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It's just as you describe.
The game only has a recruitment date, and then uses death probabilities depending on how long they've been in service.
They refer to generals and admirals.
And I think we should make this visible to Paradox so they would add this long-waited 'feature' which is pretty easy to make.
I am referring to the ability to predict anything (or lack thereof) - It's a percentage chance, not a static number.
I'm starting to doubt the fact that death rate for military leaders depends on their "age".
Wiki says their life expectency is around 12 years (without any source), browsing old saves I found an average of 15 on a game with few short battle (meaning the leaders were not deployed much).
Apparently leaders have 3 death rates (existing, commanding and in-battle) : I found this one on a reddit with source to paradox forums.
When you turn your king or heir into a general, the game file registers this as recruiting a general, and saves the recruitment date. If the death rate was modified by the time since the recruitment, 15 years old heirs turned into general would get very high yearly death rate in their early 30s due to being in service for too long.
Another hypothesis would be that the death rate is a constant. Making the overall life expectency being a simple case of exponential decay.
This remains a simple hypothesis, but it would explain why the recruitment date isn't shown on generals, since it would have no impact on the rate of death.
Depending on what Random Number Generator they are using, it can be (somewhat) predicted. Bad random functions have a pattern and often use some external information (like time). I have the feeling the random number generator is not that good which is used in EU4, but one cannot really test that in the game itself.
For instance the excel Random function often returns a somewhat uniformly distributed outcome for every random setup you plug in. While you would expect at least 1 outlier if you would run it 1 million times. Simply put if you throw a coin 10000 times. Excel would give you 5000 head, 5000 tail. It will never give you 10000 head, 0 tail. While the probability of this happening is just as big as 5000-5000. Since it is always 0.5^10000.
the probability of getting 5000 heads and 5000 tails is enormous compared to 10000 heads.
if you toss a coin twice, the probability of 2 heads is 0.5 x 0.5 = 0.25. HH
the probabilityof 1 head and 1 tail is 0.5 x 0.5 + 0.5 x 0.5 = 0.5 as it can go HT or TH.
basic probabilities
I get your point, but in this case what I was trying to say is that the probability of HH = P(TH) = P(HT) = P(TT). So if you get an outcome of 5000 heads and 5000 tails in a given order then the probability should be the same as 10000 heads. And excel's random would give you values similar to TH and HT but not TT and HH. I hope it is somewhat clear, so P(TH) = P(HT) =/= P(HH). Because in that randon function it becomes more likely to get head (tail) when you have gotten a lot of tail (head) previously. So it is biased.
On a larger size, it would be the same as this question:
You flip a coin 6 times, which answer is most likely to occur?
a) THHTTT (4 tails, 2 heads)
b) HHHHHH (6 heads
c) HTHTHT (3 tails, 3 heads)
d) all are equally likely.
People tend to answer c) because it looks like what we expect (50% head, 50% tail). The answer, however, would be d) (unless the coin is biased). Which in excel's case (and probably EU4 as well) is true. The program tries to average out the values to something we would expect rather than something that is purely random. In EU4 it could mean you could have a real bad luck stroke if everything was purely random or the opposite of an abundunce of luck. It can also mean that there could be a pattern which can be used in your advantage.
That is some huge pile of nonsense.
Each of your proposition presents 2 answers. Let's take a) THHTTT (4 tails, 2 heads).
and c) HTHTHT (3 tails, 3 heads).
While the probability to get THHTTT and HTHTHT are the same, the probability to get 4 tails and 2 heads is inferior to the probability to get 3 tails and 3 heads.
The only objection would be if you were considering the draw order, but then again THHTTT is not TTTTHH (4 tails then 2 heads), nor is HTHTHT the same as TTTHHH (3 tails then 3 heads).
No, that's not how it happens. As you mentionned, the RNG generators usually use some key obtained by following mathematical series or by dividing prime numbers, and then add factors like time.
If you base your observation on a single 10000 long cast, you will have more chances to observe a 5000/5000 (that's the basics of probability there, higher probability to happen means higher chance to reach it on a single observation).
On the other hand, if you do hundreds of casts, then you'll see that you might have some imbalanced 4800/5200, with million of casts you might even see a 4000/6000, or maybe a 10000/0. I say maybe because the probability for that to happen is in the range of 10^-3000, so even with a million of casts, you're far from sure to even see one.
It seems you've yet to pass that statistics class.
Lol really? That you do not understand, does not mean that I am wrong ;)
I have passed enough statistics classes thank you very much.
Make a 100x100 matrix of Rand(0;1) in excel. So 0 for tail, 1 for head. This would be a test of flipping a coin 10000 times in a row and it would give you a serie (outcome). Now sum up all these values and repeat the process several times. You will never get a sum of 0 (all tails) or 10000 (all heads). You can press delete on an empty cell to refresh the random function infinitely times. The random function is made in such a way that it is not random at all but tends to revert to a mean which is the expected value -> (50%*0 + 50%*1) * 10000 = 5000
If it were completely random the sum of the matrix of 100x100 with random binary (0,1) would lead to a similar (not same) result as a random function with rand(0;10000). But it does not... The point being that the function is not random. It looks at the previous values it has already given, and then changes the probabilities making a certain outcome more or less likely.
Isn't that what I just said?
I wrote tails and heads just to include the unordered sum results of the previously mentioned (so you would not have to count yourself or might misread otherwise). The order is fixed.
Anyway we are deviating from the original discussion. Long story short: the random function in EU4 does not have to be random, but it can revert to a mean or follow a certain behavior. If one would know the process one might be able to predict it's outcome and thus manipulate the game in his favor. (something might be that 1 february might be a "random" lucky date for a fight, so if you have a war, you fight them on 1 february). One might be even able to use it for rolling military leaders which "randomly" happen to be very good.