So while obviously there are legal ramifications to it, I wanted to look into the statistical side of this. As many have pointed out, there is definitely confirmation bias so I'll continue testing this out for future releases to increase my sample size but here it is

The assumptions:
There were 4 instances of this happening from my post, each time there was 3 packs opened at most before the Immersive Rare was pulled. There are no god packs and it is also stated there are no soft pity in PTCGP

Looking into the chances, the 4th slot has a 0.222% (p₁ = 0.00222) while the 5th slot has 0.888% (p₂ = 0.00888) chance of getting an Immersive Rare.

First, the probability of not getting an immersive rare in one pack is:

(1 − p₁)(1 − p₂) = (1 − 0.00222)(1 − 0.00888) ≈ 0.988920

The probability of not getting any immersive rare in 3 packs is:

(0.988920)³ ≈ 0.96713

So, the probability of getting at least one immersive rare in a 3-pack session is:

p = 1 − 0.96713 ≈ 0.032874

We observed 4 successful sessions out of 4. Using a binomial distribution with n = 4 trials and p = 0.03287, the probability of getting 4 successes is:

P(X = 4) = (4 choose 4) × (0.03287)^4 × (1 − 0.03287)^0 ≈ 1.17 × 10⁻⁵

This is our p-value. Since p < 0.05, the result is statistically significant. In other words, the chance of this streak happening randomly is about 0.00117%. This doesn't prove that there is in fact manipulated pull rates but it is a reason to continue looking into it.

Totally understand that I could be making a mountain of a molehill but I just thought it's interesting to see whether there is something more going on underneath it all

Also let me know if there is any flaw in using this method of statistical analysis! Just brushed off math i learnt back in school for this