The points system has caused much confusion. We've seen multiple posts from people wondering why they didn't win when they were the last man standing, or complaining that they should have won. And it's true: the points system is not the way you would intuitively expect a four-player game to work.
On the other hand, we do need some incentive for people to come out and fight instead of sitting back in a defensive position and waiting for everyone else to fight; otherwise you have a boring game where everyone just shuffles their pieces back and forth. Despite its drawbacks, the points system provides that.
However, I have an idea that is easy to understand, easy to implement, would eliminate the points system and allow us to go back to last-man-standing, while still creating a significant incentive to come out and fight. As an added benefit, I think it even disincentivises teaming (except for temporary cooperation as demanded by the position on the board).
1. No more points. The winner is the last man standing.
2. No more check and checkmate. You can move your king into check, or leave it in check; you would rarely do so deliberately, but it would be legal, and there would be rare situations where you might want to do so (I'll explain that below).
3. You are not eliminated until your king is captured.
4. And the key change: when you capture someone else's king, you take control of their remaining pieces. If red captures blue's king, on red's next turn, they can move either a red piece or a blue piece, as they are now combined into a single army. However, the pieces should retain their original colour to indicate which direction the pawns can move (but perhaps they should be given hats or something to indicate who now controls them).
This creates an incentive for aggressive play: if red loses half his army taking blue out and kills half of blue's army in the process, the combined army will still be very substantial. Additionally, if you take out your neighbour, your strong control over one corner of the board will potentially make it easy for you to promote several pawns in quick succession.
This also disincentivises teaming (except on a temporary basis as demanded by the position on the board): if red helps green take blue down, he's just helped green get a powerful army that will soon be used against red. Red might work with green to weaken blue if blue is too powerful, but will be careful about pushing it until blue is eliminated as he doesn't want to strengthen red.
A typical game will probably see one player eliminated relatively early, with the other three gradually wearing each other down until you get into a 3-man endgame, and whoever is better positioned in the endgame will win; however, 2- and 3-way draws will not be unheard of. Having your neighbour eliminated will be good for you in the endgame if you have any pawns left on that side of the board, thus increasing the incentive to try to take out one of your neighbours early in the game.
Thoughts?
P.S. As for the situation where you might deliberately move into check, here are two possible scenarios:
1. Player 2 is in check from Player 3. Player 1 can safely move into check from Player 2, as Player 2 must save his own king.
2. Player 1 deliberately moves into check from Player 3. Player 2 does not want Player 3 to take over all of Player 1's pieces, so he must intervene. The only way he can intervene is to put Player 3 in check, and the only way to put Player 3 in check is to sacrifice his queen for one of the pawns in front of Player 3's king. Thus, Player 1 has put his king in danger to force Player 2 to give up his queen, while opening up Player 3's king in the process. Of course, that could backfire if Player 2 thinks he can take on Player 3 even if he controls Player 1's pieces.