New "Intensity Cubes"

[Dako]

Do you know that the six die on the dice is lighter and odds of it going up are more than 1/6?

Yes, 500k is easier to maintain because it gives more precise random distribution and it is easier to use it as an array of numbers, rotating, shuffling and rewinding them. And it is not normal so it won't be 83.(3) of each number.

[danfrank]

EDIT: If you have a list of 500k random numbers, then you need exactly 83,333.333333... of each number in order to maintain your probability of 1 out of 6. If your random list of numbers doesn't have a perfect distribution between the numbers(which it won't since it's random), then the odds won't be correct.

This is an interesting point that was raised.. im curious to how the so called MODS will address this issue ..

[Dako]

Easy. If you want 500k numbers to have an equal amount of all numbers (1..6) then such a list will not be random anymore. Because random is a concept of non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination.

And yes, odds are not correct (what is correct anyway?) - they are random.

[bedub1]

Easy. If you want 500k numbers to have an equal amount of all numbers (1..6) then such a list will not be random anymore. Because random is a concept of non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination.

And yes, odds are not correct (what is correct anyway?) - they are random.

Yes, but random and correct are not the same thing. The odds for the dice MUST remain 1 out of 6 else the dice are rigged.

[carlpgoodrich]

Easy. If you want 500k numbers to have an equal amount of all numbers (1..6) then such a list will not be random anymore. Because random is a concept of non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination.

And yes, odds are not correct (what is correct anyway?) - they are random.

Yes, but random and correct are not the same thing. The odds for the dice MUST remain 1 out of 6 else the dice are rigged.

No, you are not understanding the concept. Before the list is generated by random.org, there is exactly a 1/6 probability that each number will be a 1, or a 2, etc. However, that does not mean that exactly one sixth of the numbers end up being a 1, 2, etc. So any given file will have an uneven distribution, but it is still a correct sample of random numbers. It is both random and correct.

You are worried about the fact that, since in a given file there might be a lot more 6's (for example), therefore as long as that file is used the dice will be "rigged." As sound as that argument seems, it is simply not correct. The excess of 6's is simply a product of natural fluctuations in random numbers. To make this point more clear, lets pretend we want a list of 6 random numbers, each with a integer value between 1 and 6. Say the first one is randomly chosen to be a 1. If we force the proportions to be the same, then no number can appear twice, so the second number would have a 1/5 probability of being a 2, 3, 4, 5, 6, since it can not longer be a 1. However, random numbers must be entirely independent of any past or future events, so the restriction that the proportions be the same breaks the randomness of the numbers.

I hope this helps. Random numbers are a fascinating subject, and I would be more that happy to discuss this in more detail if anyone wants.

[bedub1]

Easy. If you want 500k numbers to have an equal amount of all numbers (1..6) then such a list will not be random anymore. Because random is a concept of non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination.

And yes, odds are not correct (what is correct anyway?) - they are random.

Yes, but random and correct are not the same thing. The odds for the dice MUST remain 1 out of 6 else the dice are rigged.

No, you are not understanding the concept. Before the list is generated by random.org, there is exactly a 1/6 probability that each number will be a 1, or a 2, etc. However, that does not mean that exactly one sixth of the numbers end up being a 1, 2, etc. So any given file will have an uneven distribution, but it is still a correct sample of random numbers. It is both random and correct.

You are worried about the fact that, since in a given file there might be a lot more 6's (for example), therefore as long as that file is used the dice will be "rigged." As sound as that argument seems, it is simply not correct. The excess of 6's is simply a product of natural fluctuations in random numbers. To make this point more clear, lets pretend we want a list of 6 random numbers, each with a integer value between 1 and 6. Say the first one is randomly chosen to be a 1. If we force the proportions to be the same, then no number can appear twice, so the second number would have a 1/5 probability of being a 2, 3, 4, 5, 6, since it can not longer be a 1. However, random numbers must be entirely independent of any past or future events, so the restriction that the proportions be the same breaks the randomness of the numbers.

I hope this helps. Random numbers are a fascinating subject, and I would be more that happy to discuss this in more detail if anyone wants.

