Randomisation

[yeti_c]

A query for you MrBenn...

How would you read from your new matrix?

Would you randomly read a column from the row for each dice?

If so - Where do you get the random read from?

My point - which I'm sure people will have missed - is that the earlier example (Where data is parsed into preassigned rolls) is more random as you are only assigning the random data once...

In your instance - you would need to read from your new matrix "randomly" using the PHP random number generator... which is distinctly less random than random.org... Thus making that method more constrained and less random...

C.

Yeti_c, my intention was to read the numbers from the matrix sequentially, but only when each dice is rolled... (rather than getting numbers and discarding them when attacking/defending with 1, for example)

Ah I see - there is a flaw here too though...

As the first dice of each (A1, D1) would be read more often than the others?

C.

[MrBenn]

Yes, you're right, but each dice has it's own random list of numbers, so the impact of this would be minimal... It's like saying "I prefer to use my blue (fair) dice to my green (fair) dice...

The length of the random-number-lists doesn't need to be the same for each dice... but if the number-lists get 'out-of-synch', the combination of dice will be less deterministic, with more random variables such as the total number/types of attacks, rather than always keeping 5 consecutive numbers together...

[MeDeFe]

Yes, you're right, but each dice has it's own random list of numbers, so the impact of this would be minimal... It's like saying "I prefer to use my blue (fair) dice to my green (fair) dice...

The length of the random-number-lists doesn't need to be the same for each dice... but if the number-lists get 'out-of-synch', the combination of dice will be less deterministic, with more random variables such as the total number/types of attacks, rather than always keeping 5 consecutive numbers together...

True, the 1st dice of the attacker and defender will appear more often than the second, which will appear more often than the attacker's third.
But even so, with 100k numbers per dice, I think the overall effect is minimal.

[Death To All]

Ok,

There is no memory with the dice. Your arguments are flawed. Why? Let me explain.

The theory that the list gets stale, that the probability changes when a large percentage of the list is used up, would be vailid if this was a deck of cards. If you have only 2 cards left in the deck and never saw the Ace of spades and two of hearts, you have a 50% probability of each.

The list CC uses is composted of numbers taken out of thin air (literally). Lets say 499,998 dice rolls have been used and only 2 are left. Lets say that you were witness to all previous 499,998 rolls and wrote them down. Can you predict the probablily of the next two rolls? will it be different than 1/6? No, It will not. Each roll is not dependant on the previous. The last 2 rolls will be just as random as the first 499,998.

In essance, there's no difference between getting a 'live' random number out of thin air, or taking it from a list of previously 'live' random numbers out of the air. They are just as random.

I will add the caveat that if the list of 500,000 numbers is skewed, so will the probability of drawing a 1/6 dice roll. I would be shocked if it were statistically significantly skewed though, as 500,000 is more than ample a sample size.

[owenshooter]

500,000 is more than ample a sample size.

i completely agree... i had to give a stool sample once, and ONE was enough.-0

[Bean_]

Ok,

There is no memory with the dice. Your arguments are flawed. Why? Let me explain.

The theory that the list gets stale, that the probability changes when a large percentage of the list is used up, would be vailid if this was a deck of cards. If you have only 2 cards left in the deck and never saw the Ace of spades and two of hearts, you have a 50% probability of each.

The list CC uses is composted of numbers taken out of thin air (literally). Lets say 499,998 dice rolls have been used and only 2 are left. Lets say that you were witness to all previous 499,998 rolls and wrote them down. Can you predict the probablily of the next two rolls? will it be different than 1/6? No, It will not. Each roll is not dependant on the previous. The last 2 rolls will be just as random as the first 499,998.

In essance, there's no difference between getting a 'live' random number out of thin air, or taking it from a list of previously 'live' random numbers out of the air. They are just as random.

I will add the caveat that if the list of 500,000 numbers is skewed, so will the probability of drawing a 1/6 dice roll. I would be shocked if it were statistically significantly skewed though, as 500,000 is more than ample a sample size.

This actually isn't quite right, because of the re-use of the file. So the file in effect becomes like a deck of cards. Obviously, if the list were just used once, the 499,999th and 500,000th lines would be random.

There is also a different argument supporting your case, which goes like this: assume instead of 2,500,000 dice, we had 500,000 coin flips, and the coin file happens to have 250,000 heads and 250,000 tails. Reuse of the coin file means that there is a total number of possible sequences of the 500,000 coins equal to 500,000 C 250,000, which is much less than the random, 2^500,000. However, assuming their randomization is otherwise good, none of the 500,000 C 250,000 sequences is any more likely than any other. Even if on the last 2 coin tosses, all of the heads have been used up and the last 2 must be tails, that is still sort of random *considering the whole sequence* because the entire sequence of 500,000 flips was randomly generated. It can be shown that the chance of the last 2 being tails *considering the whole sequence* is actually not 1/4, but 499,999/1,999,998.

