I captured 6 days of Eagle Mountain play, from Sunday (yellow) to Friday (blue) pretty much opening the same door (what I call Door 3) except at some No Pig levels. I almost always make it over level 10 without hitting a pig and in the video, on red day, I didn't hit the pig until level 19. This is the only day I paid the 20 gems to keep going because the next door was free. This was also the only day I hit a silver ticket. So for 6 days I opened Door 3 a total of 81 times and hit 1 silver ticket. I think my video will show that there is no randomness as to which door the ticket is behind. It is behind any of the doors you don't choose.