# Chances of getting 5 golden legendaries in a single pack?

I found this forum post about chances of getting legendaries.

Quote:

• 1 Rare each 0,85 to 0,90 packs

• 1 Epic each +- 5 packs

• 1 Legendary each +- 20 packs

Golden:

2% Chance of Golden Common (1 Every 50 Cards)

1% Chance of Golden Rare (1 Every 100 Cards)

0.25% Chance Golden Epic (1 Every 400 Cards)

0.05% Golden Legendary (1 Every 2000 Cards)

Where a golden legendary is 0.0005% chance per card in a pack.

I assume getting 5 golden legendaries would be `0.0005% x 0.0005% x 0.0005% x 0.0005% x 0.0005%`.

But I'm not sure.

• Maybe this is more of a math question? – Ryad Shaanbi Nov 17 '16 at 10:46
• They don't have to ALLOW this scenario to happen. They can hard-code the game to limit to, say, 2 Legendaries. – Nelson Nov 18 '16 at 2:07

Yes, the math is right. The chances of having a golden legendary is 0.05% (1 over 2000).

So, that's exactly `0.05% x 0.05% x 0.05% x 0.05% x 0.05% = 3.125e-15%` chances that happens, that is to say once chance in `3.2e+14`. In other words, you have to open 150 thousands of billions packs (in average) before hoping to open the 5-golden-legendaries pack. Good luck !

EDIT: The math is right if you consider no pity timer (thanks Rob). As Blizzard does not provide any detail about this, the straight-forward calculation gives a nice idea of the chances to have such a pack.

• Just golden legendaries. – Ryad Shaanbi Nov 17 '16 at 11:04
• Oops, deleted my comment accidentally. Here it is again: You assume each probability of a card being a golden legendary is independent from other probabilities. If this is the case, you are right. – Rob Nov 17 '16 at 11:11
• @Rob Yes. I assume there is no such pity timer you are talking about. – Ksyqo Nov 17 '16 at 11:16
• You have to treat each card idependantly... if you have 0.25% chance of having a pack with a golden legendary you can't multiply that by 5 because you are taking the probability of a pack for a card. So if the first percentage is correct, 0.05%^5 would be the correct equation. – Karlyr Nov 17 '16 at 12:50
• And the "pity timer" would only affect the first card... So it wouldn't increase that much the probability. Final verdict : Go buy a lottery ticket instead of trying this. ;) – Karlyr Nov 17 '16 at 14:02

Only considering your information you would be correct. Your information assume that any probability of a card being a (golden) legendary is independent from the probabilities of other cards.

However, this doesn't seem to be the case. On reddit somebody analyzed the probabilities of getting legendaries. Quote:

The probability is increasing as the amount of packs increases and it also shows a significant gain after 30 packs.

I don't know if there is some official source confirming the existence of such a Pity Timer as it is called there.

Thus, the probability of getting a legendary appears not to be the same for every card and, consequently, does not seem to be independent from other probabilities. That means the calculation is probably much more complicated than just (0.05%)^5.

• Nice that's exactly the stuff I wan't to find out , shame blizzard doesn't release more official data about this. – Ryad Shaanbi Nov 17 '16 at 11:09
• a "Pity Timer", more frequently known as "Bad Luck protection" is something that's frequent in Blizzard games that involve RNG. If something has a low chance of occuring, like the player receiving a rare item or the player triggering an effect from one of their spells with a low random chance, the chance of that event occuring increases every time something happens that can trigger that event, based on the intended frequency of that event occuring. World of Warcraft uses it to increase the chance for a player to get a random legendary, for example. – Nzall Nov 17 '16 at 12:03
• @Nzall I would be interested in some official source about that. Do you have one? – Rob Nov 17 '16 at 12:38
• Concerning the pity timer, there is also something to take into consideration. Is the probability increase valid for the first legendary of the pack or for all the cards ? I suspect that while picking the cards, if the first one is already a legendary, the pity timer is immediately cancelled for the 4 others picks. Consequently, I guess we can say that (0.05%)^4 * X would be the correct math, where X is something between 0.05% and 1. – Wis Nov 17 '16 at 14:02
• @Rob us.battle.net/forums/en/wow/topic/8197741003 explains how Bad Luck Protection works for RPPM trinkets, the first system with this random element that got this kind of protection. twitter.com/wowhead/status/743509560762064896 is a tweet from a fansite that highlights a message from a Twitch Q&A from that day, available on youtube. If I had the time for it, I could probably look up all other systems where that's known to be used. – Nzall Nov 17 '16 at 20:35