Math and Spawn Rates

[Snagglepuss]

I've noticed that we have some mathematically oriented minds on the forums (Tecmos, Loraen, Koros, Ele, etc). It seems like every few weeks someone is asking about what is normal for a spawn rate as far as what is a good run or bad run of variance and to what extent.

I've played a enough poker to understand things like risk of ruin and how variance can be your best friend or your worse enemy. Many older players at the table will always say to a bad beat, "I'd rather be a lucky player than a good player..." From the point of view of a professional poker player, you should look at each table siting as the piece of one big game that never ends. This way, your actions that have positive expected value will pay off over time...

Now, what I want to know concerns spawn rates. I was camping a mob that "according the wiki" had a 5% chance to pop on a standard outdoor timer. Being static, I had no reason to worry about any other variables or PHs. The bugger was killed immediately as he spawned, then I would reset my timer. Between two people, we camped the mob 29 hours straight this weekend to no avail. I guess we saw around 265 to 270 spawns.

Obviously, this is a run of bad luck, but what I'm interested in knowing is how bad. If you normally distributed its chance to pop, what would be considered outside one standard deviation? Also, should I look at this knowing the old gambler's fallacy and interpret my chances of camping a mob as "one big camp." It's hard to tell yourself after a 12 hour session that he's got to pop within the hour, but we all know fortunes have been lost from the words, "I can't keep getting these cards. One more hand; I know I'll get some good cards soon!" All actions are independent of the outcome, correct? Every chance is 5%, even if you have gotten no pops 267 times in a row? Wouldn't that be as unlikely as getting 12 pops in a row though? Still 5%...

Could someone explain some math or statistics about how long a camp like that could take and still be within the realm of "reasonable bad luck"?

[Vayder]

If the spawn chance is really 5% and you were killing the correct PHer you're results are literally right around 1 in a million (1.13 in a million rounded).

This is far more likely than getting the named to pop 12 times in a row however (which is around 24 in a quadrillion chances).

[Itap]

Reminds me of raster camp in lguk. I remember helping a friend do it back in 2001 and we sat down there for around 36 hours straight before he popped.

[Ele]

Sounds like a pained soul thread. That camp leaves plenty of time to ponder the deeper things in life.

You've already addressed the biggest mistake I've seen people make about these kinds of camps, which is the gambler's fallacy. "Just one more spawn, I've been here forever, it has to happen soon!" Each and every spawn is an independent event (in most cases) that has no bearing on the what the last place holder was. It was 5% last time, it is 5% this time.

With a 5% chance to occur, there is a 95% chance that it does not occur.

[Itap]

"Just one more spawn, I've been here forever, it has to happen soon!"

Lol, I think this is just what people to say to keep themselves from slipping into senility.


What hurts more is when soandso goes in there and gets spawn within an hour.

[zanderklocke]

I sort of just posted this on another thread, but I'm wondering where people pull most of their data from spawn rate percentages to drop rate percentages. I'm not a computer wizard, so I'm not sure if people have readily available access to source code somewhere? Or, is this proprietary information, and I'm just being naive?

[jerok88]

The math is: 95%^267, which is .000000112% chance of it not spawning every single time. 1/.000000112 = this happens once every 886,742 times.

[Briscoe]

Assuming everything is "working as intended," I tend to think that 5% is a bit too optimistic of a reported spawn rate. If we assume instead a 1% spawn rate, then the chances of 270 consecutive placeholders is 1 in 15, which is five orders of magnitude more likely to occur than 1 in 1 million (which is indeed the right number, as calculated by Vayder above).

[Handull]

One important thing to look at is how long this server has been running for.

Flip a coin 8 times, you'd expect to get at least one heads and one tails (ie you won't likely see a streak of 8 of the same outcome). Flip a coin 1000 times, you have a pretty good shot of at some point over that 1000 to see a streak of 8 heads or 8 tails in a row.

If you ask people to imagine they flipped a coin 20 times and to make up the results (asking someone to make a randomized distribution), most people will avoid longer streaks of the same result, even though statistically they aren't unlikely.

The last thing to consider is that the people who get the bad luck of not getting a spawn over X hours will likely be more vocal about their failure than the person who just found the mob up randomly, or got a spawn in only a short period of time. So just by browsing the forums it would sound like tons of people have this bad luck, but there are just as many who have good luck and don't post about it.

And like Ele said, each spawn is an independent event. Though don't give up, cause then you'll never get it.

[zanderklocke]

One important thing to look at is how long this server has been running for.

Flip a coin 8 times, you'd expect to get at least one heads and one tails (ie you won't likely see a streak of 8 of the same outcome). Flip a coin 1000 times, you have a pretty good shot of at some point over that 1000 to see a streak of 8 heads or 8 tails in a row.

If you ask people to imagine they flipped a coin 20 times and to make up the results (asking someone to make a randomized distribution), most people will avoid longer streaks of the same result, even though statistically they aren't unlikely.

The last thing to consider is that the people who get the bad luck of not getting a spawn over X hours will likely be more vocal about their failure than the person who just found the mob up randomly, or got a spawn in only a short period of time. So just by browsing the forums it would sound like tons of people have this bad luck, but there are just as many who have good luck and don't post about it.

And like Ele said, each spawn is an independent event. Though don't give up, cause then you'll never get it.

Posts like this are such a great read. That was excellent.

[Snagglepuss]

I sort of just posted this on another thread, but I'm wondering where people pull most of their data from spawn rate percentages to drop rate percentages. I'm not a computer wizard, so I'm not sure if people have readily available access to source code somewhere? Or, is this proprietary information, and I'm just being naive?