When you roll a real dice, the probability of rolling any number is 1 out of 6. When random.org builds the file, it is populated based upon this. When I attack, the probability that I receive any number MUST REMAIN 1 out of 6. Once the file is created, it can be analyzed, and probabilities determined. If the file isn't evenly distributed, then the probability of pulling a number won't remain 1 out of 6. It was 1 out of 6 when you built the file, but now it's 8954 out of 50000 for 1's, and 8936 for 2's, and etc....

EDIT: Maybe this from random.org will help

"When discussing single numbers, a random number is one that is drawn from a set of possible values, each of which is equally probable, i.e., a uniform distribution. When discussing a sequence of random numbers, each number drawn must be statistically independent of the others."

So I'm talking about the single numbers that I get when I roll dice. Everybody else is talking about the list. Of course the list is random, I agree with that. But it doesn't mean the single numbers that I pull from the list are, and doesn't mean that the way we pull numbers from the list is "proper".

Maybe we should use a pseudo random number generator to pick a spot from the true random number generator list for every dice roll and not read anything sequentially. I think we would need a file of 60,000 numbers, each number being represented 10,000 times, but they are all mixed up and arranged randomly within the file.

[natty dread]

Maybe we should use a pseudo random number generator to pick a spot from the true random number generator list for every dice roll and not read anything sequentially.

We are already doing that. You apparently missed lack's announcement about it.

[bedub1]

Maybe we should use a pseudo random number generator to pick a spot from the true random number generator list for every dice roll and not read anything sequentially.

We are already doing that. You apparently missed lack's announcement about it.

No...he reads the next 4 numbers sequentially... and that file doesn't have an even distribution as it's random....so the single numbers we pick aren't random.

Each number in the list of random numbers is a random number until it comes time for me to choose it. At that point when I choose a number, it's not really a random number because of the way I have picked it. Read random.org again...."a random number is one that is drawn from a set of possible values, each of which is equally probable, i.e., a uniform distribution." When I choose a number i'm not picking it from a set of possible values with uniform distribution, because the list doesn't have uniform distribution, because it's random.

[carlpgoodrich]

bedub1, a uniform distribution does not mean that every number appears the same number of times. It means that the probability of any number being a 1 is the same as it being a 2, etc., which is exactly what we have.

You made a comment earlier:

If you guys love this list full of random numbers so much, then next time you play risk in real life or maybe yahtzee, try to convince all your friends to give up on the dice and just use the list of random numbers instead. Try and convince them that it's the same.

The thing is is that they ARE EXACTLY THE SAME! Rolling dice is just a way to produce a list of random numbers.

Let's try this another way: Say you are playing Risk with your friends, and you record every dice thrown during the game. After the game, you look at your notes and see that there were a lot more 5's than 2's. Your friend, who's butt you just kicked, says "hey, no fair! The dice were not really random! I demand a rematch." I think we would all disagree with the friend, but since rolling dice is just a way to produce a random list, as is going to Random.org, this argument is the same as yours.

[carlpgoodrich]

Or here's another way to look at it: Instead of having a list of 50,000 numbers, lets say we use a list of 1 number and then get a new one every time you roll. Even though the lists we would be using would certainly not have the same number of 1's, 2's, etc., I'm pretty sure you would agree this is random. Now, what if we used lists of 2 numbers? Still random? What about 5? 10? 50,000? At what point does the fact that we import the list and then read them off differ from importing them as we need them?

[Dako]

Wanted to write a long post but when I reread it it looked pointless. Here is the sort version:
Everyone on this site uses the same dice mechanism. So even if it is flawed - it is equal for everyone.

[mpjh]

I like that -- sorta like the football team all being screwed by the same girl. Everybody get the same stds.

[bedub1]

bedub1, a uniform distribution does not mean that every number appears the same number of times. It means that the probability of any number being a 1 is the same as it being a 2, etc., which is exactly what we have.

You made a comment earlier:

If you guys love this list full of random numbers so much, then next time you play risk in real life or maybe yahtzee, try to convince all your friends to give up on the dice and just use the list of random numbers instead. Try and convince them that it's the same.

The thing is is that they ARE EXACTLY THE SAME! Rolling dice is just a way to produce a list of random numbers.

Let's try this another way: Say you are playing Risk with your friends, and you record every dice thrown during the game. After the game, you look at your notes and see that there were a lot more 5's than 2's. Your friend, who's butt you just kicked, says "hey, no fair! The dice were not really random! I demand a rematch." I think we would all disagree with the friend, but since rolling dice is just a way to produce a random list, as is going to Random.org, this argument is the same as yours.

