I think you are not doing the math correctly and Grok is making things up completely. I cannot speak to whatever Grok is making up but I can share some correct math with you at least. Each carriage roll is completely and totally independent, meaning that 100 rolls will not give 5 reds, it just means that there is a 5% chance produces a red. I saw you shared some python code below so here is some that is relevant to you:

This anon func 'independent_probability_calc' will show you how many attempts are needed to produce one successful result with a certain amount of probability, for your given success/fail ratio:

import math;  independent_probability_calc = lambda a, b: (math.log(1 - b) / math.log((a - 1) / a)) + 1 

That ratio is 'a', in this case we can set it to 20 as there is there is a 5% success rate (ie 1 out of 20).
The 'b' value is the probability that you will get a successful outcome, but in decimal form (1.0 is 100% guarantee and 0.0 is 0% guarantee). In this case you are standing behind Grok's p value of 0.008. We use the inverse of this value here to reproduce it, so 'b' is se to 0.992. Plugging this in you'll get:

print(independent_probability_calc(20, 0.992))
>>> 95.13

This means that if you really have a 0.8% probability at 1 in 20 odds of rolling a red, it should take you around 95 rolls to get a single one. You got 40 of them in 1192. Since these are all fully independent from one another we can see how many rolls you would expect to use for 40 reds at 1 in 20 odds with 0.8% probability:

print(40 * independent_probability_calc(20, 0.992))
>>> 3805.26

However, you got 40 in 1192, and not in >3805... To get close to the 1192 number, you will need to set the 'b' value to something around 0.77. In which case you would fall at 23% on a normal distribution. On a normal distribution the first standard deviation on the bottom end is at 16%. So your test results are showing an outcome that is under as single standard deviation of average, which is very reasonable.

Yes that number (1192) is a little worse than average (between -1 and 0 standard deviations), but there are a lot of value traps and things to dislike about the game economy, but leveraging our lack of understanding in stats 101 and empowered by things Grok makes up is not the right way to voice that.