Checkmate in three-player chess

[Millstone85]

Spoiler: So I have this really cool chessboard for three players.

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The only issue was these shades of blue and green being surprisingly easy to confuse. That's why I put some white paint on the blue pieces.

Now, regarding the game itself, I see that the addition of a third player leads to some peculiar situations. Let's assume that players take their turns in a clockwise manner: first red, then green, then blue, then red again.

• Even if the red king is in check by a blue piece, that might no longer be the case when Blue's turn comes.
• Red can move in such a way that Green's turn begins with the blue king already in check by a green piece.

And that makes it somewhat difficult to define checkmate, or what moves should be illegal in regard to kings. I find myself hesitating between two approaches.

In the first approach, the rule becomes that a player can not end their turn with an enemy piece giving check, be it to the player's king or to the king of the third player. If that requirement can not be met, then the game ends and the owner of the check-giving piece wins, even if the next turn would not have been theirs.

The second approach is to abandon the concept of checkmate and all associated illegal moves. Instead, the first player to capture a king wins. Or it is the last player to stay in possession of their king, but then a player must wait for the other two to finish the game. Either way, I worry about chess without checkmate feeling inelegant.

Which do you think makes the most sense? Or is there a better way to define the winning condition?

Update: I am now going with the rule that a player can not end their turn with the next player giving check, be it to the current player's king or to the king of the third player. If that requirement can not be met, then the game ends and the next player wins. Unless the next player wasn't theatening any king yet, in which case it is a stalemate.

[The Glyphstone]

If you make it a last man standing victory, you could have the defeated player become an allied 'vassal' of whoever took their king, making it an effective 2v1. Likely a guaranteed victory, but depending on the board state and what is still intact it might still work.

[halfeye]

How do pieces cross colour boundaries, particularly in the centre?

[Millstone85]

If you make it a last man standing victory, you could have the defeated player become an allied 'vassal' of whoever took their king, making it an effective 2v1. Likely a guaranteed victory, but depending on the board state and what is still intact it might still work.

Sorry, but I dislike both the 'vassal' and 2v1 aspects of this.

Anyway, does it mean that you would abandon checkmate in favor of king capture?

How do pieces cross colour boundaries, particularly in the centre?

Different rule sets give different answers, but I like the version where a diagonal move can only be from a light tile to another light tile, or from a dark tile to another dark tile, and the center point works as a forking path.

[warty goblin]

Simplest definition to me seems to be that player A loses if, on their turn, they cannot get their king out of check. This avoids needing weird precident rules, always gives the threatened player an opportunity to respond, and feels quite consistent with the two-player definition. As a bonus, it expands gracefully to n-player games as well.

[Millstone85]

Simplest definition to me seems to be that player A loses if, on their turn, they cannot get their king out of check. This avoids needing weird precident rules, always gives the threatened player an opportunity to respond, and feels quite consistent with the two-player definition. As a bonus, it expands gracefully to n-player games as well.

How would that apply to the situation I mentioned, where...

Red can move in such a way that Green's turn begins with the blue king already in check by a green piece.

For example, there is a red pawn betweeen a green rook and the blue king, and Red moves their pawn out of the way. Thus, not only is Green giving check to Blue, but it is also Green's turn to play.

Would you forbid Green from capturing the blue king, perhaps on the reasoning that kings can only be checkmated, never actually captured?

[Lord Torath]

How would that apply to the situation I mentioned, where...

For example, there is a red pawn betweeen a green rook and the blue king, and Red moves their pawn out of the way. Thus, not only is Green giving check to Blue, but it is also Green's turn to play.

Would you forbid Green from capturing the blue king, perhaps on the reasoning that kings can only be checkmated, never actually captured?

Yeah, I probably would. The green player could move to reinforce the rook, or eliminate escape routs for the blue king, or even threaten the red king, but he couldn't take the blue king. Kings can only die on their own turn.

