How likely is it that there aren't any branches on one side of the tree for 100 segments? More importantly, is it possible at all? I'm thinking about making a TAS for kicks :)

I think its 50/50. Also if you wanna TAS try to find a pirated copy of an older version. In older versions you can get more than 1 point per branch if you're fast enough.

I'm not using an older version, Just the one that I downloaded of the current 2021 IOS appstore and I I think the way that works is if your timer bar is filled up or really close to full (because it's consistently going down) you get double points per branch or something) I might go through one of my recordings in slow mo to see exactly how this works.

I'm still not entirely sure how it works but I have a feeling that when u click too fast between one piece of wood and then the tree falling down so you can hit the second piece, if you manage to click in between this animation, it will give u a point for free without starting a second animation. This makes sense to me because my CPS for two fingers is around 12-15 and I got about 7 seconds for the 100 run. This fact would still be fair though because played must still tap 100 times but it makes you wonder if there is an optimal way to click for some levels.

Zeekeenee and the mod are right in his statements, older versions of the game has a variation of the newer versions. You can get more points per branch, in fact, yesterday I was checking that. In newer versions. Example: Steam Version, multi tap becomes harder because you don't get more points per branch, instead you cut branches faster.

That doesn't change that you click 100 times the touchscreen, keyboard.