Examination of heirloom probability of single packs

[Anjunakrokus]

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@OldTreeCreeper wrote:

How can it not be Independant, as a packs number opened is a number lost into the ether and has no bearing on the next packs outcome? Other than pack 500. And with packs are we not talking about whole numbers? 

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So first of all it cannot be independent because you are guaranteed to get an heirloom on pack 500. Which is indeed what I was referring to.

But more annoyingly,there is no actual way to know whether pack 1, pack 239 and pack 456 actually have the same probability.

All we know is that when you open a pack sometimes you get shards.

There is some RNG box which spits out whether or not you get one and we don't know how it works!

I'm making the assumption in my model that they have the same probability, but that's in no way guaranteed.

Another option would be that the probability starts out lower but slowly ramps up as you open more packs. How could we possibly know without Respawn telling us

[sceptic-noob]

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.

[OldTreeCreeper]

@sceptic-noob chance 

All packs have 500 to 1 to get shards

Up to pack 500 which is 100%

But if we look at it this way

Pack 1 is 500 to 1

Pack 2 is 499 to 1 as only 499 packs left to go.... Etc 

Down to pack 499 which is evens. 

[OldTreeCreeper]

@Anjunakrokus I'm not sure that there's a true rng at play here. Youngtree's 2 friends bought 150 packs in event and both got a heirloom at pack 7. I do not know their pack count. 

I'm not sure how you can conclude that most real heirlooms are got between packs 320 and 440, and not in fact in pack 500. Anecdotally very few get the heirloom early and it is strange that a pack counter is not available ingame. 

[Anjunakrokus]

@sceptic-noob 

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.

@OldTreeCreeper 

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

[KelRiever]

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)

[Cheese9Man]

@Anjunakrokus Just finished my thesis on the prevalence and incidence of liver cancer snd all these research mumbo jumbo is giving me war flashbacks. LMAO. Awesome work man!

[CrazieAtesPS4]

All I know is that 500 packs is a bit much lmao 

I'm day 1, level 1,586, 3+ "YEARS" of playing consistently, and no heirloom.

But here is pack 450 as I track my unlucky streak in this subject lol 

[Cheese9Man]

@CrazieAtesPS4Lmao! Same here man and I just got my heirloom last Christmas. You’re so close! I guess we’re one of the unlucky ones who didn’t get an heirloom pre level 500.