Zander, I got mine from the wiki, but I'm not sure how accurate it is. I've heard that the data is pulled from a source other than P1999. Anyone confirm?

Ele, I was refering to the Rotting Skelly, but yes, both camps are very... well.. let's say you can get some good reading done haha.

If you had coin that was skewed to land on heads 95% of the time and tails 5% and you flipped it every 7 minutes, what is the normal distribution of times you'd get a tails? It would be cool to see some projections where you could compare to eq spawns to get an idea of where you are falling on the luck curve. Isn't the AC like 10% in OoT?

[eqravenprince]

It is far more likely you were killing the wrong ph or doing something wrong or the spawn rate % is wrong. The chances of killing a ph with a 5% chance of spawning 270 times without getting it to spawn at least once is so small that I would consider it statistically impossible.

[Splorf22]

A lot of good stuff in this thread already. Ploktor is absolutely right; with 1000+ people on the server you will expect some people to get fucked. I am pretty sure I am one of the most unlucky people on the server, having gone 0/20 on fungi tunic rolls in 2-3 man groups (something like 1/1000 chance).

I think the pained soul is more like a 1/100 chance to spawn, and assuming you are killing him every 8 minutes or so that means one pained soul every 800 minutes (expected pained souls = 0.00125/minute). Slightly elaborating on Jerok's math, the probability of the pained soul not spawning is 0.99*0.99...*0.99 = 0.99^n. Google gives 0.99^260 as 0.066 which makes you unlucky but not the most unlucky person on the server :D If we set 1/1000 = 0.99^n -> n = log[0.99](1/1000) = log[10](1/1000)/log[10](0.99) = -3/-0.004 = ~750 pained souls. Ouch! I'm pretty sure Shiftin was at the pained soul for 60+ hours.

One last trick you can use: (1-x)^n = sum[m:1-n] (n choose m)x^m. If x is small, you can throw out the high powers of x leaving 1-nx. So for example (1-0.001)^5 will be very close to 0.995. This breaks down for really high powers of x like in your example.

edit: I've had better luck with the rotting skeleton; if you camped him for 30 hours you are *probably* doing some wrong, but I have heard of people having trouble. We had a wizard in VD whose name escapes me who spent that amount of time there.

[khanable]

Well good. Now I know which of you are mathematically inclined so you can peer-review my analysis of the current AC system in a few weeks.

Also, I just wanted to point out I have claimed the title of Zanderr's worst customer.

:(

[eqravenprince]

My guess is it is not a 5% chance of spawning. 1% sounds far more likely.

At 1% chance of spawning
After 100 kills: 36% chance of not getting spawn
After 200 kills: 13% chance of not getting spawn
After 300 kills: 5% chance of not getting spawn

At 2% chance of spawning
After 100 kills: 13% chance of not getting spawn
After 200 kills: 1.7% chance of not getting spawn
After 300 kills: .2% chance of not getting spawn

At 5% chance of spawning
After 10 kills: 59% chance of not getting spawn
After 25 kills: 28% chance of not getting spawn
After 50 kills: 8% chance of not getting spawn
After 75 kills: 2% chance of not getting spawn
After 100 kills: .5% chance of not getting spawn
After 200 kills: .0035% chance of not getting spawn
After 300 kills: .000020753% chance of not getting spawn

[Snagglepuss]

Thanks guys! This is great.

Loraen, that math is nice. I know enough about stats from my college course to communicate, but thank you for helping me with this. Exactly what I wanted to see.

Eqravenprince, the spawn might be indeed 1% on the Rotting Skeleton, but like I mentioned, I took it from the wiki's "stated amount" for what its worth. Thank you for the table, that is exactly the type of data I wanted to see. It's a nice gauge of where you fall in the luck-o-meter.

For all the "p99 iz fullz of Tr0LLz" and people who ask if the community is nice or not, this thread shows that we have some really helpful people here.

Thanks everyone for who contributed!

[webrunner5]

We are talking a Random Number generator here on some of this stuff. Good luck guessing that at times. And as the rumor mill goes most people including Devs have never figured out how Sony did it yet.

[zanderklocke]

Also, I just wanted to point out I have claimed the title of Zanderr's worst customer.

:(

Nah. We just had bad luck. You were nailing placeholders above and beyond needed, and we had good conversation. Sometimes, good conversation is better than a night of "good drops".

[Frieza_Prexus]

The RNG on live was considered to be notoriously streaky. My inner conspiracy theorist suspects that something has been done here in an attempt to recreate the frustratingly "off" nature of EQ's RNG.

[Tecmos Deception]

Though don't give up, cause then you'll never get it.

Or you might never get it. Ever. In a million years.

<3 numbers.

[Vayder]

What I really want to see after this thread is the correlation between enchanters, warriors, and a love of statistics.

[Sirken]

its random. and 5% = 5/100 or 1/20

that being said, it's random. if u have a 5% chance, you essentially are rolling a 100 sided die and hoping for a 1,2,3,4,5. but its a new roll each time. so its no really like you are improving your odds with each ph kill, as they do not get you closer to popping a mob like Quillmane for example,

for example, i've seen the AC in oot pop 4 times in 6 spawns, and i've watched people kill the PH and never see the AC.

embrace your random number generator

[falkun]

I, for one, welcome our new random number generator overlord.

[Nlaar]

I remember speaking with a friend circa summer 2010 about the RNG and how it was his and his guild's belief that sometimes the RNG "got stuck."

In other words, when clearing a plane (Hate for example) one would note that the same rare item would drop with increased frequency, all within a single raid e.g., cleric legs dropping 3 times in one raid or the shaman bp dropped twice in one raid. I don't raid as much as these days, but I remember examples of this sort of thing happening very frequently during planar clears.

