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Hi, I’ve been recording data for levels 9 and 33 and thought they might be useful to this thread. The way I do it is to restart the level if I don’t see a box in the first stage, so the following data should be interpreted as “trials of first stage”.
For level 9 I played 738 rounds, getting 36 R(ed) and 34 B(lue) boxes, so roughly you’d need to start 20 times for getting a box of a specific colour, or 10 times for getting a box of any colour. Among the 36 R boxes, I got 22 F(eathers) and 13 S(pells) (and 1 unknown as I couldn’t shoot a bird to reach it). There is no significant difference between the chances of R/B boxes (i.e. should be 50-50), or Feather/Spell split (but it looks like you get a feather more often, see next paragraph).
I’ve more data for level 33 since that was the preferred level suggested in this thread. There I played 1,700 rounds, getting 78 R and 64 B boxes (this R/B split is not significant, i.e. consistent with 50-50 ratio). Among the 78 R there are 52 F, 24 S and 2 unknown. The difference here is significant, which means you’re more likely to get feather in a R box. The average number of attempts needed to get a R/B/Any box is 22/27/12 respectively.
The proportions in level 9 and 33 (70/738 and 142/1700) are not significantly different, i.e. these two levels give you roughly the same chances of getting a box.
TL;DR: Level 9 gives you roughly 10% chance of a box of any colour; blue/red ratio seems to be 50-50. There doesn’t seem to be much difference between levels 9 and 33, but of course playing level 9 is a better choice since it only has two stages (so you can finish it off faster when you see a red box).
The spreadsheet here contains the full data. The numbers in the first column are how many trials before I get the box to the right of them. Feel free to use it to your advantage, and let me know if you find something wrong. :)