As to my chess credentials, I can easily beat someone who's never played before. I've also been told that I don't really know what to do with a queen, so if I have the chance to trade queens with my opponent, I should probably take it. So keep that in mind when considering my opinion.

[warty goblin]

How would that apply to the situation I mentioned, where...

For example, there is a red pawn betweeen a green rook and the blue king, and Red moves their pawn out of the way. Thus, not only is Green giving check to Blue, but it is also Green's turn to play.

Would you forbid Green from capturing the blue king, perhaps on the reasoning that kings can only be checkmated, never actually captured?

Yes. The alternative is that Blue loses the game because of actions they had no chance to respond to, and which if given the opportunity they could prevent the loss - for instance if Blue could capture the offending rook. This is generally understood as frustrating and bad game design.

Note that this also removes the need for rules concerning the capture of kings, which otherwise ends up both messy and inelegant. For instance if Green can capture Blue's king, do they have to? If doing so removes all of Blue's pieces, doing so might lose them the game - indeed will necessarily lose them the game if it puts them in check and you allow king capture. But if they don't have to take the king, then you could end up with a king who was otherwise checkmated but left uncaptured, which is just ugly.

No, I think by far the lowest complication approach, and the approach most consistent with normal chess is for a player to lose if they cannot, on their turn, get their king out if check.

[Millstone85]

Note that this also removes the need for rules concerning the capture of kings, which otherwise ends up both messy and inelegant. For instance if Green can capture Blue's king, do they have to? If doing so removes all of Blue's pieces, doing so might lose them the game

The question of what is to become of Blue's pieces remains the same no matter whether the blue king was captured or left unable to escape check. There is a variant where Green would take control of the blue pieces, and another where the blue pieces would be left unmoving on the board (but still capturable). The blue pieces being instantly removed from the board is probably a bad idea, yes.

Or the game could end right there, not just with Blue's defeat but with another player's victory. If Green captures the blue king, then obviously Green is the winner. If instead we demand a checkmate on Blue's turn, then there is the possibility of the blue king being threatened by both green and red pieces, in which case it is unclear who won.

The alternative is that Blue loses the game because of actions they had no chance to respond to, and which if given the opportunity they could prevent the loss - for instance if Blue could capture the offending rook. This is generally understood as frustrating and bad game design.

Hmm, would an immediate victory also fall under that bad game design?

But if they don't have to take the king, then you could end up with a king who was otherwise checkmated but left uncaptured, which is just ugly.

Maybe not. Another option would be for Blue to skip their turn until the Red/Green conflict frees the blue king from check. The goal then, is to become the only player whose king is not currently checkmated.

Yes, I am adding that to the options I am seriously considering.

[Erloas]

Or the game could end right there, not just with Blue's defeat but with another player's victory. If Green captures the blue king, then obviously Green is the winner. If instead we demand a checkmate on Blue's turn, then there is the possibility of the blue king being threatened by both green and red pieces, in which case it is unclear who won.

I think this is probably the "best" solution. Red would be very much against making a move that would directly lead to blue losing their king without being able to respond.
All players would also be incentivized to play it in such a way that sometimes helping protect the enemy king is in their best interest. I don't think the concept of checkmate is entirely central to chess, the acknowledgement of the end of the game is that there is nothing else that can be done without losing their king, the actual taking of the king is a given. That you are forced to protect the king at all costs is the important part, and this still maintains that drive and direction.

[warty goblin]

The question of what is to become of Blue's pieces remains the same no matter whether the blue king was captured or left unable to escape check. There is a variant where Green would take control of the blue pieces, and another where the blue pieces would be left unmoving on the board (but still capturable). The blue pieces being instantly removed from the board is probably a bad idea, yes.

The question of what to do with the defeated player's pieces remains, yes. I'd go against giving control of them to the person who defeated them, since it so drastically favors that player. It'd be pawn promotion on steroids, and basically the winning strategy deteriorates into bum-rishing the first player with a disadvantage because if the other player knocks them out you're done.