So when one hears about AC popping 4/6 times for some people and "never" for others it's hard not to think that the RNG is "bursting" at some points and "off" at others leading one to question the reliability of the RNG.

However, do I have any actual evidence? Of course not, that would be to convenient!

[Briscoe]

I think we've all had times where we felt like the RNG is just running off of the RANDU algorithm, amirite guys? (Expecting at least Loraen to laugh at this).

[Sirken]

I remember speaking with a friend circa summer 2010 about the RNG and how it was his and his guild's belief that sometimes the RNG "got stuck."

In other words, when clearing a plane (Hate for example) one would note that the same rare item would drop with increased frequency, all within a single raid e.g., cleric legs dropping 3 times in one raid or the shaman bp dropped twice in one raid. I don't raid as much as these days, but I remember examples of this sort of thing happening very frequently during planar clears.

So when one hears about AC popping 4/6 times for some people and "never" for others it's hard not to think that the RNG is "bursting" at some points and "off" at others leading one to question the reliability of the RNG.

However, do I have any actual evidence? Of course not, that would be to convenient!

http://bigrab.files.wordpress.com/2011/01/tin-foil-hat.jpg

[Tanthallas]

This way, your actions that have positive expected value will pay off over time...

This is highly misleading. The conditions that have to be met in order to calculate the probability of events in terms expected value are extremely unrealistic and in most cases make the calculation itself moot.

Best way to think about it is like Sirken said. It doesnt give you a practical answer because there is no practical answer.

[zanderklocke]

Game of luck, EverQuest is. Sure, it helps to know people who can get you into camps like Fungi, but all drops and spawns are at the mercy of the random number generator. The only thing that is for certain is that not trying a camp/mob at all will always yield no results.

[Snagglepuss]

This is highly misleading. The conditions that have to be met in order to calculate the probability of events in terms expected value are extremely unrealistic and in most cases make the calculation itself moot.

Best way to think about it is like Sirken said. It doesnt give you a practical answer because there is no practical answer.

Well, that was an anecdotal reference to an infinite poker game / casino game where you could calculate expected value. I was using it as a "lede" to discussing the concept of gambler's fallacy or independent outcomes. The idea that we've all been at a camp and said to ourselves,

"It's gotta spawn; I've been here so long. Just one more round... I'll set the alarm a little later in the morning...".

Once on a cruise ship, I observed a roulette wheel show black 15 times in a row. Man, you should have seen the looks on some of those poor gambler's faces!

It's fascinating how sunken costs play a huge role in our decisions. "I've already been at this camp for 6 hours! What's another 5! i'm not leaving until it's mine!"

[August]

http://bigrab.files.wordpress.com/2011/01/tin-foil-hat.jpg

No need to be patronizing. A random number generator, based on implementation, can very well get 'stuck', or atleast provide very non-random outcomes with regularity

I'll give an example. I work at a pretty nice software firm that suffered a problem whenever running... things through other things.

See, the test in question always got hung and no one could figure out why. It was a series of logic steps that required a Random() call 10 times. It just so happened that if a certain number hit during this random jump, then the test would enter into an infinite loop. Shoddy programming, and the fix was easy. The strange part, however, was the frequency in which it happened.

See, the calculated frequency of this happening was below 1% if you went by pure odds. However, we noted that on 33% of our runs this would happen.

But, August! you say, what if you used the same SEED -- of course it would happen over and over! And so I investigated and found that seed was taken off of milliseconds of the current time -- 'random' to the 1000 chance, I suppose.

So, I made a little program that does the same thing as the test without the encumbrance, of, say, the test. And then I printed the results out with the different seeds, the random numbers generated, etc.

I found a couple of things upon parsing:

1) The same seed repeatedly got used when I ran the test -or rather, the same 'set' of seeds got cycled over and over. We were just taking milliseconds, but the same 3 digit seeds kept popping up. This could be a problem in numerous places, but maybe the system clock!

2) When we modulo'd by our bound there was the dreaded value in about 1/3 of these sets of numbers. Hence our near 33% hang rate. I then went and force-seeded all 1000 millieseconds and found that in around 23% of them, the first 10 rands on our modulo would produce a hang-result by random 10.


So, what can we learn?

1) Nothing is random
2) Implementation is everything

The OP may be unlucky, or there may be something wrong w/ the code behind it, or the OP may be doin something wrong -- I don't know.

But let's not call people tinfoil hatters when there could be a logical explanation. Programmers aren't perfect, and nobody that I'm aware of has ever created a truly 'random' implementation in software.

[Zenlina]

I conclude u probably killing the wrong skeleton. That one is quick to spawn.

[Sirken]

btw, your poker analogy is good, but doesnt apply because you are removing cards from the deck, hence every round your odds of drawing to that flush change for better or worse depending on the previous card or cards put out (depending which game ur playing).

a closer analogy would be blackjack, but with a brand new deck for each hand.

each pop (be it ph or the rare mob) is a completely separate encounter, and what pops has absolutely 0% to do with what popped before that.

not trying to be a dick, just explaining ;)

[Splorf22]

This is highly misleading. The conditions that have to be met in order to calculate the probability of events in terms expected value are extremely unrealistic and in most cases make the calculation itself moot.

Best way to think about it is like Sirken said. It doesnt give you a practical answer because there is no practical answer.

You must be an undergraduate. I'm not sure whether you just dismissed the entire discipline of statistics with an airy wave of your fraternal hand or whether you have never heard of machine learning. There are computer poker players that use precisely this concept to play poker. Obviously you cannot know for sure what your opponent will do when you checkraise him on the turn, which is why you can estimate it from training data using any number of techniques.

