I've read similar accounts as well, and allegedly some of the most prolific lockbox aficionados use this method. But I've not seen anything myself.
Here's the kicker, though: even if that's the case, it would explain some people getting strangely lucky but wouldn't really explain people getting strangely *unlucky.* Pseudo-random works well such that if you aren't deliberately trying to exploit it, it will appear random. (In fact, very little is actually random these days.) So, we wouldn't expect someone just testing to have numbers that would consistently deviate from their expectation.
Edit: I'm trying to figure out how you've gotten confused and have locked in on a couple possibilities. First, your very first standard deviation calculation was incorrect. The variance of a binomial distribution is np(1-p), which here is (1000)*(.01)*(1-.01) = 9.9. (So you were off by an order of magnitude). That shrinks the standard deviation to 3.14. Second, one source of confusion may be arising from your desire to look at the distribution across players, but using statistics associated with trials for a particular player. When you sum up many distributions, that's where the Central Limit Theorem does kick in, and things start to look normally distributed. However, at that point, the relevant statistic is the standard **error**, not the standard **deviation**. When doing those confidence intervals for normal distributions, it's the standard error (not deviation) that's multiplied by the confidence coefficient for the confidence level in question.
Hope this helps.
I will repeat again: I understand what you are saying. Stop explaining that. The math errors are not relevant except by virtue of scale. The loot generation matters. I am claiming that the loot system tries to impose a normal distribution across players which is different than if it had a set quantity in a bin. The results will be measurably different. You can test this in a simulation... as long as your simulation accounts for the difference between:
A hundred rooms with one room having a diamond inside. (I know you get this. Open a hundred rooms, find a diamond.)
VS.
An indeterminate amount of rooms with a computer deciding to place a diamond in 1% of the time when they are created.
VS.
An indeterminate number of rooms that monitors attempts and makes adjustments to maintain 1% diamond-find rate.
Taken at a large scale, across the population, either way will produce 1% of attempts yielding a key. However, for your individual set of observations, you will see different distributions if your sample is too low.
My point is not strictly speaking a math point. It is a comment on how I believe the loot generation system distributes loot.
It's not that I am attempting to impose a normal distribution. Rather, I think that Cryptic's loot algorithm attempts to artificially create a normal distribution across the entire population, which would mean that you would not necessarily see a binomial distribution in a low sample, which could cause the streakiness we have seen. Still 1% chance on any given box.
Again, to be clear, my conjecture is that the loot system is creating a normal rather than binomial distribution. Not that one occurs randomly. And when imposing, artificially, a normal distribution, the odds within a small sample will be very different than they would be with a binomial distribution because the variance in drop rate within a set of observations that is small exceeds the average imposed drop rate.
I will repeat again: I understand what you are saying. Stop explaining that. The math errors are not relevant except by virtue of scale. The loot generation matters. I am claiming that the loot system tries to impose a normal distribution across players which is different than if it had a set quantity in a bin. The results will be measurably different. You can test this in a simulation... as long as your simulation accounts for the difference between:
A hundred rooms with one room having a diamond inside. (I know you get this. Open a hundred rooms, find a diamond.)
VS.
An indeterminate amount of rooms with a computer deciding to place a diamond in 1% of the time when they are created.
VS.
An indeterminate number of rooms that monitors attempts and makes adjustments to maintain 1% diamond-find rate.
Taken at a large scale, across the population, either way will produce 1% of attempts yielding a key. However, for your individual set of observations, you will see different distributions if your sample is too low.
My point is not strictly speaking a math point. It is a comment on how I believe the loot generation system distributes loot.
It's not that I am attempting to impose a normal distribution. Rather, I think that Cryptic's loot algorithm attempts to artificially create a normal distribution across the entire population, which would mean that you would not necessarily see a binomial distribution in a low sample, which could cause the streakiness we have seen. Still 1% chance on any given box.
Again, to be clear, my conjecture is that the loot system is creating a normal rather than binomial distribution. Not that one occurs randomly. And when imposing, artificially, a normal distribution, the odds within a small sample will be very different than they would be with a binomial distribution because the variance in drop rate within a set of observations that is small exceeds the average imposed drop rate.
I'm not really sure that you do understand, because you're using statistical jargon incorrectly (and that's aside from pretty much every calculation you made being wrong).
