Math and Spawn Rates

[Lagaidh]

Originally Posted by rahmani [You must be logged in to view images. Log in or Register.]

No, you can't construct a system to behave randomly, because in order to create it, you must know the inputs. [You must be logged in to view images. Log in or Register.]

This is the fundamental theory behind quantum mechanics, by nature of our limited senses and their attachment to our brains (See: 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]

Originally Posted by Splorf22 [You must be logged in to view images. Log in or Register.]

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 [You must be logged in to view images. Log in or Register.]

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:

1. 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)
2. gravity
3. temperature
4. 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![You must be logged in to view images. Log in or Register.]

Anyhow just my two cents on the subject. [You must be logged in to view images. Log in or Register.]

[Telados]

Originally Posted by eqravenprince [You must be logged in to view images. Log in or Register.]

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]

Originally Posted by Lagaidh [You must be logged in to view images. Log in or Register.]

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]

Originally Posted by Splorf22 [You must be logged in to view images. Log in or Register.]

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]

Originally Posted by Telados [You must be logged in to view images. Log in or Register.]

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]

Originally Posted by Lagaidh;838438
Could I not challenge the assertion that the example of coin-flipping students represents truly random sequences? It [i

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/facebo...blem-solution/