Bottom line, assuming mechanical perfection and no programming bugs:
1. From the second use of the dice file on, the dice do have memory
2. The rolls depart from randomness
3. The size of the file helps mitigate the departure from randomness.
4. Tentative hypothesis is that the rolls should be *less* streaky at a macro level (I know this is different from what I said before, but had a chance to work out some of the math yesterday).

[MeDeFe]

1. How so? The lines are shuffled after the file has been "used up". The individual lines remain the same but the order of the lines is randomised, as far as I have understood the process.

[MrBenn]

I'm not sure if the file is 'shuffled' when it is used up... The FAQ simply says that once all the dice rolls have been used, the file is 'reloaded'.

[Bean_]

1. How so? The lines are shuffled after the file has been "used up". The individual lines remain the same but the order of the lines is randomised, as far as I have understood the process.

I was told by Twill that it was shuffled (no details on the shuffling process, but it would seem you would need just as many random numbers to shuffle it as it would to draw entirely new numbers), but you are then still dealing with a fixed "deck". If the dice file had 85,000 1s in the A1 column, the shuffled file will still have 85,000 1s in the A1 column (whereas a new file would again tend to have 83,333, but could be any number between 0 and 500,000).

[Twill]

Uhhhh, when did I tell you it was shuffled?

It's not shuffled....It's just reused.

You might also be off on your dice flip analogy - that is based on the assumption that the dice are evenly distributed (i.e. we started with a fixed amount of each - 250000 heads/tails and then the randomness is based on where they appear, not IF they appear). If they were evenly distributed then yes, there would be a "memory" (i.e. you could calculate the last two dice if they HAD to make the numbers add up correctly) but that memory doesn't exist if those last two dice (or coin flips) don't HAVE to be heads or tails, they could randomly be both heads, both tails, Heads then tails or tails then heads.

So while the last line in the file might be the same every time, the number of hours it takes to get there varies based on the number of people taking turns and number of dice they roll per turn, so the time is random; The contents of those last two lines are also completely independent of any dice line which has come before it meaning that it cannot have a memory.

We don't set the dice to be evenly distributed, but rather, randomly distributed.

[Bean_]

Uhhhh, when did I tell you it was shuffled?

It's not shuffled....It's just reused.

You might also be off on your dice flip analogy - that is based on the assumption that the dice are evenly distributed (i.e. we started with a fixed amount of each - 250000 heads/tails and then the randomness is based on where they appear, not IF they appear). If they were evenly distributed then yes, there would be a "memory" (i.e. you could calculate the last two dice if they HAD to make the numbers add up correctly) but that memory doesn't exist if those last two dice (or coin flips) don't HAVE to be heads or tails, they could randomly be both heads, both tails, Heads then tails or tails then heads.

So while the last line in the file might be the same every time, the number of hours it takes to get there varies based on the number of people taking turns and number of dice they roll per turn, so the time is random; The contents of those last two lines are also completely independent of any dice line which has come before it meaning that it cannot have a memory.

We don't set the dice to be evenly distributed, but rather, randomly distributed.

Your response here implied that they were shuffled, but please clarify:

http://www.conquerclub.com/forum/viewto ... ht=#984875

Twill wrote:


Without saying too much about how the system works...it doesn't work that way Smile

The dice file is random, thus meaning that if we cycle over it is still random...it's just the same random random numbers over again.

It is also impossible to predict/reserve which number you are getting, even if you had access to the file and a millisecond timer and trigger finger (there are what, 10 dice rolls ever second?).

The system doesn't just "cycle through" the numbers. there is a bit more randomness added in and the randomness which is added in is in fact based on randomness pulled from a random source. (that makes it several layers of random deep I think)

Aaaaaaaand, the dice file is replaced from time to time just to keep things interesting and add more randomness to the system.

Hope that puts your mind at ease there a bit Smile

Have a good one
Twill

Also, I have no problems with the first time through the dice file (although your recent numbers cast that in doubt -- see the other thread -- but I'll assume random.org numbers are random for purposes of this discussion). The second time (and any later time) using the same file, however, the number of occurrences of any roll is fixed. Say the first time through, 500,000 coins were flipped and it turned out there were 249,850 heads and 250,150 tails. If the same coin file is used the next time, there will be the same number of heads (249,850), and if all 500,000 lines/flips are cycled through, then they do have to end up with the same number of heads.

[zimmah]

i have the best solution. get a guy put him in chains and each time somebody clicks the attack button a small electric shock forces him to throw the dice.
now that would be truly random with real dice.
of course the guy may have to be changed every few hours because of the electric shocks but we can live with that for true randomness.

even that will not be trully random, the outcome of the dice will depent on the speed of the dice thrown, and the way it is thrown