When you say something like, “the loot system tries to impose a normal distribution across players,” that statement is non-sensical. As in literally does not make sense in English, because of the truncation at the zero value means that it CAN NOT BE A NORMAL DISTRIBUTION. Not everything that looks kind of bell-shaped is normal. A normal (Gaussian) distribution REQUIRES the two tails to be able to extend symmetrically in both directions. Without that, it isn't normal. Any skew means non-normality. So please, for the love of all that is holy, stop saying “normal distribution.”
With that out of the way, you have a theory. However, you’ve yet to supply any evidence or testing to support your theory. You cite “streakiness,” but streakiness would be expected in a binomial distribution being applied dynamically, which is your second scenario. We’ve seen only one truly anomalous result—the alleged opening of 1000 boxes with no ships—but as @repetitiveepic noted, it wasn’t substantiated or documented. If further documented testing were to show similar results, then we’d have reason to believe there’s something funky going on here. Right now, though, the only two large-scale documented (logged and screenshotted) tests—of 2000 and 10,000 boxes, respectively—are perfectly compatible with the theory of a binomial distribution with p=0.01. There's an ongoing test of 25,000 boxes, and it will be interesting to see if it follows the same pattern as expected.
And just to be crystal clear, if it doesn't, and there is some anomaly, that still does...not...mean...a "forced" normal distribution. Enforcing a 1% rate over the long-term (which would be peculiar but not impossible) rather than letting it play out on a roll-by-roll basis does not make the distribution "normal."
I will repeat again: I understand what you are saying. Stop explaining that. The math errors are not relevant except by virtue of scale. The loot generation matters. I am claiming that the loot system tries to impose a normal distribution across players which is different than if it had a set quantity in a bin. The results will be measurably different. You can test this in a simulation... as long as your simulation accounts for the difference between:
A hundred rooms with one room having a diamond inside. (I know you get this. Open a hundred rooms, find a diamond.)
VS.
An indeterminate amount of rooms with a computer deciding to place a diamond in 1% of the time when they are created.
VS.
An indeterminate number of rooms that monitors attempts and makes adjustments to maintain 1% diamond-find rate.
Taken at a large scale, across the population, either way will produce 1% of attempts yielding a key. However, for your individual set of observations, you will see different distributions if your sample is too low.
My point is not strictly speaking a math point. It is a comment on how I believe the loot generation system distributes loot.
It's not that I am attempting to impose a normal distribution. Rather, I think that Cryptic's loot algorithm attempts to artificially create a normal distribution across the entire population, which would mean that you would not necessarily see a binomial distribution in a low sample, which could cause the streakiness we have seen. Still 1% chance on any given box.
Again, to be clear, my conjecture is that the loot system is creating a normal rather than binomial distribution. Not that one occurs randomly. And when imposing, artificially, a normal distribution, the odds within a small sample will be very different than they would be with a binomial distribution because the variance in drop rate within a set of observations that is small exceeds the average imposed drop rate.
I'm not really sure that you do understand, because you're using statistical jargon incorrectly (and that's aside from pretty much every calculation you made being wrong).
When you say something like, “the loot system tries to impose a normal distribution across players,” that statement is non-sensical. As in literally does not make sense in English, because of the truncation at the zero value means that it CAN NOT BE A NORMAL DISTRIBUTION. Not everything that looks kind of bell-shaped is normal. A normal (Gaussian) distribution REQUIRES the two tails to be able to extend symmetrically in both directions. Without that, it isn't normal. Any skew means non-normality. So please, for the love of all that is holy, stop saying “normal distribution.”
With that out of the way, you have a theory. However, you’ve yet to supply any evidence or testing to support your theory. You cite “streakiness,” but streakiness would be expected in a binomial distribution being applied dynamically, which is your second scenario. We’ve seen only one truly anomalous result—the alleged opening of 1000 boxes with no ships—but as @repetitiveepic noted, it wasn’t substantiated or documented. If further documented testing were to show similar results, then we’d have reason to believe there’s something funky going on here. Right now, though, the only two large-scale documented (logged and screenshotted) tests—of 2000 and 10,000 boxes, respectively—are perfectly compatible with the theory of a binomial distribution with p=0.01. There's an ongoing test of 25,000 boxes, and it will be interesting to see if it follows the same pattern as expected.
