Consider a country selecting its ceremonial head of state by chess ability. It may seem silly, but things like male primogeniture and the royal bloodline are also quite silly.
Chess at least provides an objective way of settling succession disputes, analogous but less bloody than the traditional method of war. Chess likely avoids the extremely mentally disabled from inheriting the throne (in contrast to incest).
One king and one queen, probably not married to each other.
I could see it working in a chess-obsessed country like Armenia. Perhaps go 囲碁 in an Asian country like Japan.
Elite players are invited into a "house" from which a head of the house is selected as monarch, while others serve as advisors. Perhaps suitability for head of state and other politics are taken into account (but this could be a political quagmire). Vaguely like go 囲碁 houses of ancient Japan. There could be an elegance of deposing the previous king by checkmate, though succession need not strictly be that way. Perhaps the strongest player as determined by tournament selects the next monarch, possibly him or herself, but could be someone he or she respects and believes will manage the house well.
Probably needs a head of state with very few official duties like Japan (other than to play a lot of chess), in contrast to the United Kingdom.
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