You failed to also mention the gifted Rook at the end of the game. Blue and Red are tied at 24 and Yellow can't resign or they both get second. This is what I would consider aggressive teaming.
Although the players did not start this game with my suggested King's worth only 5 points, watch what happens if we just change that simple rule.
On the first checkmate by Yellow the score would've been Y18-G7-B16-R14.
One move before Blue gets mated the score is Y20-B24-G7-R24.
After the mate it is Y25-G7-B24-R24.
Now some will immediately say but they will still get 1st and 2nd. Remember they did not go into the game knowing this system so the flow of the game probably would've been much different.
At least players have a chance against even aggressive teaming under this system. Also let's say they knew going in how it was scored now they have to really fight to the end instead of a quick gifted Rook and a Claim win.
First of all, please look at game https://www.chess.com/4-player-chess?g=407545
In short: Yellow and Red checkmated Green together, and after that Red didn't capture yellow queen. That signed their teaming contract. Right after that Yellow could checkmate Red in 1 move (and Yellow is a 1700+ player, who has definitely seen that checkmate), but he didn't.
23rd move: rook to k1 #.
That checkmate was the best possible move for Yellow in that position, it guaranteed the 1st place for Yellow and the 2nd for Blue. But Yellow is in a team with Red (in Solo Play?!), and as a teammate he feels that he must help Red become the 2nd. So, instead of checkmating Red in 1 move right now, or in 2-3 moves later, he starts a long attack against Blue together with Red, and at the end of the game resigns to gift Red +20.
(You can see more details and a screenshot at https://www.chess.com/clubs/forum/view/lets-compromise-conversations-with-dogmanstar7-yalin-hest1805-oleg-and-claudius-2018-11-04 ).
Lots of anti-teaming solutions were proposed on this forum during the last couple of weeks. They all have some advantages and disadvantages. And the main idea is: Let's make teaming unprofitable and it will stop teamers.
As a result we see ideas like:
1. Let's make an assisted checkmate +10 (not +20).
2. Let's give 0 points for pieces captured when the piece owner in is check.
3. Let's give double points for capturing pieces of your opposite.
4.-10. etc.
They all sounds reasonable. But they suppose that teamers tend to make profitable (and/or best) moves in their own interest.
Now look at the game above. Did Yellow make the best, rational moves? No, he did not. He did the moves that secure the 1st place for him and 2nd for his partner. He thought about his own profit also, of course, but as a caring partner, he also thought about Red's profit.
And this is what really must be solved. In Solo Play (FFA) everyone must care about his own profit only.
But how can they care about their own profit when they have obligations and must repay to partners for their help? That means we should make help and/or repayment unprofitable (or restricted).
We should create a contradiction between players so they feel they are opponents, not teammates.
And one of the most obvious ways is to let only 1 player to win. If Yellow cannot repay Red, then why Red will help Yellow checkmate Green? If Yellow wins and all 3 other player lose, then teamers cannot guarantee the 2nd place to their partners.
This idea was proposed many times. For example, recently at https://www.chess.com/clubs/forum/view/ffa-ratings-like-risk-on-gambit-com Also there is a brave and creative idea in https://www.chess.com/clubs/forum/view/another-idea-for-non-teaming-gameplay-2018-11-03
I know that "The Winner Takes It All", "The Last Man Standing" and "Rating like in RISK game" are incomplete and may have some negative consequences like "more passive/defensive play", "longer games", "self-destruction", etc. But I believe they can be improved and polished to a usable state. There is a strong anti-teaming potential (look above).
As I said in https://www.chess.com/clubs/forum/view/ffa-ratings-like-risk-on-gambit-com , I don't like the change of a "casual game, 2 winners" to a "highly competitive, 1 winner only" variation. But other solutions do not solve the teaming problem.
Correct me if I am wrong.
Is it possible to have 2 winners (2 players getting + to their rating after a Solo Play game) and at the same time make teaming unprofitable?