Discussion of Statistical records of users dice results

[e_i_pi]

This thread is intended for any discussion surrounding the Statistical records of users dice results thread.

Please try to discuss the results only, I do not want this thread merged with the astronomically large All dice complaint threads [merged] thread.

Regards,
e_i_pi

[bigimg]http://i285.photobucket.com/albums/ll71/e_i_pi/2209Dice.jpg[/bigimg]

[rabbiton]

moved comment to other thread, per the RULES.

my statistical record of dice is perfect. all 6s.

[rabbiton]

i don't think anyone who is at minimum borderline sentient is questioning the distribution of dice rolls. in part because the data is easy to collect and clearly shows that said distribution is statistically acceptable. even the feeblest of man-mouse brains can see that right?

what the borderline to marginally sentient folks can more easily question are the sequences of rolls... which is somewhat harder a complaint to quell as most people cannot even approximate such a statistical test with their brains.

but there are statistical tests to do exactly this and i don't know why someone just doesn't go and run them.

[Frop]

what the borderline to marginally sentient folks can more easily question are the sequences of rolls... which is somewhat harder a complaint to quell as most people cannot even approximate such a statistical test with their brains.

Why are you stealing my good dice sequences?

[Kemmler]

you'd wonder why dice results even out over time. If they're random, they shouldn't be predictable. Obviously the more your roll the more accurate, but I still don't understand probability....

[wcaclimbing]

but there are statistical tests to do exactly this and i don't know why someone just doesn't go and run them.

Here's a nice quote from Twill with lots of information:

Tests that have been run on random.org data:
* Frequency Test: Monobit
* Frequency Test: Block
* Runs Test
* Test for the Longest Runs of Ones in a Block
* Binary Matrix Rank Test
* Discrete Fourier Transform (Spectral Test)
* Non-Overlapping Template Matching Test
* Overlapping Template Matching Test
* Maurer's Universal Statistical Test
* Linear Complexity Test
* Serial Test
* Approximate Entropy Test
* Cumulative Sums Test
* Random Excursions Test
* Random Excursions Variant Test
* A chi-square test
* A test of runs above and below the median
* A reverse arrangements test
* An overlapping sums test
* A binary rank test for 32×32 matrices

The document pluto linked to is 107 pages of graduate level mathematician thesis work proving the randomness of random.org

I personally started running Magdoogles battery of tests but our dice file was too big and crashed my computer so I didn't try again

And the M guy isn't THE DEFINITIVE SOURCE for random stuff...the NIST battery of tests (provided by the ever so efficient US gov't) is just as highly respected and incorporates some of Mdoodle's tests.

Random.org passed all of those tests.

If you need visual aids:

Random but not "realistically random" should be debunked by this:
which shows the output of all the files are relatively evenly distributed within expected random variation. If the dice weren't "realistically" random, the tops of the different colour bars wouldn't come so close to matching.

If you'd rather us use a pseudo-random number generator, without spending millions of dollars (because we all know we're ROLLING in cash charging what we do) we could always use the built in rand () function in PHP...but then we'd get something like the image on the right...

On the left is random.org...one seems a little more random than the other, no?

Granted, these have been provided by random.org...but I have personally watched some of the dice's most ardent critics (who are actually mathematicians) run analyses on the dice and come up with the same conclusion.

You roll thousands and thousands of dice here. Hulmey, you have personally probably rolled more than 50,000 dice here (762 games, assuming 10 rounds per game, 3 rolls per round, 2 dice per roll...at a conservative guess). How many do you think you have rolled in real life?

Yes, you WILL see odd combinations and streaks here but you also play a LOT more games and roll a LOT more dice meaning you a re a LOT more likely to see them.

Again, if anyone can give me a test they want me to run on the file, please, do send it to me, I'd be happy to run it for you to prove once and for all that the dice are random.

[e_i_pi]

i don't think anyone who is at minimum borderline sentient is questioning the distribution of dice rolls. in part because the data is easy to collect and clearly shows that said distribution is statistically acceptable. even the feeblest of man-mouse brains can see that right?

I have been arguing that the dice are fairly distributed for a long time. The main reason I have had to argue this is that so many people complain about the amount of 6s the defence rolls. This is why I'm posting these stats. So no, there are in fact some man-mouse brains to febrile to grasp this.

what the borderline to marginally sentient folks can more easily question are the sequences of rolls... which is somewhat harder a complaint to quell as most people cannot even approximate such a statistical test with their brains.

