Lack of 0 roll, shows that it is not big enough sample. There should be at least 100 dice throws alltogether(50 for each side), actualy 200 would be better.
20 combat die rolls vs computer in iron man game.
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Don't understand why this convo is still going on, the code was posted as well as what prng is being used. That should have been the end. Is it really going to take someone posting results of 100, 200, or as some people have advocated, 2,000 dice rolls? 
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Don't understand why this convo is still going on, the code was posted as well as what prng is being used. That should have been the end. Is it really going to take someone posting results of 100, 200, or as some people have advocated, 2,000 dice rolls?
Even trained statisticians are relatively terribad at statistical intuition, so it's probably just not going to end unless someone does a full analysis, no.
Yes you are, you're trying to infer from 20 dice rolls that the dies are loaded in favour of the AI, which is akin to saying that the entire 'population' of die rolls (i.e. every die that will ever be rolled by every EU4 player in every game) has a bias towards the AI.
If I collect a million dice rolls from all my battles, then focus on just the battles whcih annoyed me and which I lost, then post these as my "sample" surely you can see that this is misleading, will give wrong conclusions, and this is exactly why you do need a random sample.
I just ran my own random sample, and the results were shocking.
I, like you, used to think the AI was given preferrential treatment by the dice.
But as you'll see in this shocking video, you are about to get information that will completely turn your life around.
What I will do in the following 20 minute representation is explain the facts that you will need to make a life altering decision.
You just need to post your credit card information..
Wait.
Wrong forum.
Here's the results:
ME - AI
8 - 0
2 - 4
7 - 3
9 - 6
From these very revealing results, I just calculated that my average roll was 6,5 (a VERY strange number, on a 10 sided die, I'm sure you'll agree) while the AI's average roll was 3,25.
It quickly became obvious that I am given a 100% advantage on the AI.
"But wait! What difficulty setting did you use!"
And you'd be right to question me.
Maybe I set it to easy, and the player gets easy mode on the dice.
But no, it's at normal, which would imply that neither the AI nor the player be given advantages.
This smells, my good audience.
Badly.
Are Paradox making the game easy in order to appeal to a broader audience? Are we seeing the money grubbing effects of rampant robber capitalism?
It is not up to me to pass judgement. I just inform you, the public, about what I find.
You must be the jury, and the judge. And the concession stand outside the courtroom.
If anyone wants the screenshots I made during this experiment, they are freely available via my steam page. http://somethingisrotteninthekingdomofparadox.com
I, like you, used to think the AI was given preferrential treatment by the dice.
But as you'll see in this shocking video, you are about to get information that will completely turn your life around.
What I will do in the following 20 minute representation is explain the facts that you will need to make a life altering decision.
You just need to post your credit card information..
Wait.
Wrong forum.
Here's the results:
ME - AI
8 - 0
2 - 4
7 - 3
9 - 6
From these very revealing results, I just calculated that my average roll was 6,5 (a VERY strange number, on a 10 sided die, I'm sure you'll agree) while the AI's average roll was 3,25.
It quickly became obvious that I am given a 100% advantage on the AI.
"But wait! What difficulty setting did you use!"
And you'd be right to question me.
Maybe I set it to easy, and the player gets easy mode on the dice.
But no, it's at normal, which would imply that neither the AI nor the player be given advantages.
This smells, my good audience.
Badly.
Are Paradox making the game easy in order to appeal to a broader audience? Are we seeing the money grubbing effects of rampant robber capitalism?
It is not up to me to pass judgement. I just inform you, the public, about what I find.
You must be the jury, and the judge. And the concession stand outside the courtroom.
If anyone wants the screenshots I made during this experiment, they are freely available via my steam page. http://somethingisrotteninthekingdomofparadox.com
You can say that for a coinflip because coin flips only have two possible outcomes. The same absolutely cannot be said of an average of 3.4 when the null hypothesis is a mean of 4.5 and standard deviation of 3. That is obvious to anyone with any inkling of statistics. So the fact is that everyone WAS right within this context. Going all "but if you were talking about something totally different to the thing you actually are talking about" doesn't make them wrong. It makes it nitpicking.
This is just a load of nonsensical pseudo-arguments. Looking at a survey of battles to infer something about the whole combat rolls system, is EXACTLY the same as doing a telephone poll to extrapolate information about the population.
Translation: When I win a battle it is due to my strategy/planning/being-me, but when I lose it is due to insanely arbitrary dice rolls that are clearly biased in favour of the AI.
The reason you think it is "usually" anything is due to selective memory and confirmation bias.
No, I am not, nor have I ever been. Like everyone else in the first few pages in this thread, I absolutely agreed that while the player performed poorly, it was not quite a statistically significant result.
The main problem here is that people keep saying "You can't get a statistically significant result with only 20 rolls" when this is absolutely incorrect. In fact if the player had performed slightly worse there, it would have been statistically significant, depending on the desired significance level; it was a significant result at p < .06 as it was. But we probably want a more demanding significance level before we start raising eyebrows, which is why, like, everyone else, I said "needs to do more rolls."
Come back when you can show that p < 0.0000003.
Because right now the Higgs boson is more real than the supposed anti-player bias in Paradox's RNG.
Because right now the Higgs boson is more real than the supposed anti-player bias in Paradox's RNG.
I agree, this was not a statistically significant result. You're missing the principle, though: it is possible to have a statistically significant result for only 10 coin flips, or only 20 d10 dice rolls. You would just need a more extreme result than we got.
No, it's not at all. The combat rolls system is an abstract system. The population is composed of concrete individuals. In theory you could actually survey the entire population and get a 100% correct result. It would be the definitive results and there would be no need to make any statistical inferences.
With the combat system, you will never have the "truth," only the abstract expression of the rules versus the results. The results will almost never exactly match the abstract expression of the rules.
Sadly, I think this vastly overestimates the ability of this community to recognize and accept a full analysis even if someone did do one.
In any case, all of this talk about p-values and such is moot given that we do not know whether selection bias was involved in OP.
Nobody is saying there is anti-player bias.
What I am trying to explain to people in this thread is that their understanding of the process of how to find that bias, if it existed, is wrong.
For example, this post on the first page:
No, if you got just 1s with 20 dice throws, you definitely have a problem.
I disagree, take a look at post #2.
I know, that was pretty clear. I was just poking fun at the discussion in general, not actually trying to refute any particular opinion
This above response is very well put. One thing that drives me crazy is that in these sort of threads everyone spouts out "you need to have a bigger sample size!" Sample size is generally important when you are looking at the statistical power of a test. That is to say, the smaller the effect size you are looking at, the more samples you will likely need to reject the null hypothesis.
This is very intuitive. Let's say I take 2 unfair coins, 1 with a probability of getting a heads as .9, the other with a probability of getting a heads with .500001. It will take far far fewer coin tosses to determine that the first one is rigged than the second one, which follows our intuition.
My PhD was in pure mathematics, most of my publications are in PDEs (I have some great results on the KdV that just got accepted if anyone else here does math!), and I NEVER touched statistics until I took my postdoc job, so I still get plenty of things wrong. In one of our current experiments to see effects of obesity on gene expression, the size of each group in our experiment was 10 and we have plenty of power to detect significant genes through what is essentially a t-test that has been modified for the type of data we are looking at (plenty of great papers on the subject and everything is in R which is fantastic). Obviously, there are genes that have an effect on our phenotype that we won't find because their effect size is very small, and they will come up as not significant but that is what you would expect.
I''m just saying it looks arbitrary. Whether they're or not...
I was referencing to fights between countries with same techs and other variables (mostly), without leaders.
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