[Nlaar]

No need to be patronizing. A random number generator, based on implementation, can very well get 'stuck', or atleast provide very non-random outcomes with regularity

I'll give an example. I work at a pretty nice software firm that suffered a problem whenever running... things through other things.

See, the test in question always got hung and no one could figure out why. It was a series of logic steps that required a Random() call 10 times. It just so happened that if a certain number hit during this random jump, then the test would enter into an infinite loop. Shoddy programming, and the fix was easy. The strange part, however, was the frequency in which it happened.

See, the calculated frequency of this happening was below 1% if you went by pure odds. However, we noted that on 33% of our runs this would happen.

But, August! you say, what if you used the same SEED -- of course it would happen over and over! And so I investigated and found that seed was taken off of milliseconds of the current time -- 'random' to the 1000 chance, I suppose.

So, I made a little program that does the same thing as the test without the encumbrance, of, say, the test. And then I printed the results out with the different seeds, the random numbers generated, etc.

I found a couple of things upon parsing:

1) The same seed repeatedly got used when I ran the test -or rather, the same 'set' of seeds got cycled over and over. We were just taking milliseconds, but the same 3 digit seeds kept popping up. This could be a problem in numerous places, but maybe the system clock!

2) When we modulo'd by our bound there was the dreaded value in about 1/3 of these sets of numbers. Hence our near 33% hang rate. I then went and force-seeded all 1000 millieseconds and found that in around 23% of them, the first 10 rands on our modulo would produce a hang-result by random 10.


So, what can we learn?

1) Nothing is random
2) Implementation is everything

The OP may be unlucky, or there may be something wrong w/ the code behind it, or the OP may be doin something wrong -- I don't know.

But let's not call people tinfoil hatters when there could be a logical explanation. Programmers aren't perfect, and nobody that I'm aware of has ever created a truly 'random' implementation in software.

Thank you August (for both the info as well as calling S. out on his tone).

Well said - with my somewhat limited CS knowledge I would have butchered the point to be made.

[Lagaidh]

The RNG on live was considered to be notoriously streaky. My inner conspiracy theorist suspects that something has been done here in an attempt to recreate the frustratingly "off" nature of EQ's RNG.

I've been thinking the RNG is way streakier on p99 after the patch that brought high quality ore as drops in sol a. I've also not had the initiative to try and record any numbers =)

From one gut feeling to another, these are the assumptions of our lives.

[Shamen]

The last thing to consider is that the people who get the bad luck of not getting a spawn over X hours will likely be more vocal about their failure than the person who just found the mob up randomly, or got a spawn in only a short period of time. So just by browsing the forums it would sound like tons of people have this bad luck, but there are just as many who have good luck and don't post about it.

True, I started doing frenzy camp like 2 weeks ago and I got 3x fbss in first 7 cycles! Been doing it a lot since that (est. 60 cycles) and not a single fbss drop... its all about luck.

[Estu]

Yeah, you guys talking about faulty RNGs have a point, but so does Sirken. Someone early in the thread talked about how people don't think random numbers are as streaky as they actually are. To illustrate this, let me tell a short story.

I once took a probability course and the professor divided the class into two halves - he told one half to flip a coin and write down a string of 100 ones and zeroes for the heads and tails flips, and he told the other half to try and think of 100 random ones and zeroes in a row. He told us he'd leave the room, and to have one half of the class write their string of ones and zeroes on one side of the board, and the other half of the class on the other side. When he came back to the room, he'd have to guess which half was 'truly' random (the literal coin-flippers) and which half was trying to come up with random numbers.

He left the room, we wrote up the numbers, and we called him back in. He looked at the board for a couple of seconds and correctly pointed out the truly random numbers. How did he know? They had longer streaks. The coin-flippers had streaks of 7 or 8 zeroes or ones in a row, while the people who tried to think up random numbers never had a streak longer than, say, 5 zeroes or ones.

OK, so what's the point of the story? The point is we humans have a poor intuitive understanding of random numbers. We play EverQuest or whatever game and we see a long streak and we think, "Shit, this game's out to get me. It's not truly random, there's a bug in the code or it was done intentionally to screw with people." But we're INCLINED to think that because we intuitively believe that random numbers are less streaky than they can be mathematically shown to be.

The point is we can't rely on intuition to make these judgments. We need to take raw data and make statistical analyses, like was done in this thread. Yeah, if the skeleton has a 5% spawn rate then the probability of a guy going 270 spawns without a pop is one in a million. My personal conclusion to that story is that the wiki has something wrong in the spawn rate or the placeholder information (which is EXTREMELY common since the wiki has various sources, whether it be newer code from the game (e.g. maybe the spawn rate was increased in a later patch to make it less of a pain, which is the info the wiki is using, but in P99 it's the low original rate), hearsay (someone read something on an old allakhazam post or heard something from a random guildie), or straight-up speculation), so the wiki is giving the wrong probability or the guy trying to get the spawn is doing it the wrong way.

But if we're looking at anecdotal things without actual probabilities and data, NO WAY are we qualified to make judgments about the RNG and its streakiness based on our intuition. Which is what some people are doing later in this thread, and where I agree with Sirken and his tin foil hat image.

[Lagaidh]

Phil Spector's Wall of Text

I agree with you whole heartedly. Like I said of myself, I didn't have the will to truly analyze what I was perceiving.

Even as I type now, I know I've put in enough time at a camp that I begin to let "instinct" tell me something is different before and after a patch. Too bad instinct is a tool to keep us alive and feeling justified in decision making.

