[Sharlin]

"King-crown=ruler" is IMO absolutely apt. Arguing that "crown" can be used metaphorically is a bit disingenuous because first, it's very rarely applied to non-monarchs, and is a very physical, concrete symbol of power that separates monarchs from other rulers.

"King-princess=man" can be thought to subtract the "royalty" part of "king"; "man" is just as good an answer as any else.

"King-queen=prince" I'd think of as subtracting "ruler" from "king", leaving a male non-ruling member of royalty. "gender-unspecified non-ruling royal" would be even better, but there's no word for that in English.

[FabHK]

“King - queen = male” strikes me as logical, if we take king = (+human, +male, +royal), and queen = (+human, -male, +royal), then the difference is (0human, 2male, 0royal).

[godelski]

  > it's very rarely applied to non-monarchs

I take your point but highly disagree that it's disingenuous to view this metaphorically. The crown has always been a symbol of the seat of power and that usage dates back centuries. I've seen it commonly used to refer to leadership in general. Actually more often.

  - https://en.wikipedia.org/wiki/Heavy_Lies_the_Crown
  - https://en.wikipedia.org/wiki/Heavy_Is_the_Head

Notably even in the usage of Henry IV that the idiom draws from is using it in the metaphorical sense, despite also talking about a ruler so would wear a literal crown. There's similar frequent usage in widely popular shows like Game of Thrones. So I hope you can see why I really do not think it's fair to call me disingenuous. The metaphorical usage is extremely common.

I'll buy the king price relationship. That's fair. But it also seems to be in disagreement from the king queen one.