H. G. Muller wrote on Tue, Sep 12, 2017 05:12 PM UTC:
Reference to FIDE rules is moot, as those rules could never create a position where one player has more than one King. It all depends on how you generalize the rule that "it is not legal to expose your King" to capture. With multiple Kings this could be done as "it is not legal to expose any of your Kings to capture", (absolute royalty), or as "it is not legal to expose your only King to capture" (extinction royalty). The concept of 'check' would be defined as a situation where it would not be legal to pass your turn when turn passing would have been a legal move in general. So with extinction royaly, if one of your two Kings is attacked, this is not considered check, and you are under no obligation to resolve it. You can just allow it to be captured, no harm done.
In Spartan Chess the rule is somewhat intermediate: "it is not legal to expose all your Kings simultaneously to capture". So there you lose when both your Kings are 'checkmated', although the latter is just a figure of speech, as it is actually the player that is checkmated when he cannot get out of check, while check is a situation where both Kings are attacked. 'Checkmating' one of the Kings then merely indicates that you can force capture of that King on the next move, which the player owning it might not mind at all if that King was protected, so that he can recapture.
In Spartan Chess a second King is worth 4.5, i.e. slightly less than a Rook, so protecting it is a good defense against capture by Rook or Queen. (This depends of course a bit on how save your remaining King is.) With two absolute royals, the value of the second royal is about 0, even in absense of Queens, i.e. it is as much a liability as an asset. In Pawn endings it is a great asset, however, and two Kings versus one would win such endings easily. With the Queens still on the board, it would probably have a negative value. (But the value is only good for estimating who is winning, as you would not be able to trade the King under those rules.)
Reference to FIDE rules is moot, as those rules could never create a position where one player has more than one King. It all depends on how you generalize the rule that "it is not legal to expose your King" to capture. With multiple Kings this could be done as "it is not legal to expose any of your Kings to capture", (absolute royalty), or as "it is not legal to expose your only King to capture" (extinction royalty). The concept of 'check' would be defined as a situation where it would not be legal to pass your turn when turn passing would have been a legal move in general. So with extinction royaly, if one of your two Kings is attacked, this is not considered check, and you are under no obligation to resolve it. You can just allow it to be captured, no harm done.
In Spartan Chess the rule is somewhat intermediate: "it is not legal to expose all your Kings simultaneously to capture". So there you lose when both your Kings are 'checkmated', although the latter is just a figure of speech, as it is actually the player that is checkmated when he cannot get out of check, while check is a situation where both Kings are attacked. 'Checkmating' one of the Kings then merely indicates that you can force capture of that King on the next move, which the player owning it might not mind at all if that King was protected, so that he can recapture.
In Spartan Chess a second King is worth 4.5, i.e. slightly less than a Rook, so protecting it is a good defense against capture by Rook or Queen. (This depends of course a bit on how save your remaining King is.) With two absolute royals, the value of the second royal is about 0, even in absense of Queens, i.e. it is as much a liability as an asset. In Pawn endings it is a great asset, however, and two Kings versus one would win such endings easily. With the Queens still on the board, it would probably have a negative value. (But the value is only good for estimating who is winning, as you would not be able to trade the King under those rules.)