It's sort of amazing... on one hand, I'm a human that understands the staggering improbability of Joe DiMaggio's 56-game hitting streak, but on the other hand, I "kinda" listen when my gut is telling me that the RNG is a bit "too" streaky.

We really are still an infant species aren't we? I know better, but my biochemical programming likes to interject lies...

Man. I'd better start smoking pot again if I'm going to get all metaphysical over a RNG discussion.

[rahmani]

btw, your poker analogy is good, but doesnt apply because you are removing cards from the deck, hence every round your odds of drawing to that flush change for better or worse depending on the previous card or cards put out (depending which game ur playing).

a closer analogy would be blackjack, but with a brand new deck for each hand.

each pop (be it ph or the rare mob) is a completely separate encounter, and what pops has absolutely 0% to do with what popped before that.

not trying to be a dick, just explaining ;)

Just a side note on the Gambler's Fallacy.

Gambler's Fallacy is only the wrong assumption that any individual random event is influenced by the previous random events.

However, it is true that over long periods of time and large values of n the binomial distribution will approach the probability of the possible outcomes. This is in fact how probabilities are deduced.

It is correct to say that it is increasingly improbable for the set of n observations to deviate significantly from the distribution as n increases.

So, if there is a probability of 5% (p=0.05) of an event producing a 1, and all other times (p=0.95) will produce a 0, then at n=1,000,000 you will have a distribution that is very close to the probability. In other words, if you don't have very close to 50,000 1s, something is seriously broken.

* Binomial Distribution (http://en.wikipedia.org/wiki/Binomial_distribution)
* Law of Large Numbers (http://en.wikipedia.org/wiki/Law_of_large_numbers)
* Gambler's Fallacy (http://en.wikipedia.org/wiki/Gambler's_fallacy)

[rahmani]

Also, no computers generate truly random numbers, which is a real problem. Computers that generate the most random-acting numbers sense environmental changes caused by fluctuations in the atmosphere.

However, EverQuest like all games, uses a pseudo-random number generating algorithm, and must, by definition, fail at the serial randomness test, which compares all identical lengths of digits and weighs them against other sequences of the same length.

Go to Random.ORG (http://www.random.org), a site dedicated to presenting with the most seemingly random numbers. The numbers are not determined by a set algorithm, instead they are sensed.

In the following sequence, for any string length, L there should be an identical number of occurrences as the total number of digits approaches infinity. And as the digit length increases by 1, the digits should be ten times less frequent.

Sample of single digits:
0:205x, 1:207x , 2:214x, 7:199x, 9:189x

Sample of double digits:
00:19x, 01:20x, 69:26x, 99:17x

The sample size of triple digits is small, although they do exhibit some of the same random properties.

Sample of triple digits:
100:4x, 999:1x, 434:2x, 901:1x



60801468158158128265500664544694727122124230258075 89571133284564798639346318666510097025111188884005 21923075241160765601985943448956025269830536604941 99504230101058822671207931152613178877543677697509 02706771661102759463379639530443615657163698062759 06337782166957101973173212845041749226483640829555 86423040123454106792574561123269430351901285071917 86620163674835453275555190813444328411810157776825 13234587722475732237420540620556244139615521226905 81598019524566660334579294592358173180858402456420 60342278560260571770605545673269139285436949040963 30631986605922117878478030732571918682208101686355 29768144509889511043749779223728743822621155920732 36368577581258703118950979428887523049210023168408 37427100135119107190534513416545895979251093257271 79042017501900644993469774830551072737674466300623 59739756943917079386634900082442716979766978266522 45471379075300444617560397168250547024130633105838 51880321514936357619795116325315994695612797571243 98436734812197672492480992432227236861653412859863 21364291004588255654211046475385828878867224992808 14151174625825430174357532675458656989750344694063 15091271709802352516436199242258530307756137327440 15705758761765938234998973921542774665875715631334 76368242047502643509555881716221668548280049122183 81667194126560994767831904541927309933743864620394 51851359628452986890550026423125255750838304060402 77216336873695117866982789903107180513800797868540 43313265047972927614346809614367102894172556879749 52825882627033025084021055514790494200502341827015 10966860314288573746489647976518028880180564128814 81050576929140396109697527053447366369392520319779 99590609037699619266954394131024058087880493199574 80381552872508846866412026033903449269278810722898 17264966881768923809416025761438974757512589601200 62056044130156627607563524672328072411751402038849 28602825848721207866700913852009939022369127335074 95818145156261571036972631389596368739085531394331 28376550816382510244987659629574966734292129941784 23792086413272992712103998674454880545579600500516

Try the same test on ANY pseudorandom algorithm, it'll fail.

[Estu]

Try the same test on ANY pseudorandom algorithm, it'll fail.

Without actually having a program to test it, I don't believe this statement. Just because you have a pseudorandom generator doesn't mean it can't produce uniform numbers in the sense you described. You can do something as simple as expand pi or the square root of two to get digits between 0 and 9, and it will satisfy your test.

[Lagaidh]

There was a certain finite automata professor at W&M that could have used your elegantly direct explanation of pseudorandom in computing versus true randomness, rahmani.

In the physical realm, are there any grander (read: pie-in-the-sky) theories that the very concept of randomness is a fallacy? I.e., given the proper resources and computational power, could humanity construct a model that deconstructs an event that appears random? For example, could the model tell you that a flipped coin is going to land head-side-up if all physical conditions are known? If humanity had this capability, could we model all interactions that led up the flipping of the coin back to the beginning of space time?

Hmm. I think I read "The Last Question" too recently ago.