I think the same holds true for playing I til the defeat of a single player; as soon as anybody is disadvantaged, tou only have two choices: gun straight for them, or perversely align with them against the third, since to Green, Blue losing becomes symmetric with Green losing.

I think the least degenerate case is last player standing wins.

Or the game could end right there, not just with Blue's defeat but with another player's victory. If Green captures the blue king, then obviously Green is the winner. If instead we demand a checkmate on Blue's turn, then there is the possibility of the blue king being threatened by both green and red pieces, in which case it is unclear who won.

This is easily resolved though, either Red or Green has to make a move that puts Blue in check. It seems the most straightforward therefore to say that the player who does so is the player who defeats Blue. This does create an incentive to attack the player directly after you in the play order, since there's no opportunity for the third to move and defang your mate.

Hmm, would an immediate victory also fall under that bad game design

Yes. Losing not because you played badly but because the third player was a scrub who got killed off is poor design since it reflects less in your skill. Imagine for instance a game between two grandmasters and a terrible player like myself. I'm definitely going to lose, but declaring the winner to be the first player to beat me just incentiveses the grandmasters to throw everything at me rather than actually play each other. The winner in that case could basically and predictably come down to turn order.

Maybe not. Another option would be for Blue to skip their turn until the Red/Green conflict frees the blue king from check. The goal then, is to become the only player whose king is not currently checkmated.

Yes, I am adding that to the options I am seriously considering.

This is even worse, since it's basically being eliminated from the game except you can't even go and watch Netflix or whatever. Multiplayer games generally don't include strong, long term stun effects because getting ganked while paralyzed is annoying as hell, and that's basically what you're proposing. Sitting around watching the other two players eliminate my pieces one by one is not even an interesting defeat, at best its spectator mode.

[Lord Torath]

Question: After one player is eliminated, can pawns still be advanced to queens by reaching the eliminated player's back row?

[Erloas]

Yes. Losing not because you played badly but because the third player was a scrub who got killed off is poor design since it reflects less in your skill. Imagine for instance a game between two grandmasters and a terrible player like myself. I'm definitely going to lose, but declaring the winner to be the first player to beat me just incentiveses the grandmasters to throw everything at me rather than actually play each other. The winner in that case could basically and predictably come down to turn order.

I think that basically ignores the fact that all 3 players are playing on the same board at the same time. It's chess, there are pieces that can easily cross the entire board in a single turn. Rushing the weak player, even a really weak player, will still put you at a big disadvantage to the other good player. If you're the other good player and see them rushing the weakest player you can easily throw off that plan, killing their attacking/setup pieces.
You also know, based on the rules, that the weak player can't totally throw the game either, because they have to protect their king at all costs, so they can't just choose to not protect their king and lose. So both other players have a chance to react to the attacking player's move.

Pretty much every multiple player games I know, helping another player, even if they are also your enemy, is often the best option in some cases. The asymmetry that the extra player adds is what makes those games more interesting.

[Millstone85]

I think the same holds true for playing I til the defeat of a single player; as soon as anybody is disadvantaged, tou only have two choices: gun straight for them, or perversely align with them against the third, since to Green, Blue losing becomes symmetric with Green losing.

Pretty much every multiple player games I know, helping another player, even if they are also your enemy, is often the best option in some cases. The asymmetry that the extra player adds is what makes those games more interesting.

Indeed, I don't see anything "perverse" about it. This is a feature, not a bug.

This is even worse, since it's basically being eliminated from the game except you can't even go and watch Netflix or whatever. Multiplayer games generally don't include strong, long term stun effects because getting ganked while paralyzed is annoying as hell, and that's basically what you're proposing. Sitting around watching the other two players eliminate my pieces one by one is not even an interesting defeat, at best its spectator mode.

Yikes! Yeah, scratch that idea.

But neither am I happy with Netflix becoming an option at all until the game is over. So I would much prefer victory to be decided by the first defeat instead of the last.

Question: After one player is eliminated, can pawns still be advanced to queens by reaching the eliminated player's back row?

