The crowns refers to the difficulty type of when you play that bot. If you play a “regular” game with no assistance, then a win results in 3 crowns. You can win and get less crowns for more “help.” For example, having “hints” on may give you 2 crowns, whereas having engine assistance may give you only 1 crown. I don’t remember the details, but you can see before you select the game. It shows near the bot (somewhere) before you begin.
Bots
Radovan I like you You cool sent you FR hope you accept. You are definitely a New Yorker type. Fit right in on the island of Staten LOL Good game Have to run but be my friend I'l give you an opportunity to redeem yourself to the beat down I gave you later. PS Kidding I got lucky that game
I think @KeSetoKaiba already said everything, but let me add:
Basically, everything that gives you a sense of the right move (Like Hints, Feedback, Takebacks or Eval Bar etc.) make you loose one crown while using everything that instantly shows you the best move (Like Arrows, Computer lines etc.) results in only earning one crown.
Playing Bots Some Bots have 2 or 3 crowns - what does that mean