A seventh-side view on intensity cubes

[stahrgazer]

New "Intensity Cubes"
by lackattack on June 21st, 2010, 12:20 pm
We haven't touched the dice... erm, intensity cubes since February 14, 2006 because they were pretty darn random (see here). However, thanks to some prodding and advice from Dako, sherkaner and jakewilliams I became convinced that it is worthwhile to make some alterations.

This is how the intensity cubes now work:
• We have a series of 50,000 high quality random numbers from random.org
• 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)
• When the last number in the series is read, we "rewind" and continue with the first number in the series

The advantages are twofold:
• Each individual number in the series is used for both attacker and defender, so our intensity cubes cannot be biased for either side.
• The series is stored in memory so the dice perform much faster. This makes a huge difference when auto-assault is used with large numbers of troops on both sides.

50,000 numbers means there are 8333.333 dice “sides” (6-sided die, divide 50000 by 6) which means that there are 2 extra numbers. Whichever the extra 2 numbers are, makes the odds of getting those numbers higher than the odds of getting the other numbers.

When the “rewind” is first done, that first roll has the most likely chance of being random, but future rolls become more and more affected by what happened last (picking from what’s left).
For the dice to be totally random, someone rolling 5 dice should have a set of 7776 combinations to choose from (simple statistics: 6 sides exponentiated by the number of cubes being used. In this case, 6 to the 5th power); four dice, 1296 (6^4); 3 dice 216 (6^3); 2 dice 6*6 or 36.

That’s not what happens. Instead, someone programmed in 50,000 numbers with some combination of 6s, 5s, 4s, 3s, 2s, and 1s and either one number is repeated 2 extra times or 2 numbers are each repeated 1 extra time…skewing the results. It’s also feasible that the first 49,998 numbers are not even representations of all 6 sides of the cube. In other words, the system could have more 3’s in it than would be found in 8333 dice (or more 1’s or more…) Does it? I don’t know.
Either way, the system is NOT statistically random.

And, since the set of numbers (that are already slightly skewed and may be more skewed than we realize just from the math) does not reset until numbers are used up, that means what happened a roll ago affects what happens now and what happens now affects the next roll…because you only have what’s leftover, until the series of 50,000 numbers gets reset. This means that only the first rolls in the refreshed series have the same chance to be truly random as the last “new” roll of the reset series…but as mentioned above, the series is skewed at least by 2 numbers, if not more… again, because 50,000 does not divide by 6 evenly, and the remainder reveals that there are 2 extra numbers.. and again, that assumes that the first 8333*6 (49998) uses exactly the same number of 6s, 5s, 4s, 3s, 2s, and 1s.. and, again, I do not know that this is true.

Thus, statistically, the intensity cubes are not truly random, cannot be truly random, and any claims that they are are mathematically bogus. I just showed you that.

The next question is, of course, “are they random enough?”

Well, since each player has no real chance of affecting which roll he is in a refreshed series; and since each player has no real chance of helping the computer decide where to begin in the series, we could argue that the cubes are “random enough.”
But, we cannot use that “random enough” to argue against players seeing ‘streaks’. They probably do see streaks. I cannot prove to you that I see ‘streaks’ but I assure you, I do. Sometimes my streaks are good, in which case I usually comment on that. Sometimes my streaks are bad, in which case I frequently comment on that. Sometimes (and this seems more rare) there are no discernable streaks in a game, in which case I enjoy the game the most because it seems, then, that neither player had the odds stacked in favor of.

So, what have we learned today? The intensity cubes are not, and cannot be, statistically random. They could be considered “random enough,” but not so random as to avoid the streaks people complain about. Since streaks can and will occur, dice complaints are to be expected and tolerated, especially if the system cannot or will not be addressed so that the statistical odds are pure for each and every roll for each and every player.

[rdsrds2120]

I'm sorry...but you're voiding some basic laws of probability (central limit theorem, law of large numbers) and your approach is full of bias for someone that's TRYING to look for something wrong in the dice. Sorry stahr, I disagree. I vow to not post any more on this as to avoid losing a heartbeat, lol.

[stahrgazer]

I'm sorry...but you're voiding some basic laws of probability (central limit theorem, law of large numbers) and your approach is full of bias for someone that's TRYING to look for something wrong in the dice. Sorry stahr, I disagree. I vow to not post any more on this as to avoid losing a heartbeat, lol.

No, my approach is simple math. You try it

After all, statistics are really very simple math. Also, a six-sided die doesn't require a law of large numbers.

[natty dread]

That's not how the dice work now. They are not read in sequence, they are read in random order.

[natty dread]

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

[Metsfanmax]

Honestly, the OP makes zero mathematical sense. Trying to make a connection between actual dice, and the mathematical idea of picking a random integer from {1,6} inclusive, is completely futile. The only correct way to look at it is to understand that each particular number is the side of the die that faces up after you've rolled it. You can't just pick groups of six numbers from the list and claim that they are different "sides" of the same die.

[Crazyirishman]

sorry star, you don't seem to understand the statistical definition of random

[stahrgazer]

Honestly, the OP makes zero mathematical sense. Trying to make a connection between actual dice, and the mathematical idea of picking a random integer from {1,6} inclusive, is completely futile. The only correct way to look at it is to understand that each particular number is the side of the die that faces up after you've rolled it. You can't just pick groups of six numbers from the list and claim that they are different "sides" of the same die.

You make no statistical sense. Picking an integer between 1 and 6 for each die is exactly what a "roll" does.

Rolling a set of die and using those as random generator numbers to select from, restricts a player to the values someone previously rolled, and since it is more restrictive, it is less random.

[stahrgazer]

sorry star, you don't seem to understand the statistical definition of random

erm.. it's you, who doesn't understand it.

Check las vegas odds on combinations of rolls available with 5 6-sided dice, and you'll see, my numbers do agree.

[stahrgazer]

That's not how the dice work now. They are not read in sequence, they are read in random order.

Which means you've restricted the random series to numbers that came up in previous dice rolls, rather than allow each player to roll his or her own set of dice, each getting a possible 6 sides... which means you're less random (more restrictive is less random) than just holding dice in palm and rolling... which, again, means that complaints that the dice "don't act like they do when I roll them," are accurate.

[AndyDufresne]

You are right the intensity cubes don't act like you do when you roll them in reality---we can't throw them with our special techniques in order to get the numbers we want.

I also usually put magnets in my real life intensity cubes. I never get tired of always winning.


--Andy

[Metsfanmax]

You make no statistical sense. Picking an integer between 1 and 6 for each die is exactly what a "roll" does.

Rolling a set of die and using those as random generator numbers to select from, restricts a player to the values someone previously rolled, and since it is more restrictive, it is less random.

The history of rolls that came before the current one has no bearing on the current roll, since the algorithm contained in the PRNG does not look at the previous rolls in determining the spot on the list to start from.

[jimboston]

That's not how the dice work now. They are not read in sequence, they are read in random order.

Which means you've restricted the random series to numbers that came up in previous dice rolls, rather than allow each player to roll his or her own set of dice, each getting a possible 6 sides... which means you're less random (more restrictive is less random) than just holding dice in palm and rolling... which, again, means that complaints that the dice "don't act like they do when I roll them," are accurate.

Sounds like 'holding the dice in palm and rolling' is the only way you will except that the "roll" is random. You might as well give up playing anything but the real Risk in real life. What you are asking just ain't possible with a computer or internet game.

[jimboston]

Perhaps CC can hire 50,000 chinese sweat shop workers to roll and log dice rolls 24/7.

Maybe then we will be satisfied?