And just to be crystal clear, if it doesn't, and there is some anomaly, that still does...not...mean...a "forced" normal distribution. Enforcing a 1% rate over the long-term (which would be peculiar but not impossible) rather than letting it play out on a roll-by-roll basis does not make the distribution "normal."
My conjecture (ie. spitballed idea which I need you to accept as a premise to have a conversation) is that the system trying to impose a normal distribution on the POPULATION (ALL LOCKBOXES EVER) which is what allows the truncation at zero within a sample set of openings that is too small.
It is not that samples have normal distributions. It is that the population (of lock box openings) has a normal distribution. And that imposing this would truncate at zero on a small sample set of observations and would not truncate at zero on a larger sample set of observations.
My conjecture (ie. spitballed idea which I need you to accept as a premise to have a conversation) is that the system trying to impose a normal distribution on the POPULATION (ALL LOCKBOXES EVER) which is what allows the truncation at zero within a sample set of openings that is too small.
It is not that samples have normal distributions. It is that the population (of lock box openings) has a normal distribution. And that imposing this would truncate at zero on a small sample set of observations and would not truncate at zero on a larger sample set of observations.
This is still gibberish for the reasons I've already explained (holy smokes, please stop saying normal distribution--you clearly don't know what that term means) and that you keep ignoring, but it doesn't matter. We get it. You have a theory that there's some globally enforced 1% target but that batches of data will exhibit distinctly non-random behavior. And right now, there's no evidence to support this theory. If you'd like to replicate some experiments on Tribble and document your findings, I'm sure we would all be eager to read the results.
What I'm suggesting is that the droprate varies but has an average of 1%. So maybe 68% of lockboxes have a 1% droprate. Ie. maybe, for example, a multi-roll system.
The server determines which group you are in when you opens the box (ie. a random droprate with a normal distribution and a mean of 1%) and then after setting your odds, rolls the dice a second time.
I'm saying you might use something like this to obfuscate the system against cheating/exploiting.
Or maybe the odds fluctuate with rate of purchases or server activity but balance out so that, over time, 1% of boxes have the ship.
Ultimately, all I'm saying is that it doesn't have to be a binomial distribution. It's somewhat random but isn't necessarily random in every way. And if it has an imposed rate of 1 per 100 packs over the length of the promotion, it's fair to call that a 1% droprate but it might have a pattern that gets truncated in small sample sizes while the pattern holds FROM CRYPTIC'S PERSPECTIVE when observing all the data of all lockbox openings.
I know a few years ago there was a lively debate on the LOTRO forums speculating that they were using the character's internal database number as a seed. That could explain why some people were always lucky in getting drops but others never anything. Nothing was ever admitted or confirmed. I suspect that is not the case here but only Cryptic knows for sure how they seed.
Comments
Here's the kicker, though: even if that's the case, it would explain some people getting strangely lucky but wouldn't really explain people getting strangely *unlucky.* Pseudo-random works well such that if you aren't deliberately trying to exploit it, it will appear random. (In fact, very little is actually random these days.) So, we wouldn't expect someone just testing to have numbers that would consistently deviate from their expectation.
I will repeat again: I understand what you are saying. Stop explaining that. The math errors are not relevant except by virtue of scale. The loot generation matters. I am claiming that the loot system tries to impose a normal distribution across players which is different than if it had a set quantity in a bin. The results will be measurably different. You can test this in a simulation... as long as your simulation accounts for the difference between:
A hundred rooms with one room having a diamond inside. (I know you get this. Open a hundred rooms, find a diamond.)
VS.
An indeterminate amount of rooms with a computer deciding to place a diamond in 1% of the time when they are created.
VS.
An indeterminate number of rooms that monitors attempts and makes adjustments to maintain 1% diamond-find rate.
Taken at a large scale, across the population, either way will produce 1% of attempts yielding a key. However, for your individual set of observations, you will see different distributions if your sample is too low.
My point is not strictly speaking a math point. It is a comment on how I believe the loot generation system distributes loot.
It's not that I am attempting to impose a normal distribution. Rather, I think that Cryptic's loot algorithm attempts to artificially create a normal distribution across the entire population, which would mean that you would not necessarily see a binomial distribution in a low sample, which could cause the streakiness we have seen. Still 1% chance on any given box.
