty dread]

Actually, yes it is, by definition. 1 is between 1 and 6, therefore a random 1 is a random number between 1 and 6.

Then lets play a game. I'll use a 6 sided dice with 6's on each side, and you guys can use a 6 sided dice with 1's on each side.

Sure, as long as we'll play with my special rules where 1 beats every other number.

the word "random" usually means "random with a uniform distribution."

Way to quote out of context.

[bedub1]

A random number is a number chosen as if by chance from some specified distribution such that selection of a large set of these numbers reproduces the underlying distribution.

The underlying distribution is 1/6th, because that's the distribution of a die.

I didn't quote out of context, I quoted exactly in context. I offer proof and world-renowned references. Who are you? You aren't arguing with me, but the people I'm quoting.

Is this how you guys are using the word random?

while the term "random" is reserved for the output of unpredictable physical processes

Cause that's just silly...we are talking about dice here.

[natty dread]

You aren't arguing with me, but the people I'm quoting.

That's just so wrong I don't even know where to begin.

I offer proof and world-renowned references.

What proof? Did I miss something?

Who are you?

Hello, my name is argument from authority.


Try this on for size:

http://dictionary.reference.com/browse/random

ran·dom
   /ˈrændəm/ Show Spelled[ran-duhm] Show IPA
–adjective
1.
proceeding, made, or occurring without definite aim, reason, or pattern: the random selection of numbers.
2.
Statistics . of or characterizing a process of selection in which each item of a set has an equal probability of being chosen.

So as you see the definition you use applies to statistics. Statistics are not what we are discussing here. The first definition is for selection of numbers, and it basically says that when there is no predictable pattern to a stream of numbers, it is random.

[bedub1]

Try this on for size:

http://dictionary.reference.com/browse/random

ran·dom
   /ˈrændəm/ Show Spelled[ran-duhm] Show IPA
–adjective
1.
proceeding, made, or occurring without definite aim, reason, or pattern: the random selection of numbers.
2.
Statistics . of or characterizing a process of selection in which each item of a set has an equal probability of being chosen.

So as you see the definition you use applies to statistics. Statistics are not what we are discussing here. The first definition is for selection of numbers, and it basically says that when there is no predictable pattern to a stream of numbers, it is random.

We are in fact talking about statistics. Thus the 2nd definition is correct.

Suppose I roll a die. Is that a statistical experiment?

Yes. Like a coin toss, rolling dice is a statistical experiment. There is more than one possible outcome. We can specify each possible outcome in advance. And there is an element of chance.

[Metsfanmax]

I offer proof and world-renowned references. Who are you? You aren't arguing with me, but the people I'm quoting.

Just for clarity here, never quote any information from Stephen Wolfram if you're looking for an unbiased, objective source.

[bedub1]

I offer proof and world-renowned references. Who are you? You aren't arguing with me, but the people I'm quoting.

Just for clarity here, never quote any information from Stephen Wolfram if you're looking for an unbiased, objective source.

Why? I am looking for that kind of source. Is he not one?

Plus he referenced all this:

Bassein, S. "A Sampler of Randomness." Amer. Math. Monthly 103, 483-490, 1996.

Bennett, D. J. Randomness. Cambridge, MA: Harvard University Press, 1998.

Bratley, P.; Fox, B. L.; and Schrage, E. L. A Guide to Simulation, 2nd ed. New York: Springer-Verlag, 1996.

Dahlquist, G. and Bjorck, A. Ch. 11 in Numerical Methods. Englewood Cliffs, NJ: Prentice-Hall, 1974.

Deak, I. Random Number Generators and Simulation. New York: State Mutual Book & Periodical Service, 1990.

Evans, M.; Hastings, N.; and Peacock, B. Statistical Distributions, 3rd ed. New York: Wiley, p. 5, 2000.

Forsythe, G. E.; Malcolm, M. A.; and Moler, C. B. Ch. 10 in Computer Methods for Mathematical Computations. Englewood Cliffs, NJ: Prentice-Hall, 1977.

