they said its a fixed chance up to 500 where chance is 100%, the fixed chance <500 is very low but constant (not known exact number though), but that does not mean the statistics will be supporting the technical definition when measuring reality, because if you check the measurements with how many opened shards on their first apex pack vs the people who opened at 420 packs vs 499 packs it will differ for sure, most people I heard got their above 3-400. Sadly only Respawn has the real numbers so its very hard making an accurate model, but you can model based on the information you have to make a best guess model.
While Respawn may claim that the single pack probability is fixed, unless we the people are able to confirm this we can never be certain.
I claim that the AVERAGE pack probably lies somewhere between 400 and 500 because that would make early heirlooms rare but not impossible (as we observe).
When the single pack probability is lower than 1 in 900 (or so) more than half the heirlooms will come from pack 500.
The difference lies in the mean (average) and mode (maximum).
The following example might clear this up:
Imagine that we have 100 people.
- 90 get an heirloom on pack 500
- 9 get an heirloom on pack 400
- 1 get their heirloom on pack 100
Then the average is (90*500 + 9*400 + 1*100)=487
But most people will get their heirloom on pack 500.
I hope this explains why I concluded that the single pack probability probably lies between 1 in 500 and 1 in 5000
Since then a significant group would need to wait until pack 500, but "early" heirlooms are still possible
Don't buy packs to get heirlooms, that's the main takeaway.
I've gotten two sets of shard on my way to level 500 and none since. Been playing mostly since season 4 (some season 1 then quit until 4). That's a lot of packs since then, never have I spent money on rng packs. I don't know, maybe I shaved off extra coins on a pack as I've had them left over but never went and purposely spend $$$ just to go buy loot ticks.
Even if you do, which in and of itself is pretty rip off with the statistics, you should never buy them to get heirlooms because you can just search for the tears of those who've done that and posted on these forums. It's actually kind of sad.
(on a personal note, I'm very happy with my luck. I regretted not holding 150 heirloom shards in anticipation for Wattson's. But since Respawn has dumped that character hard, and her heirloom is awful, I don't mind anymore)
