Theory of the RNG

[Naedea]

I think any veteran tradeskiller would agree when I characterize the pattern of skillups and success/failure as streaky. A 250 smith might have an overall 50% chance of succeeding at a particular combine, but on a given night, he may go 2 for 10 with 7 failures in a row, or succeed in similar fashion. This happens far more often than you would expect if you were flipping a series of coins with independent probability.

What, then, is the model of random number generation that produces these agonizing (or delightful) streaks? I believe that the probability of a particular result of a combine fluctuates is using a "random walk" algorithm.

For example: Go out to a large open field and mark a spot on the ground. Take with you a coin like a nickel or a quarter. Stand on the spot and flip the coin. If the coin comes up heads, turn to the right and take a large step. If the coin comes up tails, turn to the left and take a large step. Keep doing this many times and see where you end up.

If you flip the coin 25 times you will probably be about five steps away from where you started. This is because five times five equals 25. How far would you expect to be if you flipped the coin 100 times? A random walk is not a very fast way to get anywhere!

When you try this, you will notice that sometimes you go much farther than you expect and sometimes you end up very close to where you started. But if you repeat it many times or get several of your friends to do it with you with coins of their own, the average distance should come out as expected. In science we can often predict what will happen on the average even when the process is random.

As this pertains to tradeskills, you don't always have that 50% chance of failure. Over the long haul, you may average 50%, but your success pattern will tend be streaky, if the probability of successful combines follows a random walk model.

Another visualization of the random walk model is one of Brownian motion: the movement of molecules in a fluid environment. Einstein received the Nobel Prize in 1905 for his mathematical theory explaining this phenomenon.

<APPLET codebase="http://home.earthlink.net/~cbi4/applet/brownian/" code="BrownianApplet.class" ARCHIVE="brownian.jar" width=400 height=200>
<param name=magnification value=5>
<param name=nballs value=5>
<param name=averagevelocity value=30>
</APPLET>

White NoiseBrown Noise
A model using independent completely random trials, such as flipping a series of coins, or rolling a series of dice, would result in a pattern with an even distribution of points. This is the mathematical model used to generate white noise.
A model using the random walk algorithm would result in a pattern in which the value of one point on the graph is the previous value adjusted a small amount. This is the mathematical model used to generate brown noise, and I believe, the one used by Everquest's RNG.


Random Walk example is blatantly stolen from the chemistry department of the http://scifun.chem.wisc.edu/WOP/RandomWalk.htmlUniversity of Wisconsin-Madison</a>
Brownian Motion example is borrowed from the physics department of the http://www.phys.virginia.edu/classes.../brownian.htmlUniversity of Virginia</a>
Noise waveforms are from http://www.geocities.com/SiliconVall.../algorith.htmlFractMus</a>, a developer of fractal music composition software.

[Itek]

Interesting theory.

Problem.

Your theory presupposes that the RNG is unique to each character/account. (As it supposes that the RNG "changes only a little" per the "brown noise" method.)

This WAS true, before they moved the RNG to the server side. (Remember when people could alter their /rand 100 rolls from their computer, thereby always winning loot rolls?)

[eqNichola]

Re: Theory of the RNG

I think any veteran tradeskiller would agree when I characterize the pattern of skillups and success/failure as streaky. A 250 smith might have an overall 50% chance of succeeding at a particular combine, but on a given night, he may go 2 for 10 with 7 failures in a row, or succeed in similar fashion.

I'll give you that.

This happens far more often than you would expect if you were flipping a series of coins with independent probability.

But not that. Not without some hard evidence.

[Naedea]

Interesting theory.

Problem.

Your theory presupposes that the RNG is unique to each character/account. (As it supposes that the RNG "changes only a little" per the "brown noise" method.)

This WAS true, before they moved the RNG to the server side. (Remember when people could alter their /rand 100 rolls from their computer, thereby always winning loot rolls?)

I'm not sure what in my theory presupposes unique RNGs. Why could the RNG on the server side not use a "brown noise" or "random walk" algorithm? It need not be unique to each character or account. There could be a pool of RNGs available to supply random numbers to various functions. Think of them like the stock tickers on the New York Stock Exchange, with your "luck" factored into equations as a function of an extremely volatile stock price. I'm not saying this is the case, but moving RNG from client to server would not preclude this type of model being used.