Yikes again. Yeah, I really really don't want the game to continue without a player.

This is easily resolved though, either Red or Green has to make a move that puts Blue in check. It seems the most straightforward therefore to say that the player who does so is the player who defeats Blue. This does create an incentive to attack the player directly after you in the play order, since there's no opportunity for the third to move and defang your mate.

Then it could become good manners to only announce "Check!" on a previously unthreatened king. This way it becomes clear to the table who is in a position to checkmate.

That's feels nice, but it leaves the annoying possibility of giving check outside of your turn.

I am being a bit of a weathercock in this thread, but I am leaning again on my first approach. Each player explicitly has two imperatives:

• Defend their own king from check.
• Defend another player's king from check by the third player.

[halfeye]

Indeed, I don't see anything "perverse" about it. This is a feature, not a bug.

Yikes! Yeah, scratch that idea.

But neither am I happy with Netflix becoming an option at all until the game is over. So I would much prefer victory to be decided by the first defeat instead of the last.

Yikes again. Yeah, I really really don't want the game to continue without a player.

Then it could become good manners to only announce "Check!" on a previously unthreatened king. This way it becomes clear to the table who is in a position to checkmate.

That's feels nice, but it leaves the annoying possibility of giving check outside of your turn.

I am being a bit of a weathercock in this thread, but I am leaning again on my first approach. Each player explicitly has two imperatives:

• Defend their own king from check.
• Defend another player's king from check by the third player.

Why mess about with chess?

I mean, presumably you are not the ultimate grand master, so there are still things in ordinary chess you could learn, and if you don't like chess that much there are other games.

[Millstone85]

Why mess about with chess?

I mean, presumably you are not the ultimate grand master, so there are still things in ordinary chess you could learn, and if you don't like chess that much there are other games.

Why diss on chess variants?

There are many, with different boards, new pieces and more. And I am fairly certain that they do not come from a place of not liking chess, nor are you required to have mastered chess before you can enjoy them.

And while this is not about improving chess, it is noteworthy that its modern form started out as a "mad queen" variant, to say nothing of earlier Eastern origins.

[Forum Explorer]

Personally I'd go with you need to actually capture the King to eliminate the player, at which point it become a 1v1. The player is eliminated, but their pieces remain on the board and can be captured, but can't actually capture anything, effectively forming obstacles.

I don't like the game ends when a king is eliminated, because it might turn the game into a 2v1, where two players are racing to eliminate the third, who in turn, doesn't actually have a chance to win, but instead basically chooses who loses with them.

[Millstone85]

I don't like the game ends when a king is eliminated, because it might turn the game into a 2v1, where two players are racing to eliminate the third, who in turn, doesn't actually have a chance to win, but instead basically chooses who loses with them.

But the same 2v1 can happen in the first part of a last-man-standing game. It should even be worse, as "racing to eliminate the third" ultimately involves the two sabotaging each other's progress, whereas a last-man-standing game allows a full truce until after the third player is eliminated.

[LibraryOgre]

I'm in favor of the "Last King Standing" solution, myself, which I think leads naturally to "You cannot end your turn with your king in check". Checkmate happens when a king cannot get out of check, regardless of who threatens. That does not accord a win to whoever "killed" the king, but it removes the rival from the field.

If you don't like the "have to wait for the others to play out the game", consider this option... with their king dead, they cannot win, but their other pieces remain on the board, and can still be played. This means that the remaining players must contend not only with each other, but with "soldiers" with nothing left to lose. Because victory goes to the last king standing, those pieces can be a strategic asset to both players, setting up checks, but are also a hindrance, in that they can destroy their own plans.

I might allow the "ronin" a way to win, but it would be hard... putting both kings in checkmate at once.

[Thane of Fife]

One option I've seen (from three-handed chess) is:

1. The game ends when one king is captured, with the player making the capture being declared the winner,
2. A king can only be captured while in a checkmate position,
3. If you start your turn with your king in checkmate, you have to skip your turn.