If any of you mentions Chaos Theory in any reply to this post, I spirit you back to 1993 so that you may once again thrill at Jurassic Park in theatres. Just remember that at the same time, Kris Kros will be very popular, the national NASCAR craze will be exploding all around you and Tim Allen will have a hit TV show... so... you know... careful.

[Fael]

Supposedly, Pain soul is supposed to spawn 1/2 as many times as rotting skeleton.
Whether those numbers (.25 and .5%) are accurate or not is hard to say. Most people tend to camp RS for 8-12 hours and PS for 16ish.

RS took me 12 hours on my main. When getting my alt his vp key, I killed the PH once and spawned two Rotting Skeleton's back to back. Getting two in 18 minutes is probably much more rare than you not getting one in 26 hours.

Dolic

[rahmani]

Without actually having a program to test it, I don't believe this statement. Just because you have a pseudorandom generator doesn't mean it can't produce uniform numbers in the sense you described. You can do something as simple as expand pi or the square root of two to get digits between 0 and 9, and it will satisfy your test.

Pi, or any other irrational number, has never been proven to be random

[Estu]

Pi, or any other irrational number, has never been proven to be random

It hasn't been proven to be random but you can't just say "it will definitely fail this test". If you actually perform your test you'll see that it appears to succeed, you just can't prove that it will succeed no matter how long you run it.

[rahmani]

There was a certain finite automata professor at W&M that could have used your elegantly direct explanation of pseudorandom in computing versus true randomness, rahmani.

In the physical realm, are there any grander (read: pie-in-the-sky) theories that the very concept of randomness is a fallacy? I.e., given the proper resources and computational power, could humanity construct a model that deconstructs an event that appears random? For example, could the model tell you that a flipped coin is going to land head-side-up if all physical conditions are known? If humanity had this capability, could we model all interactions that led up the flipping of the coin back to the beginning of space time?

Hmm. I think I read "The Last Question" too recently ago.

If any of you mentions Chaos Theory in any reply to this post, I spirit you back to 1993 so that you may once again thrill at Jurassic Park in theatres. Just remember that at the same time, Kris Kros will be very popular, the national NASCAR craze will be exploding all around you and Tim Allen will have a hit TV show... so... you know... careful.

No, you can't construct a system to behave randomly, because in order to create it, you must know the inputs. :cool:

This is the fundamental theory behind quantum mechanics, by nature of our limited senses and their attachment to our brains (See: Epistemology (http://en.wikipedia.org/wiki/Epistemology)).

We can never fully understand the processes that govern subatomic particles, because of how they react to light, i.e. photons which then react with our eyes. Our understanding of location and frequency breaks down exponentially the smaller the particles are, and they appear to behave randomly. And also, by measuring them, we are affecting their behavior.

However, for us humans there is one method to get truly random numbers, in the sense of quantum mechanics. We can attach a radioactive material to a sensor, which then counts the time between nuclear particle decay. However, the numbers would be random, their measurements of central tendency (mean, median, mode) would change over time, as there were fewer and fewer nuclear particles to produce said phenomena.

[Estu]

Getting two in 18 minutes is probably much more rare than you not getting one in 26 hours.

Say the chance of it spawning is 5%. Then the chance of getting two in a row the moment you start camping it is .05^2 = .0025. The chance of getting none for 270 consecutive spawns is .95^270 = .00000097, i.e. much less likely.

Say the chance of it spawning is 1%. Then the chance of getting two in a row from the get-go is .01^2 = .0001. The chance of getting none for 270 consecutive spawns is .99^270 = .067, i.e. much more likely.

So if the Wiki information is correct, getting the spawn twice in a row is by no means an impressive feat compared to missing it 270 times in a row. If the assumed probability of 1% people have suggested in this thread is correct, then neither one is astronomically unlikely but getting the spawn twice in a row is the rarer occurrence (although, again, the event here is that you just come in to camp, and the next two spawns are both what you're looking for, not that you camp it for a while and at some point get two in a row).

[rahmani]

It hasn't been proven to be random but you can't just say "it will definitely fail this test". If you actually perform your test you'll see that it appears to succeed, you just can't prove that it will succeed no matter how long you run it.

Pi cannot work for a random number generator because although the numbers may roughly conform to the serial randomness test, the numbers aren't random. So if you are a player and you can see that you are on the portion 3.1415, you know the next digits are 926535... A random number generator must be dynamic or it's utterly predictable, and purposeless.

[Estu]

Pi cannot work for a random number generator because although the numbers may roughly conform to the serial randomness test, the numbers aren't random. So if you are a player and you can see that you are on the portion 3.1415, you know the next digits are 926535... A random number generator must be dynamic or it's utterly predictable, and purposeless.

How on Earth is a player of an MMO like EverQuest that generates thousands of random numbers per minute going to know which digit of pi is currently being used for his rotting skeleton spawn??? Or that it's pi that's being used and not the fifth root of 19?

[Splorf22]

By definition it is impossible to compute random numbers. This should just make good intuitive sense. Personally I don't believe that random numbers even exist. I read a really interesting physics book (I forget the name sadly) that proposed that quantum mechanics isn't random; what is random is our ability to measure quantum events. In the mean time you will obviously do better trying to use large, highly-chaotic systems like the weather or whatnot to produce pseudorandom numbers. IIRC lava lamps are actually good for this :D

[Lagaidh]

No, you can't construct a system to behave randomly, because in order to create it, you must know the inputs. :cool:

This is the fundamental theory behind quantum mechanics, by nature of our limited senses and their attachment to our brains (See: Epistemology (http://en.wikipedia.org/wiki/Epistemology)).

We can never fully understand the processes that govern subatomic particles, because of how they react to light, i.e. photons which then react with our eyes. Our understanding of location and frequency breaks down exponentially the smaller the particles are, and they appear to behave randomly. And also, by measuring them, we are affecting their behavior.