A uniform distribution does in fact mean that every number appears the same number of times. That's what a uniform distribution is. http://davidmlane.com/hyperstat/A12237.html

After you and your friend collected that list, and realized there were more 5's than 2's, would you be willing to play another game using that list as the source for your dice? No, you would want to use a dice with an even distribution as your list.

Think of it another way. Each dice has a uniform distribution, but the lists we get from random.org don't.

[carlpgoodrich]

After you and your friend collected that list, and realized there were more 5's than 2's, would you be willing to play another game using that list as the source for your dice? No, you would want to use a dice with an even distribution as your list.

A list that requires there to be equal amounts of each number cannot be random! Every number in a list of random numbers must be independent of all other numbers. If you impose the requirement that the amounts must be equal then (at least) the last number is completely determined. In math there is a difference between a probability distribution (which is uniform, leading to random numbers) and a sample of that distribution.

I will try to explain this again using examples: lets say we want to flip a coin twice. The probability distribution is uniform (each flip has a 50% chance of being heads). The possible outcomes are HH, HT, TH, TT, each with a 25% chance of happening. There is no requirement that both come up once. Same logic applies of making a list of 50,000 random numbers between 1 and 6.

Now, I think the point that you are still clinging to is that by writing out the numbers first and then reading from them we are somehow losing the randomness. But this is not correct because it is still a list of random numbers. If, of course, the list was visible to every then it would be a bad system, but it would still be a list of random numbers, and every time you chose a number it would be independent of any previous number.

I am trying very hard not to sound like an asshole, and I really do want to make this clear. Let me refer you to an undergraduate text book I used back in the day on probability and statistics (DeGroot and Schervish. Probability and Statistics, Third Ed. Addison-Wesley, 2002. ISBN 0-321-20473-5.), specifically Ch. 3 and 4.

[natty dread]

Maybe we should use a pseudo random number generator to pick a spot from the true random number generator list for every dice roll and not read anything sequentially.

We are already doing that. You apparently missed lack's announcement about it.

No...he reads the next 4 numbers sequentially... and that file doesn't have an even distribution as it's random....so the single numbers we pick aren't random.

I have changed the way the dice work once again, it should now be theoretically impossible to cheat:

This is how the intensity cubes now work:

* We have a series of 50,000 true random numbers from random.org
* Each time the game engine processes an assault or auto-assault, it select a random spot in the series to read from using a pseudo-random computer function
* Each time the game engine generates a random intensity cube, the next number is read in sequence from the series (e.g. in a 3v1 attack 4 numbers are read sequentially)
* The series of 50,000 true random numbers from random.org is replaced every hour

SEE? SEE?!?!?!? I bet you feel stupid right now.

[Night Strike]

Think of it another way. Each dice has a uniform distribution, but the lists we get from random.org don't.

The thing is, if you want the computer to "roll" each dice on its own every time you roll, I guess you can add several seconds to every turn waiting for the dice. That's if it doesn't hang from having 100 other turns going on at the same time. There's a trade-off on every system, and as far as I can tell, these dice are as good as you're going to get in a virtual world.

[bedub1]

Maybe we should use a pseudo random number generator to pick a spot from the true random number generator list for every dice roll and not read anything sequentially.

We are already doing that. You apparently missed lack's announcement about it.

No...he reads the next 4 numbers sequentially... and that file doesn't have an even distribution as it's random....so the single numbers we pick aren't random.

I have changed the way the dice work once again, it should now be theoretically impossible to cheat:

This is how the intensity cubes now work:

* We have a series of 50,000 true random numbers from random.org
* Each time the game engine processes an assault or auto-assault, it select a random spot in the series to read from using a pseudo-random computer function
* Each time the game engine generates a random intensity cube, the next number is read in sequence from the series (e.g. in a 3v1 attack 4 numbers are read sequentially)
* The series of 50,000 true random numbers from random.org is replaced every hour

SEE? SEE?!?!?!? I bet you feel stupid right now.