Note that the variant also has rules to try to alleviate the situation of two players ganging up on the third.

To me, this appears to have the advantages that 1) the game ends when one player is eliminated, 2) you are very unlikely to "accidentally" capture a king because of the third player's poor moves, and 3) the third player is always incentivized to save the checkmated player if possible.

[Forum Explorer]

But the same 2v1 can happen in the first part of a last-man-standing game. It should even be worse, as "racing to eliminate the third" ultimately involves the two sabotaging each other's progress, whereas a last-man-standing game allows a full truce until after the third player is eliminated.

Perhaps, but you also don't want to lose too many pieces taking out that player because you have another opponent to beat afterwards. And your ally is incentivized to hold back and try and make it so you are the one who either ends up in a worse spot, or loses more pieces.

[TaRix]

Perhaps the game simply ends when a king is checkmated/taken (however that gets decided) and the attacking player gets the win, the beaten player gets the loss, and the bystander gets second place?

[LibraryOgre]

Who wins if the checkmate is the result of two player's placements? I move my knight to a point where your king is in check from me, but you are mated because moving my knight exposed you to their rook?

[Tvtyrant]

Why not just make it points based and have the game end on the first checkmate quidditch style. Losing your king is worth a lot of points, and the game ends for everyone so you have a reason to change alliances back and forth.

[halfeye]

Why diss on chess variants?

I was not writing in support of classic chess at all, it was more a criticism of chess as a whole. There are better and different games, I like go/Wei chi (https://en.wikipedia.org/wiki/Go_(game)), there are also shogi ((https://en.wikipedia.org/wiki/Shogi)where captured pieces can be played by the capturer as their own) and chinese chess (https://en.wikipedia.org/wiki/Xiangqi) which is different again.

[LibraryOgre]

I was not writing in support of classic chess at all, it was more a criticism of chess as a whole. There are better and different games, I like go/Wei chi (https://en.wikipedia.org/wiki/Go_(game)), there are also shogi ((https://en.wikipedia.org/wiki/Shogi)where captured pieces can be played by the capturer as their own) and chinese chess (https://en.wikipedia.org/wiki/Xiangqi) which is different again.

I love hnefatafl for its asymmetry you can be good at one side without being good at the other.

[Millstone85]

Alright so, next time I offer people to play this game, I am going to suggest three simple rules.

A king can never be captured, only put in check.
It does not matter if a player's turn starts with their pieces already threatening a king.

A king can only be in check by a single player.
If a king is threatened by pieces from both opponents (no matter how many of each) then that king is in fact not in check. Any such "cancelled out" tile is also a valid position for a king to go or stay on.

The winner is whoever secures the first checkmate.
If a player is unable to get their king out of check, victory goes to the player whose pieces threaten that king. The game ends on a stalemate if a player has no legal move available while their king is not in check.

[halfeye]

A king can only be in check by a single player.
If a king is threatened by pieces from both opponents (no matter how many of each) then that king is in fact not in check. Any such "cancelled out" tile is also a valid position for a king to go or stay on.

That's so twisted, I like it. It does seem to mean a player can put another player in check by removing their threat from their king.

[Fyraltari]

That's so twisted, I like it. It does seem to mean a player can put another player in check by removing their threat from their king.

Wait. Say Green's king is threatened by both Blue and Red and therefore not in check. This is Blue's turn who moves away one piece, no longer threatening Green's king. It is now Green's turn, as their king is still threatened by Red, they must move it, however all adjacent spaces are either occupied by Green pieces or threatened by Red or Blue pieces. Since Green's king cannot reach safety, there is checkmate.

But who won? Is it Red, whose piece is currently threatening Green's king, or is it Blue, whose move put Green in checkmate?

[Millstone85]

That's so twisted, I like it. It does seem to mean a player can put another player in check by removing their threat from their king.

But who won? Is it Red, whose piece is currently threatening Green's king, or is it Blue, whose move put Green in checkmate?

As you can see, I went with

victory goes to the player whose pieces threaten that king