Do you get a simple flash of an idea then jump to coding? Do you sit down and think it through? Do you write down the main points? Something more?
To me, planning is boring, but some planning is necessary to decide if an idea is worth pursuing and to minimize major refactors.
It depends on how large the game is. More planning is a good idea for bigger games.
I like to have a decent idea of the main aspects of the game before starting anything. Getting the core gameplay working first of all is also important so you can iron out problems early.
Whenever I’ve started a game too soon thinking that my initial idea will spark off further inspiration once I see it working has rarely been successful.
I almost never write anthing down because my games tend to be small and I can hold the ideas in my head. For a larger game though, getting down a few bullet points at least would be a big help.
I’m a bad example, because I’m doing one game for way too long, but I could have gather all the materials into a book and it could be comparable to the Fellowship of the Ring when comparing amount of paper used 
I have wrote down systems, RPG stats, even equations, like for some kind of paper RPG, stories, characters, etc, etc.
But generally, yeah, the smaller game the less you need to plan about it. For jam games, I usually make one page of some notes with basic structure - and what I want to accomplish, then I go to implementation, because the time is limited and I start with this list and check out everything I wanted on the go, while actually making a lot of changes in the meantime.
For example, for the last game: Cyberpunk Stories I made such notes the first day of the jam - you can judge how many of this ended up in this short game
cyberpunkgame.txt (3.6 KB)
The number “2BR02B” is a direct reference to a very short sci-fi story by Kurt Vonnegut of the very same number in the title.
You’re a good example because of this 
If you didn’t write down all of that stuff, do you think you would be in a worse position than where you are now? Do you think keeping mental notes is as effective as writing things down?
I’m definitely in a better position with notes 
And no, mental notes are not persistent definitely 
I use notes as my Hard Drive, I don’t believe anything I think of will persist in my RAM 
Some ideas just wander around your head for a while, but it’s when I put them down on paper (or rather into any form of electronic notes) it’s more safe.
But when it comes also to software development, I am also a type of person that could describe the architecture, code beforehand and then start coding
In my opinion , I think writing down your base game idea on paper even if it is a small game is a very important step. You always have something to look back on , an idea to break down and build from.
When it comes to larger games I think without a doubt it is a must. Then there is GDD’s (Game Design Documents) and that is important for teams, investors or pitching to publishers. It is necessary to pitch a clear concept in hopes of getting funding etc.
I think writing the base concept is the most important it gives you the overall idea of your game that you can break down and create your core game loop and systems from. Depending on the game, writing other things like character building , world building , lore etc are bonus details that can also help in creating something great but may not be necessary.