Chess and Jazz
I'll offer just a few thoughts on what could be a huge topic. As I play more chess, I'm finding many similarities in the thought processes involved in playing chess and playing music, specifically, improvisational music.
Both activities require one's complete attention and focus in order to do well. If you are playing a game of blitz chess, thinking about work, housework, personal issues, etc. will be a huge distraction. You will not do well.
Likewise in improvising music. If you are not focused on the music you are making, the music will not be pleasing to your ear or anyone else's. Try talking on the phone and improvising on a complex jazz chart at the same time. Doesn't work!
A strong foundation of theoretical knowledge is key to making good decisions in chess or music. Knowing where not to go on the keyboard or the chessboard, will get you better results. The more solid and embedded in your psyche this knowledge is, the better you will play at either discipline.
Flexible thinking will help one keep out of ruts and falling into the same patterns over and over again. Combined with a firm knowledge of tactics in chess/ harmony in music, mental flexibility will help your game and playing stay fresh and interesting. Trying new moves/licks keep your playing from getting stale. But there's that theoretical foundation again: if you don't know the basics, you won't know what not to do and will run into problems.
Thanks for reading!