If someone comes up with a plugin that records every dice roll, I'm quite happy to do statistical analysis on sequences. Unfortunately a plugin like that doesn't exist (yet), which may be why people are complaining about that - ie - they cannot be factually proven or rebuffed. It is very easy to take a stance that cannot be scientifically proven one way or the other.

but there are statistical tests to do exactly this and i don't know why someone just doesn't go and run them.

These tests have been done by the mods I believe. I am not a mod, but I have sufficient mathematical know-how to do them, so I am an independant tester if you will. All I'm doing is demonstrating what the dice are showing for the community that participates in this. The Law of Large Numbers states that as your sample size approaches infinity, the average of the random variables should approch the mean value (in this case, 3.5). If people are allowed to argue that one case of 15v3 -> 5v3 is 'proof' that the dice are bad, then surely I am allowed to prove, using as many million dice rolls as I can get my hands on and a globally accepted scientific law, that the dice are fine.

[e_i_pi]

you'd wonder why dice results even out over time. If they're random, they shouldn't be predictable. Obviously the more your roll the more accurate, but I still don't understand probability....

Dice even out over time because of the Law of Large Numbers. That link explains it, and also gives a nice little graph demonstrating it.

The graph to the right plots the results of an experiment of rolls of a die. In this experiment we see that the average of die rolls deviates wildly at first. As predicted by LLN the average stabilizes around the expected value of 3.5 as the number of observations becomes large.
.....
The LLN is important because it "guarantees" stable long-term results for random events.
.....
It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered.

It's also important to remember that probability and predictability aren't the same thing.
Probability states that if I roll 1 die, I have a 1 in 6 chance of any particular number coming up. But you cannot say what number will come up.
LLN states that if I roll 6 million dice, there will be about 1 million of any one number. But you cannot say for certain exactly how many will come up.

[t-o-m]

-reserved for me-

[e_i_pi]

Currently, 10 users have submitte dtheir dice results. 3 are large samples, 4 are moderate samples, 3 are small samples. More samples of all sizes are required, so if you have Dice Analyser, please post your stats on the sticky thread titled Statistical records of users dice results. If you are unsure how to do this, PM me, it's quite easy to explain.

[waseemalim]

The normal distribution is a terrible model for fitting real events. It looks good in theory, but in reality random events tend to have much fatter tails. You ll be better off using a cauchy distribution. http://en.wikipedia.org/wiki/Cauchy_distribution


Your sample size is fine. May be a few more 1v1 stat...

[dividedbyzero]

Currently, 10 users have submitte dtheir dice results. 3 are large samples, 4 are moderate samples, 3 are small samples. More samples of all sizes are required, so if you have Dice Analyser, please post your stats on the sticky thread titled Statistical records of users dice results. If you are unsure how to do this, PM me, it's quite easy to explain.

Do you want us to tell you when we update our stats ? Or will you be going through and looking every few days ?

[Robinette]

.
Oh Oh Oh... i have something to say about the dice...

Ohhh.... noooooooo.... i forgot... i can't... i just can't.....
I promised to keep it a secret...
[bigimg]http://farm3.static.flickr.com/2163/2053248490_f86f0cda8c.jpg?v=0[/bigimg]

heheeehee

[Frop]

.
Oh Oh Oh... i have something to say about the dice...

Ohhh.... noooooooo.... i forgot... i can't... i just can't.....
I promised to keep it a secret...

heheeehee

Can't you spam all those huge girly pictures in some Off-Topic tread instead? Stop wasting space.

[e_i_pi]

Currently, 10 users have submitte dtheir dice results. 3 are large samples, 4 are moderate samples, 3 are small samples. More samples of all sizes are required, so if you have Dice Analyser, please post your stats on the sticky thread titled Statistical records of users dice results. If you are unsure how to do this, PM me, it's quite easy to explain.

Do you want us to tell you when we update our stats ? Or will you be going through and looking every few days ?

I check it every day or two. No need to tell me when you update

[e_i_pi]

The normal distribution is a terrible model for fitting real events. It looks good in theory, but in reality random events tend to have much fatter tails. You ll be better off using a cauchy distribution. http://en.wikipedia.org/wiki/Cauchy_distribution

Your sample size is fine. May be a few more 1v1 stat...

I'm not sure what you mean by 'fatter tails'. Also, I'm not sure how you suppose Cauchy Distribution can be applied to a discrete random variable. Die rolls use probability mass, not probability density. I'm aiming to use the data to demonstrate adherence to the Central Limit Theorem, and also conduct Z-testing. I'm only using the distribution of the attacking and defending dice for now too, not battle outcomes.

