Math and Spawn Rates

[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

[Estu]

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

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]

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

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]

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

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.

[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.

[rahmani]

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

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. [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.

[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.

[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.