He’s not saying it’s guaranteed after X number of egg hatches so I don’t know why you’re finding an issue with his method. You can apply binomial to egg hatches.
I think where you’re confusing yourself is you think he’s doing conditional probability, e.g. where cards from the pack are removed so the ones you get affect the chances on all the subsequent draws. All Zard is doing is working out the chance of getting zero legendaries/mythics from X packs via binomial then doing [1 - result] to work out what must be the chance of getting something good.
That wouldn’t work here… binomial can be applied after a summation series is formed by extending his algorithm to x+1 eggs , then to x+2 eggs and so on till infinite tries since he already has a formula to x eggs. This would result in an infinite series and equating that series to either 1 or 0 depending on his definition of x would give a more accurate probability for non-correlated events. At this stage, I wouldn’t be surprised if number of eggs was a huge number Since RNG and probability is a complicated pair .
But then , it’s not necessary to complicate things over eggs . So fine I’ll take the 3 packs even though I know it’s possible to hatch 6 packs without a legendary !
Ps: it’s a common misconception that probability of a head or tail in a coin toss is 50%. For simpletons , yes! But not when you give a proof ! It’s necessary here to consider at least 10 experiments considering each one as a different outcome with each experiment as 3-pack hatch and then apply either Chi-2 test or normal distribution or standard deviation or some other suitable method to arrive at a conclusive result. 89 % in 3 packs is a huge number just enough to convince anyone a legendary in 4, if not 3 . I feel like a nerd lol… NVM … let’s drop it
I was thinking about crafting a response then thought this too lol. Let’s not embarrass ourselves 
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Haha ye… let’s talk about the new ss additions hahaha 