(e.g. in a 3v1 attack 4 numbers are read sequentially)

[bedub1]

I will try to explain this again using examples: lets say we want to flip a coin twice. The probability distribution is uniform (each flip has a 50% chance of being heads). The possible outcomes are HH, HT, TH, TT, each with a 25% chance of happening. There is no requirement that both come up once. Same logic applies of making a list of 50,000 random numbers between 1 and 6.

I agree with you. But think of this. HH is a list of random coin flips. HT is the same. So are TH, and TT. But would you want to use TT as the list from which to draw? No, you can't, because the list isn't uniform, and thus any flips you draw from it won't be random, because there is 100% chance of getting a T and a 0% chance of getting an H.

Read this from random.org again:

When discussing single numbers, a random number is one that is drawn from a set of possible values, each of which is equally probable, i.e., a uniform distribution. When discussing a sequence of random numbers, each number drawn must be statistically independent of the others.

So a random number must be drawn from a list with uniform distribution. IE You can use 123456 as a list to draw from, or 112233445566, but you can't use 11223445566. This distribution of the numbers has to be 1/6th.

To create a list of random numbers they must be statistically independent of each other. IE 123456 probably isn't random a list of random numbers, but 124435 might be.

I agree the list we get is random. But we can't draw from a list of random numbers, we have to draw randomly from a list with uniform distribution in order to get a random number. We don't want a list of random numbers, we want random numbers.

[Dako]

List of random numbers === random numbers. So to get a random number you are allowed to draw it from the list of random numbers because they are all random in that list!

What is the problem? You want uniform distribution to get a random odd in the end. Current system already gives you a random odd each time you query the list.

[carlpgoodrich]

I will try to explain this again using examples: lets say we want to flip a coin twice. The probability distribution is uniform (each flip has a 50% chance of being heads). The possible outcomes are HH, HT, TH, TT, each with a 25% chance of happening. There is no requirement that both come up once. Same logic applies of making a list of 50,000 random numbers between 1 and 6.

I agree with you. But think of this. HH is a list of random coin flips. HT is the same. So are TH, and TT. But would you want to use TT as the list from which to draw? No, you can't, because the list isn't uniform, and thus any flips you draw from it won't be random, because there is 100% chance of getting a T and a 0% chance of getting an H.

Read this from random.org again:

When discussing single numbers, a random number is one that is drawn from a set of possible values, each of which is equally probable, i.e., a uniform distribution. When discussing a sequence of random numbers, each number drawn must be statistically independent of the others.

So a random number must be drawn from a list with uniform distribution. IE You can use 123456 as a list to draw from, or 112233445566, but you can't use 11223445566. This distribution of the numbers has to be 1/6th.

To create a list of random numbers they must be statistically independent of each other. IE 123456 probably isn't random a list of random numbers, but 124435 might be.

I agree the list we get is random. But we can't draw from a list of random numbers, we have to draw randomly from a list with uniform distribution in order to get a random number. We don't want a list of random numbers, we want random numbers.

Ok, I'm going to try this one more time and then you are just going to have to go take a math class. When you say "draw from a list" what you mean is pick a number at random from a list. So in that sense having 123456 makes sense. But how do you pick the random way in which you draw from the list? You need a random number to do this. What we do is have random.org pick a number between 1 and 6 (you can think of it as drawing "randomly" from 123456 if that floats your boat). This number will be used for a roll. Only, instead of going to random.org every time the dice are thrown, we go to them and get 50,000 numbers, then just read them off as needed. Please trust that this is the same thing.

Anyways, I'm tired of explaining the same thing over and over. At first I thought you were genuinely interested in figuring this out, but recently it just seems that you are convinced you are right and are not putting any effort into understanding it.

[lackattack]

I'm going to take a shot at explaining this

bedub1, you feel that since the numbers are read from a list which may not have equal counts of 1,2,3 etc the source is not random, right?

Well don't think of that list as the source, because it isn't. The source is still random.org. The list is more like a "buffer" to temporarily hold the numbers before we use them. We do this because it is much more efficient to pre-generate the numbers in a batch.

Yes, the buffer won't have equal counts of 1,2,3 etc but that doesn't matter if you realize it is not the source. If you roll a 3v2, maybe God knows in advance that it will be 6,6,3 v 2,5. Does it make your roll less random because God knows the attacker will get two 6's? Of course not! Same logic applies if your rolls are generated in advance and temporarily stored in a buffer.