However, for us humans there is one method to get truly random numbers, in the sense of quantum mechanics. We can attach a radioactive material to a sensor, which then counts the time between nuclear particle decay. However, the numbers would be random, their measurements of central tendency (mean, median, mode) would change over time, as there were fewer and fewer nuclear particles to produce said phenomena.

Okay. I see from your answer that I failed to state my query clearly. Trust me, I'm not trying to move goalposts, I just didn't get my thoughts out the first time. This may be a more succinct way of asking:

Is there any mathematically-based school of thought, of which any of you are aware, that challenges the very concept of "random"?

I ask because of just another gut reaction (instinct): When I observe things occur that seem random, I can always break down the event in hindsight to see the root cause. It's like finding the source of a software bug... It didn't just happen. There was a cause, to which there was a cause, to which there was a cause...

Could I not challenge the assertion that the example of coin-flipping students represents truly random sequences? It seems more random than the kids just stating their "random" sequences. If we could know all physical properties as they have existed from a "beginning" to the moment of the coin flip, could we predict with certainty the result of the flip?

My gut tells me "Sure. You know all that has come before. Use that knowledge, with your understanding of physics, calculate what happens next." Hell, you'd have to account for your own thoughts in such a hypothetical, as the chemical reactions might have a bearing on the flip.

Aw hell. I've begun puking out another wall of prose. Hopefully, there are enough thought crumbs above for anyone that might care to revisit the thread.

[Lagaidh]

By definition it is impossible to compute random numbers. This should just make good intuitive sense. Personally I don't believe that random numbers even exist. I read a really interesting physics book (I forget the name sadly) that proposed that quantum mechanics isn't random; what is random is our ability to measure quantum events. In the mean time you will obviously do better trying to use large, highly-chaotic systems like the weather or whatnot to produce pseudorandom numbers. IIRC lava lamps are actually good for this :D

Ah okay- while I was vomiting ascii... here's the answer. Yes. Folks way smarter than this luddite have thought something similar...

Hehe, this reminds me of the time I kept trying to say that dividing by zero should be equal to infinity. Derp: Hey, if I can divide a group of 6 units 3 separate times and arrive at 2 units per 3 new sub groups. If I divide that original group 0 times, why don't I have an infinite number of new sub groups consisting of 0 elements each. I was told that my idea was fine, but in the scenario where I divide by zero, sure, you can say there are an infinite number of sub groups each containing zero elements, however, that original group of 6 is still sitting there.

GRAH!

[enr4ged]

Most of the % values (unless edited after creation) that appear in the wiki are pulled from this website: http://mqemulator.net/

Now I'm pretty new to the emu scene and project 1999 but I wouldn't take those values very seriously. As if you check up the Rotting Skeleton on that site right now the spawn rate is listed at 20%. Unless whoever added the Rotting Skeleton has updated it the page would just list that default value.

My guess is mqemulator is some kind of default value used in the eq emulator or something? not sure...

And on truly random numbers I don't believe they exist. Which is why we have pseudo random numbers. Everything has a cause so you would just look at the cause as to why something happened. In the case of random numbers generated through computers you could essentially predict the random number if you had all the variables, could you not? The fact that there is such a large degree of variance which makes it nearly impossible for a human to predict makes it appear to be random.

You could apply this to anything, even rolling a die. If you had all of the variables at that one point you could predict the result, but there are so many variables involved (that you would also need to have the variables to predict them) it appears random. For example if you roll a die you would need:

strength of roll and force behind it (for which you would need the body make up and mindset and characteristic and mood of the thrower)
gravity
temperature
and more.......

and for each of those you would have to go back to earlier points in time to get even more variables BUT at some point you would have everything needed to predict the result!:eek:

Anyhow just my two cents on the subject. ;)

[Telados]

My guess is it is not a 5% chance of spawning. 1% sounds far more likely.

At 1% chance of spawning
After 100 kills: 36% chance of not getting spawn
After 200 kills: 13% chance of not getting spawn
After 300 kills: 5% chance of not getting spawn

At 2% chance of spawning
After 100 kills: 13% chance of not getting spawn
After 200 kills: 1.7% chance of not getting spawn
After 300 kills: .2% chance of not getting spawn

At 5% chance of spawning
After 10 kills: 59% chance of not getting spawn
After 25 kills: 28% chance of not getting spawn
After 50 kills: 8% chance of not getting spawn
After 75 kills: 2% chance of not getting spawn
After 100 kills: .5% chance of not getting spawn
After 200 kills: .0035% chance of not getting spawn
After 300 kills: .000020753% chance of not getting spawn

This is the correct math.

In general some simple formulas to use are:

If the chance of spawning on any single occurence is "p", then:

1.) Chance you have to wait more than "N" number of spawns before succeeding

= 1-(1-p)^(N+1)

Using this you can match the above numbers.

2.) Average #kills required before succeeding

= 1/p

For anyone interested, distribution associated with "the waiting time until the first success" is the geometric distribution:

http://en.wikipedia.org/wiki/Geometric_distribution

[Telados]

also, does anyone know the lower bound on the spawn rate of any mob in eq?

is there any mob with a less than 5% spawn rate? It owuld seem to me that 5% is already pretty danr rare - do any mobs really have less than a 5% spawn rate?

[Splorf22]

Ah okay- while I was vomiting ascii... here's the answer. Yes. Folks way smarter than this luddite have thought something similar...

