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The differense is in the distribution set generated, if you roll 1d20 you get numbers between 1-20, each have an equal chance to appear on the first roll, but each number get an statistcaly less chance to appear again for each time it get's rolled untill all numbers on the dice have been rolled.
So for the 80% range you have 4 numbers that would be misses. Each time you roll one of these 4 numbers the chance for it to appear again before the other numbers decreses.
So if you roll 1,4,3,1,2,3,1,4 The chance for rolling one of these numbers again are extreamly unlikly, but the most likly of them is a 2.
Now on a d100 there are 20 numbers it has the exhaust, making a big difference on small amounts of rolls, as evry one of those numbers have the same chance to appear as any other number.
The reason to why do did not notice any issues with it when playing CoC RPG is because you did not roll a 1d100, you rolled 2d10 with one with power of 10 to the values. This gives a very different distrubution set to a single d100.
A good way to visualize this is to generate let's say 2000 numbers using the different sets, and then analyze them in chnuks and see wich set's include the longest chunks of numbers outside the 80% hit range.
It should not come as a suprise to anyone that the plain d100 contains far longer chunks of this.
You could try it out at home, as I said, generate those sets of numbers and start looking at them to see where you find the longest chunks of values corresponding to the condition.
Probability averages out over large sets of numbers, but smaller chunks will not adhere to it the same way.
Every die roll is independent, in Battle Brothers and in real life. If you are rolling a D20, you have a 5% chance of getting any particular number. If you roll a 10, you had a 5% chance of getting 10. Your chance of rolling 10 on the second roll is still 5%, even though the outcome 10,10 is relatively unlikely (0.25%).
If you roll the die 20 times, you have an independent 5% chance of rolling 10 on each individual roll, regardless of whether you rolled a 10 the previous single roll or not.
The reason for this is that the probability of any given specific combination in a specific order is equally likely. The likelihood of rolling 10 and then 2 is also 0.25%, just like 10 and then 10.
But considering how many "dice" are rolled each battle, and the almost infinite range of possible coincidences, its not really that surprising that you notice these sequences quite often.
Yes, but missing 3 95% shots in a row is an 8000:1 shot or 4 X 90% is 10000:1 and both have happened to me more than once, and yet, if what the devs say is a true 1000:1 shot, finding a 3x3* BB, most people have not seen once. I've seen it once.
So, there what the math is supposed to be, and then what actually happens.
I mean the obvious answer is that
A. You've made FAR more attacks than hired brothers
and
B. As Sato said above, it's not "3 95% shots in a row" or "4 X 90%" in a row, since you tend to ignore all of the random rolls you don't see behind the scenes, such as damage rolls, resolve checks, or even simply just the the random numbers generated for things like checking if an arrow should go astray, or what sound to play.
I didn't say they did, I said people ignore them.
But to answer your question, they won't cause those specific rolls, but often there are other uses of the Math.rand method, be it selecting what sound effect to play when the skill is used or misses, the random element of AI for the enemy, etc.
There are some games that offer such variants of randomness. I suggest checking this Colony Ship thread https://steamcommunity.com/app/648410/discussions/0/5805689546860220887/ where they discuss true random vs lightly adjusted vs heavily adjusted. You describe a "heavily adjusted" scheme, which results in bad results, probably because it's a set of 100 values as you point out. However, unless you use this (very non-random) pseudo-random generator, the number in the sets doesn't matter.
Actually you can see it perfectly well in coin-flip, as a coin-flip have a small set of distributed numbers, and a high liklyness for repeated numbers.
So if you flip a coin you will quite fast reach a 50/50 result, because it's a small set, but you will also see a lot of long repeats of the same numbers.
The larger "dice" you choose the longer time it will take to get to 50/50 and you will also see shorter and shorter repeats of the same number.
So insted of the coin, randoms over a set of 1 centillion, and see how fast you reach a 50/50 parity.
Unless you mean getting an even distribution of numbers, as in a d20 takes longer to roll 1, 2, 3, 4, 5, etc one time than it takes a coin to flip head or tails 1 time each; in which case, yeah; but that's because you're rolling it 18 times more at minimum. If you flipped a coin 20 times and counted the distribution of outcomes looking for 10 instances of heads, and 10 instances of tails; you'd take just as long.
The equivalent to "1d2 reveals 1 and 2 frequently" is equivalent to "1d20 reveals 1-10 and 11-20 frequently", same for d'centillion.
Why... Why am I even writing this...
After they lost there bet with 1d10 for 9 times in row in gamble house, they put everything + borrow from loanshark to play there 10th bet because they though they going to win this time... that how math work (for them).
After he lost everything then he going to make a ruckus threatening to sue gamble house for cheat him. Because he should win that 10th game accord to how 'Math' work.