Luck

I just played a game where yellow pawn-rushed successfully.  Then green and blue both flagged early in the game, and yellow was in position to take both kings and nobody could interfere.

Guess who won?

It makes a big difference when two people flag early in the game leaving it as essentially a 1v1 with extra points for whoever can get to the kings first...

yep. even if only one player flags the guy opposite him is often doomed

Well, he doomed himself by flagging.  First the guy to my right flagged.  Then the guy to my left flagged.  I'd lost my queen already, so I'm effectively down two queens in a 1v1.

Not a case of luck necessarily. Your opponent may have noticed that the other two players were about to lose on time, so he placed his pieces closer to the soon-to-be-dead kings!

Btw on the second survey question «how much should capturing a dead king be worth?» I answered «10».

Small points for the king capture reduces 4-player-chess to how many points from pieces can you capture. 20 points for the kings is actually a bit low (but resigning early is a bit of a problem). 20 is a good value at the moment, but giving 25 or 30 wouldn't be outlandish.

No, he had a queen in the middle of the board from the start of the game from his early pawn charge.  That started long before they ran low on time, which happened over the course of just a couple moves in both cases.  It wasn't anticipation and planning unless he's played with them before and guessed what would happen.

Well, now the server has a bug, lot's of people got disconnected. It happened to me 2 times in 4 games today. You were lucky enough to have 2 disconnected players in a single game. And the yellow used his chance, but you did not. Next time try to get your queen first and then wait till other players disconnect. This is going to be a winning strategy until the bug is fixed.

I wouldn't call it a reduction. It's just a change of goals. The incentive for checkmate is already strong enough, since the checkmated player is kicked out of the game, his score is frozen, and becomes easier to out-score him. (Not to mention he is reduced to a spectator)

So the +20 points award for capturing dead kings doesn't accomplish much really, on the way of encouraging some form of remarkable game performance by the players.

I don't think they were disconnected; they just weren't watching the clock.  Rated 1200 exactly, so probably new players.

@Skeftomilos: It's definitely a reduction, since you take away the possibility to score big points by checkmate. If you are two players left, the final player should be awarded. Reducing it to 10 points means people can "resign" as soon as the gap is more than 10 points. I think the points for the king should be increased to award checkmate more. I think 30 points would be very defendable, but 20 points is quite fine. 10 is too low for sure. Set it to 0 and the ways to win is reduced significantly, it's just a hacking game then.

The more points you give for the king, the closer it gets to last-man-standing.  Still, I don't think 30 would be too much to limit the incentive for aggressive play.

We can set different bonuses for the checkmates. For example:
1. +20 for the 1st checkmated king, +25 for the second one, +30 for the 3rd.
or
2. +30 for the 1st checkmated king, +25 for the second one, +20 for the 3rd. 

We just need to understand what do we want?   

@icystun fair points. But the more points you give for dead kings, the luckier the game becomes.

@BabYagun we want to reward great chess performance, and reduce luck.

What about that?
+10 points for each dead king
+10 points bonus for the last man standing
All leftover kings are awarded to the last man standing

I think last man standing is a great issue! I was always annoyed that it was basically meaningless.

Bonus for the last man standing is a good idea.

But "All leftover kings are awarded to the last man standing" is not good. Let's say you are red and attack yellow, but yellow does not want you to win. So he resigns when there is "mate in 1" just before you checkmate him. And you do not earn those points if the last man standing is blue or green. Not fair.

@BabYagun if you capture a dead king, he is not a leftover king any more! You get the points of the king instantly, and the last man standing will get nothing.

But if you are the last man standing after three successive resignations, you will get the points of all 3 leftover kings!

Ok, understood. You just use a different definition of a leftover king.

Yes, it is somewhat ambiguous. Btw I just repeated a suggestion already made by @Gilberreke, and used his term.