I've been playing this game since the beginning of December last year and I do the dailies every single day. I've ground both adventures, done all the achievements and my guess is I've opened well over 100 packs earned totally from free-to-play in-game gold.
How come then that I have never found a single legendary in all the packs I've opened and only about 4 epics?! Do they jinx the free-to-play players? You're supposed to have a 1/20th of a chance to get a legendary per pack. Each card has a one percent chance. I don't have an official source, I read claims between 1 in 22 and 6.33% (1 in 16) per pack.
Look at this graph: https://graphsketch.com/?eqn1_color=...50&image_h=525
In 104 packs there is already less than a 1 in 200 chance that they don't contain any legendaries. At 149 packs this chance drops to less than 1 in 2000!