When the Odds Are Ever Not in Your Favor, Wordscapes Edition

I was introduced to Wordscapes in late 2019, and still lightly compete for crowns on the weekends while getting steps.  During the week, there is a daily puzzle, but it otherwise feels like it's turned into a Tamagotchi game to give you rewards in the form of jeweled hearts (to get you more pets -- you can have one pet "active" at a time), cocoons (to hatch butterflies for a variety of settings), and binoculars (to find pieces of portraits that you can use).

For the month of October, there is a set of 12 portraits you can collect, and in order to get a portrait, you need to find 3 "pieces" of that portrait.  At this stage, where I'd collected 8 out of the 12 portraits, if the probability of finding each piece is roughly equal, I'd expect to get a new piece about 1/3 of the time.  Instead, I found 111 duplicate pieces before getting another pumpkin piece.  The probability of that happening is on the order of 10^-20, so that strongly suggests the probability of getting each piece is not equal.  Unfortunately, there's no indication of this in the interface.