Hehe, this reminds me of the time I kept trying to say that dividing by zero should be equal to infinity. Derp: Hey, if I can divide a group of 6 units 3 separate times and arrive at 2 units per 3 new sub groups. If I divide that original group 0 times, why don't I have an infinite number of new sub groups consisting of 0 elements each. I was told that my idea was fine, but in the scenario where I divide by zero, sure, you can say there are an infinite number of sub groups each containing zero elements, however, that original group of 6 is still sitting there.

GRAH!

Oh I remembered the book. It's 'A Different Universe' by Robert Laughlin. To expound very slightly, his theory is that a sensor is basically an amplifier. For example your computer is able to amplify the relatively small signal coming out of your ethernet cable in a way your finger can't. But the signals at the quantum level are so weak that it's simply impossible to do this process reliably. It's a very interesting book; I had to read it a few times.

[Lagaidh]

Oh I remembered the book. It's 'A Different Universe' by Robert Laughlin. To expound very slightly, his theory is that a sensor is basically an amplifier. For example your computer is able to amplify the relatively small signal coming out of your ethernet cable in a way your finger can't. But the signals at the quantum level are so weak that it's simply impossible to do this process reliably. It's a very interesting book; I had to read it a few times.

Thankee.

[Alawen]

also, does anyone know the lower bound on the spawn rate of any mob in eq?

is there any mob with a less than 5% spawn rate? It owuld seem to me that 5% is already pretty danr rare - do any mobs really have less than a 5% spawn rate?

Pained Soul and Rotting Skeleton are definitely less than 5% spawn rates. The estimates of 1% and 2%, respectively, seem reasonable from anecdotal evidence.

[August]

seems[/i] more random than the kids just stating their "random" sequences. If we could know all physical properties as they have existed from a "beginning" to the moment of the coin flip, could we predict with certainty the result of the flip?


Excellent point. Flipping a coin is not at all random. It appears random because the mathematics behind it gets very... difficult and is such that a lot of the inputs don't end up mattering. It might as well be random, but it's not.

When you flick a coin you are imparting a force upon it. The force is applied non-uniformly and usually causes a spin. So, there is rotation happening and, if a traditional coin flip, there is an upward force. It is experiencing other forces as well..

Gravity, air friction (drag), etc. If there was no rotation and it was a fixed point it is easy to calculate how high the coin will rise, and then at what speed it will be when it hits the ground. You can add the air resistance, and the rotation to this formula, and, theoretically you can determine the angle of incidence of first contact as well as the speed of rotation, and the velocity of the coin as it strikes the surface.

So, now you have the hardness of the coin and that of the table, and how it strikes. You should be able to calculate the impetus impacted upon the coin and where that impetus strikes. This creates another equation as the coin will now more than likely experience an upward force. This is the same as the first problem, except less force being applied. Rinse and repeat, eventually there won't be enough force to cause a full translation and you get to 'heads' or 'tails'.

It's really hard to do all that math for any given environment. As such, we consider it 'random' because all that really matters is the force imparted to the object when we first 'toss'.

This is a pretty good analogy for why nothing is random. Quantumly speaking, you can use radioactive decay to producea random event, but even then it's been said that it is not the event that is random, but our ability to measure it.

[koros]

Quantum mechanically speaking, all events are random, and fall into different probability distributions... if that's a fundamentally correct view of the universe is debatable.

The best way to view individual events, when trying to perceive this, is as part of a larger probability surface or distribution. Remember that game at arcades where you dropped a ball, and it would plink through a ton of metal pegs, and you'd get tickets based on how far from the center it landed? This is very similar. Assuming 100 flips of a coin, there are a lot more "paths" to 50 heads and 50 tails, then there are to 100 heads. You could get 50 heads in a row, then 50 tails, 1 head, 49 tails, 50 heads, 1 head, 48 tails, then 51 tails... just how large of a number of paths is incredibly mind bogglingly large. On the other side of the coin (no pun intended), there's only 1 possible way you can get 100 heads in a row. This is why distributions look and work the way they do.

Check this for visual reference:

http://www.nitinh.com/2011/01/facebook-hacker-cup-peg-game-problem-solution/

[Telados]

Quantum mechanically speaking, all events are random, and fall into different probability distributions... if that's a fundamentally correct view of the universe is debatable.

The best way to view individual events, when trying to perceive this, is as part of a larger probability surface or distribution. Remember that game at arcades where you dropped a ball, and it would plink through a ton of metal pegs, and you'd get tickets based on how far from the center it landed? This is very similar. Assuming 100 flips of a coin, there are a lot more "paths" to 50 heads and 50 tails, then there are to 100 heads. You could get 50 heads in a row, then 50 tails, 1 head, 49 tails, 50 heads, 1 head, 48 tails, then 51 tails... just how large of a number of paths is incredibly mind bogglingly large. On the other side of the coin (no pun intended), there's only 1 possible way you can get 100 heads in a row. This is why distributions look and work the way they do.

Check this for visual reference:

http://www.nitinh.com/2011/01/facebook-hacker-cup-peg-game-problem-solution/

I was going to respond the same way to the prior poster.

Accoridng to quantuum mechanics, everything is chance and nothing - yes nothing - is deterministic. Very different from classical physics.

[Wisteso]

How on Earth is a player of an MMO like EverQuest that generates thousands of random numbers per minute going to know which digit of pi is currently being used for his rotting skeleton spawn??? Or that it's pi that's being used and not the fifth root of 19?

While I'll agree that no one on P99 probably has the talent to reverse engineer the RNG (probably, not definitely)... Your "security by obscurity" has been proven to be a bad idea many many times before. DVD and Blu-Ray encryption cracking were both basically done by reverse engineering a type of security by obscurity that was much more complex than "using part of Pi".