An exploration of randomness.
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Vexer wrote:
The purpose of this post is to show that the site's dice generator produces rolls that come very close to the calculated probabilities and to help players better understand the nature of randomness.

Randomness and Probability

We start off with a simple coin flip. Everyone knows that when a proper coin is properly flipped there is a 50% chance of it being heads and 50% chance of it being tails. Yet flip a coin ten times and see how often you get 5 heads and 5 tails. On average it's only about 25% of the time. This means that most of the time you don't get what you expect in the short term.

But if you flip a coin 1,000 times you should expect to get pretty close to 500 heads. But it won't be exactly 50%. You would have to flip the coin an infinite number of times to get the percentage to 50%.

This small program I wrote demonstrates this:

Open it up in a new tab and refresh it a couple times. You will see that the results vary greatly in each set of 10 flips but after 100,000 flips the percentage gets pretty close to 50%.

Our dice

The site uses php's built in mt_rand function for randomly choosing a number between 1 and 6. Many players have called in to question the results of our implementation stating that they think there is something wrong with the dice that causes them to get really bad rolls. So I wrote a program to generate thousands of rolls to see if the results are accurate.

According to Wikipedia and other sources, when attacking with 3 dice vs. 2 dice the defender is supposed to lose two armies 37.17% of the time. The attacker is supposed to lose two armies 29.26% of the time and each loses one army 33.58% of the time. The attacker should win 53.96% of the rolls.

My program will show its results followed by the above calculated probabilities in parentheses. You will see that with only a few rolls there is a lot of variability. You may think that this degree of variability is a mistake but it is in fact the very nature of randomness. You will notice the other half of the nature of randomness by looking at the results after 100,000 rolls; the program never fails to get close to the desired results. Keep in mind that it would take an infinite amount of rolls to guarantee that the program hits the percentages exactly.


Why do players keep complaining about the dice when they are very accurate? The problem is that what they expect and what they get are two different things. They expect to win 54% of the rolls in every battle. But that is not how randomness works. Some of the time players get really good dice and some of the time they get very bad dice.

But why do players think that the dice are broken and produce bad dice more often than good dice? This is more of a psychological problem than a technical problem. The fact is that we remember the bad more than the good. And even worse, we speak about the bad dice more than the good.

I did a search of all the chat in all the games and found thousands of mentions of bad dice but only a few mentions of good dice. Since I have proven that our dice are accurate then the conclusion must be that our players human brain's are the problem and not the computer.

Please do me a favor and point people to this post whenever they complain about the dice.

Better Dice?

I personally would prefer dice that behave more predictable so that I can calculate my moves more accurately. I think that the game would be better with less randomness. I don't believe that all randomness should be removed, however. That is part of the fun. But the dice should be programmed to give you something close to what you expect most of the time. We do have plans to have a game option for fake dice. The fake dice would double the chances (making it 67%) that both the attacker and defender would lose 1 army in 3 dice vs. 2 dice battle. It would not, however, change the attackers advantage. The attacker would still win 54% of the rolls on average. I think that this would solve most peoples problems with the dice.

lifeinpixels wrote:
Wow, this looks great! I hope it will help explain to the complainers about bad dice. One thing I'd like to point out is that many people claim that they would never get such a bad role on the physical board game. However, they've probably never gotten such bad dice on the board game because they don't play it as much as d12. Due to the sheer number of rolls people use here, (I'd guess in the 10,000s for many), there will undoubtedly be rolls that are worse than they've ever gotten in their 500 board game rolls. It's not that the dice are much different than real life, but the significantly higher roll counts here dictate some rolls that will be worse (and some will also be better, it works both ways of course).
KingGrayson wrote:
I really like the fake dice option. You are correct, the dice are in indeed random! Thanks for the post. How long do you anticipate it will be before the new option will be available?
Vexer wrote:
Well, I already have the algorithm for it programmed but I haven't figured out how to display the results because it doesn't really use standard dice. Like I said it's fake. Also, Matty is the expert at adding game options so I could use his help but he is trying to take a break for awhile.
elysium5 wrote:
Think about going out to eat. If the meal was good, you are generally satisfied and leave it at that. If the meal is bad, you are upset and tend to let as many people as you know that you are upset. Negative things stick in your memory much more than positive things do.
Who needs toilet paper when you've got three seashells?
marcel wrote:
I think also the dice is random, some times you have luck, sometimes you have bad luck. But sometimes I lose a lot of armies, what is of course possible whit random dice.
But I don't know if it is possible, but are there maybe statistics on how often it happens that the defender has for example 3 times a 6 in a row, when he defends a one man territory?
If that is possible a better proof can be given that the dice is each time random. Because sometimes it looks like the dice hangs on one number. But probably it is because I remember the bad dice better than the good one :).

