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I got it fairly easily - keep in mind the RNGJesus is really unfair on a bad day.
My guess is that trees are nodes that predetermined drop, I will willing to be criticized for my answer.
Check post #3
Why would you want to?
Tree Fertilizer is a thing - and it's dirt cheap to craft. You'll have your forest back in less than a week in its full glory.
If you're in early game, you'll need extra wood and hardwood anyway - which is easier to get through planting wherever you need it, not where RNG decided to spawn some.
28 minutes 10 seconds in.
https://www.youtube.com/watch?v=byUYolthPc0
It also has its own calculation that ignores luck, so I guess you didn't need to bother with that.
That book and the book of mysteries are really, really tough to get. With the book of mysteries someone wrote that the chance of getting it increases very slightly each time you open a mystery box or a golden mystery box without getting that item.
The wiki isn't updated fully. They only added the spawn rate information if you go woodchopping earlier today.
You'll also find some of the new items on where you try to follow a link and the wiki page in question hasn't yet been written. I got Woody's Secret from the bookseller on his eighth - tenth visit or something like that.
Try the prediction tool and roll through your savefile.
https://mouseypounds.github.io/stardew-predictor/
For my savefile the predictor mentions Woody's Secret on Monday Fall 22, Year 6 which sounds right since I'm currently on Winter, Year 6 and only just got that item
I am sure the trees are random drops, but maybe they are pre-determined. That's a deep question
I have a funny feeling that Woody's drop chance is being checked per axe hit as I've got 2 (two) copies back to back from same tree somehow. Do note that I've read the first copy as soon as it dropped.