Gardner, M. "Random Numbers." Ch. 13 in Mathematical Carnival: A New Round-Up of Tantalizers and Puzzles from Scientific American. New York: Vintage, pp. 161-172, 1977.

James, F. "A Review of Pseudorandom Number Generators." Computer Physics Comm. 60, 329-344, 1990.

Kac, M. "What is Random?" Amer. Sci. 71, 405-406, 1983.

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 200-201 and 205-207, 1962.

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 151-154, 1951.

Knuth, D. E. Ch. 3 in The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 3rd ed. Reading, MA: Addison-Wesley, 1998.

Marsaglia, G. "A Current View of Random Number Generators." In Computer Science and Statistics: Proceedings of the Symposium on the Interface, 16th, Atlanta, Georgia, March 1984 (Ed. L. Billard). New York: Elsevier, 1985.

Marsaglia, G. "DIEHARD: A Battery of Tests for Random Number Generators." http://stat.fsu.edu/~geo/diehard.html.

Mascagni, M. "Random Numbers on the Web." http://archive.ncsa.uiuc.edu/Apps/CMP/R ... w-rng.html.

Niederreiter, H. Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia, PA: SIAM, 1992.

Nijenhuis, A. and Wilf, H. Combinatorial Algorithms for Computers and Calculators, 2nd ed. New York: Academic Press, 1978.

Park, S. and Miller, K. "Random Number Generators: Good Ones are Hard to Find." Comm. ACM 31, 1192-1201, 1988.

Peterson, I. The Jungles of Randomness: A Mathematical Safari. New York: Wiley, 1997.

Pickover, C. A. "Computers, Randomness, Mind, and Infinity." Ch. 31 in Keys to Infinity. New York: W. H. Freeman, pp. 233-247, 1995.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Random Numbers." Ch. 7 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 266-306, 1992.

Schrage, L. "A More Portable Fortran Random Number Generator." ACM Trans. Math. Software 5, 132-138, 1979.

Schroeder, M. "Random Number Generators." In Number Theory in Science and Communication, with Applications in Cryptography, Physics, Digital Information, Computing and Self-Similarity, 3rd ed. New York: Springer-Verlag, pp. 289-295, 1990.

Sloane, N. J. A. Sequence A051023 in "The On-Line Encyclopedia of Integer Sequences."

Weisstein, E. W. "Books about Randomness." http://www.ericweisstein.com/encycloped ... mness.html.

Wilf, H. S. Combinatorial Algorithms: An Update. Philadelphia, PA: SIAM, 1989.

[Metsfanmax]

I offer proof and world-renowned references. Who are you? You aren't arguing with me, but the people I'm quoting.

Just for clarity here, never quote any information from Stephen Wolfram if you're looking for an unbiased, objective source.

Why? I am looking for that kind of source. Is he not one?

I'm being a bit sardonic; it's more of an in-joke for the math crowd.

[natty dread]

We are in fact talking about statistics.

No, we are in fact not.

[Woodruff]

No, it absolutely is NOT the "definition of random".

Okay, it's not the DEFINITION, but it's definitely the first requirement. Picking a random number between 1 and 3 from this list: 1,2,3,3,3,3 will NEVER result in a random number because 3 is listed so many times. The "pool" isn't uniform.

You are wrong. Absolutely WRONG. As I previously stated, ALL OF THE NUMBERS on a six-sided die could be 1's, and the roll of the die would still pull up a random 1. The idea that there is some requirement for uniformity in order for something to be random is thoroughly non-sensical. In fact, you seem to be the only one making this particular argument. Everyone else has moved on from that to discuss how the non-uniformity ACTUALLY DOES impact things.

It might be a random "1" but it's not a random number between 1 and 6.

Oh, so close! You've almost caught on to what is wrong with your statements...but you just didn't quite get there. Keep trying...we'll get you there yet!

[MNDuke]

We are in fact talking about statistics.

No, we are in fact not.

Um, pretty sure we are. Everything about this is derived from statistics. It changes the odds when you increase your chances of rolling one number over another.