You don’t know that’s how it works. It may not be, as you suggest, 5% for any pack up until pack 40 when it suddenly jumps to 100%. It could start at 1% at pack #1 and slowly increase to 100% by pack #40 with a curve such that the overall average comes out to 5%. Or it could be some other distribution entirely.
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Their support page states you can obtain:
1 epic per 5 packs on average
And 1 Legendary per 20 packs on average.
That means we have a 20% chance to get an epic and 5% chance for Legendary per pack. They don’t mention anywhere that we are assured epics or Legendaries (apart from 1 in the first 10 packs of an expansion)
I’ve been keeping track of my epics and Legendaries,
I opened 5 packs this week, no epic.
So it really is RNG.
You could get 2 epics consecutively or not a single one even in 10 packs.
Yes, possible! Though if so, I’d expect it to start showing up at places like PityTracker.
if it’s the distribution you suggest, we’d see that the longer your losing streak goes, the higher the likelihood of a legendary. Has anyone found a pattern like that?
Also–if (as seems likely) they use the same code for epics as for legendaries, just timed for a ten-pack limit, we’d see a much steeper curve. If it’s “probability doesn’t change except for the pity-timer at pack 10”, we’d see no difference between pack 1 and pack 8. If it’s a gradual increase (so the average likelihood is 1 in 5", we’d see pack 9 with a much higher chance of an epic, like 90%–it’d be quite rare to get to pack 10 without an epic–whereas if there’s no change except at the pack-10 cliff, then we’d see ~ a 13% chance of getting a nine-packs-no-epics streak, common enough that ~ half of the players buying a big expansion bundle would have a streak like that.
Not expressing a guess one way or the other! But like I said, there’s probably data out there to answer this.
Except that there’s a lot of evidence out there that besides the pure-RNG (“1/5 chance of an epic in your pack”), there’s also an (unannounced) pity timer backstop–so if you go nine packs without an epic (in the same expansion), you’re guaranteed an epic in the tenth pack.
I once read a thread on reddit (and lost the link to, so sorry I can’t point you to it) where lots of collected data on pack openings was analyzed and the conclusion was that the chance is 5% (or at least very close to it) for the first 30 packs, and once the pity timer goes beyond 30 the chance gradually increases up to the full 100% for the 40th pack.
I will admit that I did at that time not check where they got their data from. nor double check the math. Which I guess makes it even sadder that I lost the link.
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Looking at the HS Wiki’s “Card Pack statistics” page:
https://hearthstone.gamepedia.com/Card_pack_statistics
…I found links to these two Reddit posts, which seem to match what you’re descibing:
https://www.reddit.com/r/hearthstone/comments/3zaeou/pity_timer_on_packs_opening_analysiskinda_proofed/
https://www.reddit.com/r/hearthstone/comments/3znt9m/continuing_information_on_the_pity_timer/
13% of the time based on what statistics? If 1,000 players each opened 41 packs and 130 people didn’t get a single Legendary then we’d be hearing about these hypothetical situations a LOT more often than we do. If 13% of all 40+ pack opening sequences resulted in 0 Legendaries then there would be blood in the streets. On what specific math was this 13% number based?
I’m assuming it’s an answer to the question, “If every pack has a 5% chance of having a legendary, and there is no pity timer, and I open forty packs, what are the chances that I get no legendary?”
Because the math checks out then—the chances are
(0.95)^40 ≈ 0.129 , or 13%
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And if that was correct, then we would be seeing a LOT more examples of people who didn’t get a Legendary in 41+ packs. There would be entire YouTube channels dedicated to nothing but showing the phenomenon over and over again.
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Blizzard always claimed there is no pity timer, that’s nothing new.
However. There’s videos of literally hundreds of thousands of packs being opened on youtube and not a single one has more than 40 packs between consecutive legendaries.
What are the odds that that’s the case if there’s no pity timer? Unless you can find a video that shows more than 40 consecutive packs opened without a legendary, very few people will believe you that there’s no pity timer. 
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Yes. And absence of such videos used to be taken as a proof of pity timer existence.
I wouldn’t use the word “proof”. But I would say that it is a strong indicator. It may not be proof, but it’s waggling it’s eyebrows in proof’s direction.
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Has Blizz actually said that there isn’t a pit timer? (Aside from this one convo with a CSR?)
Or have they just been silent about the matter?
It would totally make sense for them to keep quiet about it. I doubt they’d have even announced the “1 in 20 packs” figure if they didn’t have to do it for China.
Going by the stats on PityTracker’s insights page, with over 2.5 million packs open across all sets the average is 57.4 legendaries per 1000. So 5.7 per 100, which is slightly better than 1 every 20 packs.
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It is entirely possible that the algorithm was tweaked since the pity timer was “proven”, causing one to go >40 packs without a legendary.
There were reports on reddit of the same thing early in the RoS expansion. This is the second of 2 posts by a user with a image from HSDeckTracker that recorded going over 40.
www.reddit.com/r/hearthstone/comments/bdcma2/pity_timer_gm_response_does_not_exist/?utm_source=share&utm_medium=web2x
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This is good to know, thank you for sharing. It still seems probable that this is more likely to be a glitch than a change, or it would be popping up a lot more, but it is still a nice data point to have.
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I recently have started counting my packs and what rare I get in them. I pre-bought the Uldum bundles so actual cards aside, I’m looking forward to the statistics from 132 + packs that I have waiting.
It’s my biggest bulk buy for the game and a part of me hopes I have a long drought between legendary’s to confirm. I have 3000+ gold to buy extra packs to fill out a 40 pack pity timer if I fall short.
I think that it’s all RNG.
Just check out this video where the player bought like 30 packs but got 4 Legendaries.