The site's dice are accurately pseudorandom.

LOL, okay okay! Just the sort of response I expected! Glad you have checked his game logs and there is no evidence to his claims! Here is a link to the game that I played with him in which he claimed to have worked out a timer att/def bias: http://www.dominating12.com/?cmd=game&sec=play&id=223187 Happy Reading, it's quite funny! You can also see why playing rookies is sometimes bad! Anyway, it's good to know for the sake of the live game players that; [size=16][b]The site's dice are accurately pseudorandom[/b][/size]

This is very very cool. I know it's a really old post, but I just read through it all and saw the stats. The best random number generators on Earth which are truly random actually use thermo couple input (temperature converted to electrical signal), and then measure air temperature to like 12 decimals, and take the last decimal as the input to their random number generating algorithm. Since error in the thermo couple, and various random changes to that degree of temperature could not possibly be predicted, the outcome is truly random. But when your results are THAT conclusive, the php random number generator seems to be great.

Can someone explain what the third dice does? As far as can tell it's dice 1 vs 1 and 2 vs 2 but I have no idea what dice 3 does. Also when the defender is down to one troop any drawn dice seem to kill attacker which would reduce the overall ratio of attack versus defend.

The three dice the attacker rolls are first sorted high to low. Let's call the highest A1, the second highest A2 and the lowest A3. The defender throws two dice of which D1 is the highest and D2 is the lowest. Then A1 is compared to D1 and A2 is compared to D2. You are right that the third dice does "nothing", but because it will always be the lowest of the three, the likelihood that the other two dice are higher numbers is larger. That is why attacking gives you a slight advantage over defending (however, if the numbers on the dice are equal, the defenders wins). If the defender has only one troop left, only the strongest die of the attacker is compared to the defender die, which gives an even greater advantage.

[quote=Cireon - May 24, 08:44 AM]That is why attacking gives you a slight advantage over defending (however, if the numbers on the dice are equal, the attacker wins).[/quote] I thought that the tie goes to the defender?

Sorry, typo, fixed.

Vexer said: "Since I have proven that our dice are accurate then the conclusion must be that [i]our players human brain's are the problem[/i] and not the computer." Classic! ^^

https://www.youtube.com/watch?v=Kgudt4PXs28 Was watching this video and really like the way they explained the dice rolling, and the advantage the attacker dice have on the long run not just on one attack. p/s: I was thinking when it says if you continue rolling the die for a very long time THE BANANA will rot.

Maybe you could make third dice (or "no dice") for them who dont want randomness. That could work: how many defensive troops, that number of attacking dissappears, and vice versa. If you attack with 50 troops and someone defend with 20, you will kill him and have 30 troops.

I believe if you totally remove the dice this game loses a lot. Anyway we have a middle way option between randomness and non-randomness that is Balanced Dice. It is good when you want to avoid games too much luck based. If you don't know it, try it out. Normally I prefer to stay in the randomness of Standard Dice, but I'm going to try Balanced too. Supia... Nice video but that die game is not so exciting!

If you start a game against good opposition and get a bad drop there's no coming back from it, unless you are playing with standard dice. That's all

I don't doubt that the dice are fair, but I haven't seen any posts addressing serial correlation (https://en.wikipedia.org/wiki/Autocorrelation), which would make the game unfair on some level. Serial correlation is present if the results of the previous roll are correlated with the next roll. This would be the case if winning on a single roll made you more (or less) likely to win on the next roll. If this were the case, it would lead to a higher quantity of big wins or big losses than you would expect with random dice. However, even if serial correlation is present the total quantities of winning by 2, losing by 2, or tieing could still be exactly what you would expect them to be with random dice. I don't know what software is being used to test these dice, but if someone simulates 10,000 rolls, and then regresses each outcome on the previous 2 outcomes, that would test for serial correlation.

We have done exactly that: simulate something like 10.000 rolls, and the outcomes are as you expect them to be. The 'experiment' is not available for members to just run (that would slow down the site terribly), but I posted a screenshot somewhere on the forum. Having said that, we just call a new random number from a PRNG every single roll; we don't look at previous results. [b]Edit:[/b] In this topic I posted two screenshots of dice analysis: <dead link> [b]Edit 2:[/b] The link above has gone dead, here's a new place to find the results of the same simulation, but performed later: https://dominating12.com/forums/2/general-discussion/879/the-sites-dice-are-accurately-pseudorandom/post/56667#post-56667

I just found this post, I would like to clarify some things. I guess that the PRNG used in this site is good or, at least, good enough for playing risk. However, I would like to point out that Vexer’s simulation doesn’t prove that the generator is random at all. For example, lets take a coin flipper simulator that, after 100.000 flips gives a sequence like: [b]head, tail, head, tail, head, tail,….[/b] or [b]head, head, head … tail, tail, tail [/b](50% heads and 50% tails) or [b]head, head, tail, tail, head, head, tail, tail, head, head…[/b] In any of these cases, you will obtain 50% heads and 50% tails, but the sequence will be far from random. In order to prove that a sequence has good random properties, more complex tests must be made. For example, some tests available are the [url=http://www.csis.hku.hk/cisc/download/index2.htm]Diehard[/url] and the [url=http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html]NIST[/url] tests. Unfortunately, these tests are designed to test binary sequences. If your PRNG is generating random integers (from 1 to 6), the testing can be more complex. I have also read some complaints about the dice not being "True Random". The only difference between a TRNG and a PRNG is that the TRNG obtains the numbers from a physical (unpredictable) source while the PRNG obtains the numbers using a deterministic algorithm.[b] A TRNG doesn't necessarily have to be better than a PRNG[/b]. In fact, I believe that is usually the opposite. Quite often, TRNGs have bad satistical properties. Edit: I just saw that your algorithm uses the Mersenne Twister which passes the Diehard randomness tests, so the PRNG used is actually quite good.

We currently use a PRNG that is [url=https://en.wikipedia.org/wiki/Cryptographically_secure_pseudorandom_number_generator]cryptographically secure[/url]. I think that is by far sufficient for a risk site ;)