Again, to be clear, my conjecture is that the loot system is creating a normal rather than binomial distribution. Not that one occurs randomly. And when imposing, artificially, a normal distribution, the odds within a small sample will be very different than they would be with a binomial distribution because the variance in drop rate within a set of observations that is small exceeds the average imposed drop rate.
I'm not really sure that you do understand, because you're using statistical jargon incorrectly (and that's aside from pretty much every calculation you made being wrong).
When you say something like, “the loot system tries to impose a normal distribution across players,” that statement is non-sensical. As in literally does not make sense in English, because of the truncation at the zero value means that it CAN NOT BE A NORMAL DISTRIBUTION. Not everything that looks kind of bell-shaped is normal. A normal (Gaussian) distribution REQUIRES the two tails to be able to extend symmetrically in both directions. Without that, it isn't normal. Any skew means non-normality. So please, for the love of all that is holy, stop saying “normal distribution.”
With that out of the way, you have a theory. However, you’ve yet to supply any evidence or testing to support your theory. You cite “streakiness,” but streakiness would be expected in a binomial distribution being applied dynamically, which is your second scenario. We’ve seen only one truly anomalous result—the alleged opening of 1000 boxes with no ships—but as @repetitiveepic noted, it wasn’t substantiated or documented. If further documented testing were to show similar results, then we’d have reason to believe there’s something funky going on here. Right now, though, the only two large-scale documented (logged and screenshotted) tests—of 2000 and 10,000 boxes, respectively—are perfectly compatible with the theory of a binomial distribution with p=0.01. There's an ongoing test of 25,000 boxes, and it will be interesting to see if it follows the same pattern as expected.
And just to be crystal clear, if it doesn't, and there is some anomaly, that still does...not...mean...a "forced" normal distribution. Enforcing a 1% rate over the long-term (which would be peculiar but not impossible) rather than letting it play out on a roll-by-roll basis does not make the distribution "normal."
My conjecture (ie. spitballed idea which I need you to accept as a premise to have a conversation) is that the system trying to impose a normal distribution on the POPULATION (ALL LOCKBOXES EVER) which is what allows the truncation at zero within a sample set of openings that is too small.
It is not that samples have normal distributions. It is that the population (of lock box openings) has a normal distribution. And that imposing this would truncate at zero on a small sample set of observations and would not truncate at zero on a larger sample set of observations.
This is still gibberish for the reasons I've already explained (holy smokes, please stop saying normal distribution--you clearly don't know what that term means) and that you keep ignoring, but it doesn't matter. We get it. You have a theory that there's some globally enforced 1% target but that batches of data will exhibit distinctly non-random behavior. And right now, there's no evidence to support this theory. If you'd like to replicate some experiments on Tribble and document your findings, I'm sure we would all be eager to read the results.
What I'm suggesting is that the droprate varies but has an average of 1%. So maybe 68% of lockboxes have a 1% droprate. Ie. maybe, for example, a multi-roll system.
The server determines which group you are in when you opens the box (ie. a random droprate with a normal distribution and a mean of 1%) and then after setting your odds, rolls the dice a second time.
I'm saying you might use something like this to obfuscate the system against cheating/exploiting.
Or maybe the odds fluctuate with rate of purchases or server activity but balance out so that, over time, 1% of boxes have the ship.
Ultimately, all I'm saying is that it doesn't have to be a binomial distribution. It's somewhat random but isn't necessarily random in every way. And if it has an imposed rate of 1 per 100 packs over the length of the promotion, it's fair to call that a 1% droprate but it might have a pattern that gets truncated in small sample sizes while the pattern holds FROM CRYPTIC'S PERSPECTIVE when observing all the data of all lockbox openings.
You obviously have never met Crosis
...#LLAP...
That comparison is pretty unfair. To Lloyd.
maybe if this thread is too old to bump the OP will repost the same info into a new thread
Necromancy is not okay.
@pwlaughingtrendy please save us!
Support 90 degree arc limitation on BFaW! Save our ships from looking like flying disco balls of dumb!
^ so much this! holy TRIBBLE you had to dig for this one!
@askray @jodarkrider we need the zombie cannon!
This should be an episode in the new Star Trek series.