I think they want to stop teaming and unfairness
Desired Scoring Change
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Oct 31, 2017
0
#3
I have personal experience, and, trust me, its not fun
i won anyway 
Your sharing system seems extremely fair, at the cost of being overly complicated!
But actually counting the squares around the king and the influence of each player on these squares, is a poor indicator of the effort each player put to the cooperated checkmate. For example the one who made the sacrifices may control fewer squares than the one who took free material in the process.
Can't say I'm a huge fan but mostly because lots of players don't enjoy teaming.
I just made a suggestion inspired by this idea: Suggestion: Facilitate teaming with Contracts
Oct 31, 2017
0
#7
I am not sure how something like this would change the dynamic of the game? that said if it was to be tested I think you could do a small step and KISS it by just giving 20 points to the person who did the final move (as it is now) and 10 points to anyone that combines for the king to be checkmated.
Oct 31, 2017
0
#8
Teaming is not allowed unless everyone agrees before the game. I didn't make it up.
One of the best parts of 4 player chess is when I am working with another player to take down a third player. The only thing that is not so good about this is: one person gets 20 points, the other nothing. This almost makes working together not worth it.
Recommended change:
20 points for a checkmate is good. However, in multi-player checkmate scenarios, I would like the credit to be shared a bit differently.
4 points goes to the person whose move it is.
6 points gets divided between all players that are currently checking the king
10 points gets divided up between players attacking squares around the king
Dividing up those last 10 points may be a bit tricky. One way is to think of it as "shares"
For each square around the enemy king that the king can go to (basically one that is occupied by anything other than a friendly unit), 1 share is given to each player attacking that square.
After this is calculated, each person has a number of shares.
If only one person has shares, then he gets all 10 points.
If more than one person has shares, points are divvied up in the following way:
11+ total shares: reduce the number of shares in some deterministic way until there are 10 shares.
10 total shares: 1 point per share
6-9 total shares: 1 point per share, remaining points go to whose turn it is
5 total shares: 2 points per share
4 total shares: 2 points per share, remaining points go to whose turn it is
3 total shares: 3 points per share, remaining points go to whose turn it is
2 total shares: 5 points per share.
This would make cooperative conquest more equitable in dishing out points for a successful conquest. One of the more disappointing events to happen is when a good campaign is finished against a competitor... and someone else gets ALL 20 points. It also rewards agressive play a bit more, and makes it more risky to turtle up and let your other two neighbors crush a third.