Granted, the list is not read from beginning to end like a real buffer, but I don't think that makes a difference.

I of course agree it would be nicer to generate each number of the fly and not pre-generate in batches, but that would be impossible for a website this big unless we used computer-generated pseudo-random numbers which would be a huge step backwards in my opinion. I think the current dice are indeed random and all the dice analyzer and streak analyzer data people are collecting will continue to prove that.

[bedub1]

I'm going to take a shot at explaining this

bedub1, you feel that since the numbers are read from a list which may not have equal counts of 1,2,3 etc the source is not random, right?

Well don't think of that list as the source, because it isn't. The source is still random.org. The list is more like a "buffer" to temporarily hold the numbers before we use them. We do this because it is much more efficient to pre-generate the numbers in a batch.

Yes, the buffer won't have equal counts of 1,2,3 etc but that doesn't matter if you realize it is not the source. If you roll a 3v2, maybe God knows in advance that it will be 6,6,3 v 2,5. Does it make your roll less random because God knows the attacker will get two 6's? Of course not! Same logic applies if your rolls are generated in advance and temporarily stored in a buffer.

Granted, the list is not read from beginning to end like a real buffer, but I don't think that makes a difference.

I of course agree it would be nicer to generate each number of the fly and not pre-generate in batches, but that would be impossible for a website this big unless we used computer-generated pseudo-random numbers which would be a huge step backwards in my opinion. I think the current dice are indeed random and all the dice analyzer and streak analyzer data people are collecting will continue to prove that.

Random numbers cannot be picked randomly from a list of random numbers. Random numbers must be picked randomly from a list with uniform distribution.

So here is how to accomplish it and avoid cheaters.

File1. Get a list of numbers 1 to 6, each number repeated 10,000 times. The list will have 60,000 numbers in it. Randomize its order. This has uniform distribution, and is our pool of numbers. IE our DICE.
File2. Get a list of numbers 1 to 60,000, 600,000 long. Each number would be in there 10 times if it had uniform distribution, but it won't, because it's a random list. This list is how you choose which dice you get.

When a dice number is needed, read the next line from file2. It has a number, go read that spot from file1. That's your dice.

You can replace either file whenever you want, or just re-randomize file1, and replace file2. You can read sequentially, because sequentially is randomly. You don't have to use the pseudo number generator either.

Now we will have a list with uniform distribution with which to draw our random numbers, fulfilling the requirements of random numbers.

Oh, and I don't appreciate the attitude of some people here. I'm trying to be polite and explain myself. I took statistics in college, and calculus for engineers etc. No need to get rude when discussing this. I actually enjoy it. Random numbers are fascinating!

[AndyDufresne]

I've had enough intensity cube talk, I don't think I can digest anymore.


--Andy

[natty dread]

Random numbers cannot be picked randomly from a list of random numbers. Random numbers must be picked randomly from a list with uniform distribution.

[Dako]

Ok, I see your method. Let me try to make a small example visualizing your method.

We have a list of 111222333444555666. We shuffle it and get 465463152341162235 which is a uniform distribution (18 numbers there).
We generate 40 numbers from 1 to 18. We get a long list 7, 5, 12, 15, 9, 6, 4, 17, 8, 12, 9, 7, 4, 3, 1, 13, 8, 5, 1, 9, 8, 16, 2, 2, 6, 6, 14, 1, 18, 11, 8, 7, 16, 1, 3, 6, 7, 7, 4, 15.

After that we sequentially read the second list and pick numbers from 1st file. Lets say we need 10 numbers only. We will get 1, 6, 1, 2, 2, 3, 4, 3, 5, 1.

This algorithm describes your method and gives a visual example. Am I correct? And we can reuse the last 10 numbers over and over again because they were achieved pretty random. Right?

Do you know what your method produces in the end? He produces a list of random numbers. Which is exactly a mechanism CC is using right now. But we just don't need to generate that list of random numbers because they are generated for us by random.org site.

Do you understand what I am trying to say here?

Also, please refer to say like "random numbers must be picked randomly from a list" because it doesn't make sense at all - you need a random number to pick a random number. For that you need a random number which can be picked with random number. To get the last random number you need a random number as well. And so on. This is called recursion if it rings the bell.