[Frop]

The normal distribution is a terrible model for fitting real events. It looks good in theory, but in reality random events tend to have much fatter tails. You ll be better off using a cauchy distribution. http://en.wikipedia.org/wiki/Cauchy_distribution

Your sample size is fine. May be a few more 1v1 stat...

I'm not sure what you mean by 'fatter tails'. Also, I'm not sure how you suppose Cauchy Distribution can be applied to a discrete random variable. Die rolls use probability mass, not probability density. I'm aiming to use the data to demonstrate adherence to the Central Limit Theorem, and also conduct Z-testing. I'm only using the distribution of the attacking and defending dice for now too, not battle outcomes.

You're using a lot of mathematical lingo I'm obviously not familiar with and the same goes for the Excel sheet you posted in the main thread. Would it be possible to elaborate slightly on what they all mean and why they're 'good' or 'bad'? You don't have to dumb it down too much, it has just been a while.

[e_i_pi]

You're using a lot of mathematical lingo I'm obviously not familiar with and the same goes for the Excel sheet you posted in the main thread. Would it be possible to elaborate slightly on what they all mean and why they're 'good' or 'bad'? You don't have to dumb it down too much, it has just been a while.

Yep, I plan on making it all a little more layman friendly, I'm at work atm though, just reading the replies and responding where I can.

[Robinette]

.
Oh Oh Oh... i have something to say about the dice...

Ohhh.... noooooooo.... i forgot... i can't... i just can't.....
I promised to keep it a secret...

heheeehee

Can't you spam all those huge girly pictures in some Off-Topic tread instead? Stop wasting space.

Awww... that was supposed to make you smile...

Would you really rather that i actually post my dice hack thread instead?


I thought not.

[Bruceswar]

Attackers dice exsist with the Auto attack. Trust me I know.. Look at my stats...

[rabbiton]

The normal distribution is a terrible model for fitting real events. It looks good in theory, but in reality random events tend to have much fatter tails. You ll be better off using a cauchy distribution. http://en.wikipedia.org/wiki/Cauchy_distribution

Your sample size is fine. May be a few more 1v1 stat...

I'm not sure what you mean by 'fatter tails'. Also, I'm not sure how you suppose Cauchy Distribution can be applied to a discrete random variable. Die rolls use probability mass, not probability density. I'm aiming to use the data to demonstrate adherence to the Central Limit Theorem, and also conduct Z-testing. I'm only using the distribution of the attacking and defending dice for now too, not battle outcomes.

fatter tails means the distribution has more probability mass in its tails, rolls off less quickly... but the fact is that what you're doing is going to be as gaussian as all get out by the clt... although i still say it's a dandy lot of effort and falootin' conversationin' about something that is not really going to help. produce all the proof in the world and people will still say the system is biased against them personally. somehow.

[e_i_pi]

The normal distribution is a terrible model for fitting real events. It looks good in theory, but in reality random events tend to have much fatter tails. You ll be better off using a cauchy distribution. http://en.wikipedia.org/wiki/Cauchy_distribution

Your sample size is fine. May be a few more 1v1 stat...

I'm not sure what you mean by 'fatter tails'. Also, I'm not sure how you suppose Cauchy Distribution can be applied to a discrete random variable. Die rolls use probability mass, not probability density. I'm aiming to use the data to demonstrate adherence to the Central Limit Theorem, and also conduct Z-testing. I'm only using the distribution of the attacking and defending dice for now too, not battle outcomes.

fatter tails means the distribution has more probability mass in its tails, rolls off less quickly... but the fact is that what you're doing is going to be as gaussian as all get out by the clt... although i still say it's a dandy lot of effort and falootin' conversationin' about something that is not really going to help. produce all the proof in the world and people will still say the system is biased against them personally. somehow.

That's what I believe too, but it's good to have something official on the forums for people to reference anyhow

[e_i_pi]

Updated stats are up, now with added laymans graph!

[Frop]

Updated stats are up, now with added laymans graph!

Thanks! I'm just a bit disappointed we've got a zillion people bitching about the dice, but hardly anyone has bothered to contribute.

[hulmey]

Guys, you will never find your answer. We can go on on and on but there are so many variables! When im playing 1 vs 1 i like to spread my deplpoyment so i attack 4 vs 3....I find that more often than not i lose 2 straight rolls when doing this. Could it be that the dice favour higher stacks when rolling? Its just a question to show you how many variables there actually are