I am interested in the new dice option! Looks like a good idea.
MadMerlin wrote:
Actually when you flip a coin there is a chance that it lands on its edge and remains standing that way . I have seen this occur but have no idea of how you work out the odds of it occurring . Just a thought . The dice seem pretty even in the game sometimes I get hammered and sometimes I get lucky that's what happens with dice It's just that we remember the bad more vividly than the good.
scaldwell17 wrote:
I work in science, and when it comes up in lab meetings, we talk about how "randomness is clumpy". We have to constantly remind ourselves that what we think looks random is not the same as what actually is random.

For a visual representation of this effect:

A mostly unrelated tangent: scientists that have been found to be faking their data have been caught because they fabricate data that "looks" random, but isn't truly random:

"Simonsohn’s technique is complex but relies upon the fact that people are notoriously bad at faking sets of data characterized by the same sort of randomness that occurs in real events."

Vexer wrote:
^^ Best post on this site to date. Thanks scaldwell17.
Glanru wrote:
I agree with scaldwell17's post. I would swear on brain tricks, if I could assume I would win any money on them.
elysium5 wrote:
This is very true. Many studies recently have been shown to be wrong because of this data tecnique used in research papers.
Who needs toilet paper when you've got three seashells?
tryitonce wrote:
So the dice may be perfect and have almost 100% randomness; but if i attack with 20 armies with 3 dices and the defender has only 2 armies and can use 2 dices its against all odds that the attacker loses 20 armies and the defender only loses 2 armies; and i (and we all) have experienced this often; killing 4 and losing 17, killing 5 and losing 25 .................. If the attacker has 3 dices and the defender 2 its really against all odds that this occurs several times.
I love this site, i play this game since a few weeks; i played thousands of games on another risk-site (; there the dice are also random but i never never never have expierenced wicked dice like here; if you have 20 armies and the other has 2 and you have 3 dices and the other 2 its really impossible that on that other site the defender wins; here on this site it also doesnt happen every day but playing 2 or 3 games a day i have expierenced this here 1 or 2 times a week. So there is something here which the randomness that just ain't right; as if throwing with 3 dices and defending with 2 dices the randomness is influenced somehow.
Yet i keep on playing here; no problem. But its just too bad that dice play that important role on this gamesite, comparing with others risk-sites. It can ruin a perfect strategy several times a week.
tryitonce wrote:
And to conclude it: the same ofcourse is when winning against all odds; like winning with 2 armies and the other loses 20; i know: that also occurs (ofcourse; its the same situation); but that too is not normal and against all odds. And i compare it with others sites where I really never have experienced this in all the thousands of games i played there. But whatever: we keep on playing here; no (or almost no) problem. All has its up- and downside.
Matty wrote:
It is true that some of the other risk sites have pseudo random dice, granting less of these extreme cases, but sacraficing the risk in risk.

I personally like it this way, my heart always starts pounding faster, even if I have 40 troops and they only have 20 :)
"The true mind can weather all the lies and illusions without being lost. The true heart can touch the poison of hatred without being harmed. Since beginningless time, darkness thrives in the void, but always yields to purifying light." ~The Lionturtle
tryitonce wrote:
OK; that could be true (pseudo random).
But the fact they say its random here and also after 1000 turns its 50 - 50 may be true; but then i tell you there are a lot of (too many) series with 20 times win and then the same amount of series of 20 times loss; and that aint normal. Yet after 1000 turns its equal. And thats the trouble. Tactics are very badly influenzed by this. And also the attacker has 3 and the defender 2 dices; so he has an advantage and the fact that a defender only needs the same number doesnt equalize this advantage. So too many occurences with weird dices make it on this site a big issue for many; skills are too much bothered by this.
But as you say: it gives this game on this site some extra spice; pity for the skilled ones, good for the rookies. And i know: the best conclusion is: if you dont like it, dont play here. Still i like it here very much (despite of the %$%$%$ dices ..............; ha ha).