Dice: An independant thesis confirming their randomness
Posted: Thu Jul 24, 2008 6:49 amAfter hearing a raft of complaints of the lacklustre dice everyone seems to be suffering from nowadays, I've completed an independant study on the dice. You'd think making a random number generator was easy right? Just use some function like Rand() or something?
WRONG!
It's actually a very complex process. First, we start with our equation, that strictly ensures true randomness (don't listen to what people say about computers not being able to generate true randomness - they're obviously not down with this equation):
This equation will always produce a completely random result. Even when you lose 40 armies to 1. That's the way randomness works. Randomzor, the ancient Sumerian god of cubes, drew a name out of a hat, and it happened to be yours. Did you know that hat contains over six billion names? That's China's fault.
Anyhow...
This equation gets referenced by the CC website thousands of times every day. So many times in fact, that we can produce a distribution plot of results based on past dice rolls. Here's a plot of the past 3 days results:
As we can see, several factors affect the distribution plot, namely Touch, Target, Release, and Time.
So we can see there is quite a lot that goes into our dice results. Why are there two graphs you ask? Well Graph #1 (the red one) is the plot for Freemiums, and Graph #2 (the black one) is Premiums. As you can see, Freemiums actually have a higher distribution of 4s, 5s, and 6s than Premiums. But that's only if they click the Attack button -150 milliseconds after hitting the Deploy button.
This plot can be hard for the layman to digest. So, to assist the community to understand the role the dice play in our games, and to settle, once and for all, the dispute about random dice, I have provided the easy-to-read graph below. Enjoy.
Q.E.D.
WRONG!
It's actually a very complex process. First, we start with our equation, that strictly ensures true randomness (don't listen to what people say about computers not being able to generate true randomness - they're obviously not down with this equation):
- 'P' is the probability of a certain number coming up, 'r' stands for range (in our case, 1 to 6) and 't' for type (in our case, freemium or premium). Yes, premium membership does make a difference! Not only in this equation, but in other ways, as we shall discover later. Moving on...
- 'g' is for game type, which has a major impact, hence it being on top of the line thingy. Ever wondered why you never win Escalating? Well those little gt and grs might be your answer
- That funny looking upside-down 'y' is actually the greek letter lambda. No, it has nothing to do with lambs. But it does make a difference when you play on Ancient Greece or Alexander's Empire, and to a lesser extent, World 2.1 (but only if you're holding Europe).
- The 'o' with the cowlick is a miniature of AndyDufresne's avatar, were it Tin Tin. Which it isn't. But it's from a similar era, and it's easy to mix the two up. Anyhow, that's to ensure that the mods have a better chance of winning than your regular schmoes, perfectly sensible, since a mod that is a cook simply would not be taken seriously.
- The pi symbol has nothing to do with me, alas, but may explain why I am a Major at this point in time, having once been a cook. In fact, I'm almost certain that if my name actually contained the pi symbol, I probably would be Conquerer. Or Captain. Some rank with a very geometric symbol anyhow. That's how maths works. Geometry.
- r1 and r2 once again respresent range. r1 is your dice range, r2 is your opponents dice range. That's right, your opponents dice range is always twice yours. That goes for attacking and defending dice. Don't worry, it affects your opponent as much as it affects you.
- The 'dV' is only there to throw people off. Many people think computers can't produce random numbers simply because that dV is sitting there. It in fact has no effect on the equation whatsoever which, up to that point, is entirely totally 100% random.
This equation will always produce a completely random result. Even when you lose 40 armies to 1. That's the way randomness works. Randomzor, the ancient Sumerian god of cubes, drew a name out of a hat, and it happened to be yours. Did you know that hat contains over six billion names? That's China's fault.
Anyhow...
This equation gets referenced by the CC website thousands of times every day. So many times in fact, that we can produce a distribution plot of results based on past dice rolls. Here's a plot of the past 3 days results:
As we can see, several factors affect the distribution plot, namely Touch, Target, Release, and Time.
- Time is the time we take to click the Attack button after deploying our armies. Clickable maps are a godsend for many players who were once plagued with unwinnable dice.
- Target is the number we're aiming to get on our dice, as read from the lasers in our CD drives, transmitted through the internets, and into the CC servers. As you can see the average number people aim for is about 5.7. Most want all 6s. Some of us like to keep it real.
- Touch is a measure of how hard we click the mouse button. PC-rage (and Mac-rage too) doesn't pay when it comes to playing CC.
- Release is how long it takes for us to lift our finger off the mouse button after clicking it. For some reason this is measured on the same scale as Target. This is a mathematical enigma still unsolved to this day.
So we can see there is quite a lot that goes into our dice results. Why are there two graphs you ask? Well Graph #1 (the red one) is the plot for Freemiums, and Graph #2 (the black one) is Premiums. As you can see, Freemiums actually have a higher distribution of 4s, 5s, and 6s than Premiums. But that's only if they click the Attack button -150 milliseconds after hitting the Deploy button.
This plot can be hard for the layman to digest. So, to assist the community to understand the role the dice play in our games, and to settle, once and for all, the dispute about random dice, I have provided the easy-to-read graph below. Enjoy.
Q.E.D.
A fun read. 
lmao