how do you determine what phrase of the game is it?
OK, I've solved teaming!

how do you determine what phrase of the game is it?
>>The game is divided up into three scoring phases: opening, middle game, and end game. Opening is done when one player is checkmated, middle is done when two are. (Ending, for those that need closure, is done when three are.)
Ie after one checkmate you are in the middle, after two you are in the end.

now I checked mathematics part. I think biggest problem of this system would be "VERY LONG GAMES"
None would attempt checkmate especially by scarifying his some pieces. So everyone is gonna just try to make more and more queens instead of attacking each other. Also everyone will aim taking pieces for free instead of accepting exchange.
Still I am not saying that is a bad opinion.
Scoring and elo system has to be changed. Since I havent got a better idea, I really appreciate your effort.

It's an idea, It's a bit complicated and it will be impossible to calculate the points when your in a critical position and low on time. But then I guess you can ignore precise calculation and simply try to at least exchange a pawn with your opposite in order to avoid a 0 multiplier and gain access to the large point bonus.
It wouldnt solve the teaming issue. I know a guy like me would be finding lots of loopholes.

Great! Now the game is destroyed, nobody knows what to do to increase his chances of winning, and the teamers with a background in mathematics will find their way to the leaderboard anyway!

Oh so the thing is that you can team but you can't do it for the rest of the game ( as the points are being deducted ).

Great! Now the game is destroyed, nobody knows what to do to increase his chances of winning, and the teamers with a background in mathematics will find their way to the leaderboard anyway!
that mathematics calculation is actually not difficult. Simply, you shouldnt aim attacking one player, especially you shouldnt exchange your piece in the beginning. You should try to take pieces for free or value of piece you will take must be more valuable than the piece you will sacrifice.

Great! Now the game is destroyed, nobody knows what to do to increase his chances of winning, and the teamers with a background in mathematics will find their way to the leaderboard anyway!
There is always a solution for every thing according to mathematics and science. There has to be a proper solution for this situation.
@VAOhlman , you can improve this situation with more uh.. solutions.. solutions that @Skeftomilos is asking. ''nobody knows what to do to increase his chances of winning, '' , ''and the teamers with a background in mathematics will find their way to the leaderboard anyway!''

Great! Now the game is destroyed, nobody knows what to do to increase his chances of winning, and the teamers with a background in mathematics will find their way to the leaderboard anyway!
You know what.. I'll answer this question. Ignore my previous one.
First, the problem you asked ''nobody knows what to do to increase his chances of winning, ''.
I'll take x as nobody.
Actually x can take the advantage from this situation. For example : x teammate is C. x teams up with C to take on A and B. x checkmated B with the help of C but he was the one checkmated so he gains +20 while C gains +12 since he also took x bishop and queen.
Hey wait hold on..
This is complicated.
Then there has to be a high intelligent computer to detect all this.. since many players can take advantage of this situation..

There is always a solution for every thing according to mathematics and science. There has to be a proper solution for this situation.
Ha ha ha! The proper solution is to scrap this idea and then forget that it ever existed!

Then there has to be a high intelligent computer to detect all this.. since many players can take advantage of this situation..
there is no intelligent computers dude. They are as stupid as you can not imagine. They only execute the code write

There is always a solution for every thing according to mathematics and science. There has to be a proper solution for this situation.
Ha ha ha! The proper solution is to scrap this idea and then forget that it ever existed!
I hate teaming.. you do to right?
Do you ever think is this right or wrong?
Do you think that this is fair to every player?
I don't..
So, with that being said, I want a solution for this problem!!!
Many players are out there exhausted of this problem.
This thing needs to be stand out.
P.S.
I am not being rude here so don't take any of the offense real .

Then there has to be a high intelligent computer to detect all this.. since many players can take advantage of this situation..
there is no intelligent computers dude. They are as stupid as you can not imagine. They only execute the code write
Oh..
Well at least I tried my best bringing out my best in this situation..

@username_noob there is already a solution for the teaming problem. It is called: enforcing the rules.

Or maybe the perfect solution is to report the player..
Everyone has their own opinions..
My opinion is to report the player for teaming in FFA.
edit :
It is the solution.

@username_noob there is already a solution for the teaming problem. It is called: enforcing the rules.
I just posted the comment lol.
Same time..
Ok, was trying to sleep after a long night on the ambulance but, no, instead I have solved the teaming problem. One easy little rule change. Easy for the computer that is. Totally objective. It involves a scoring system I invented for another game. Follow me now...
The game is divided up into three scoring phases: opening, middle game, and end game. Opening is done when one player is checkmated, middle is done when two are. (Ending, for those that need closure, is done when three are.) Here is the way points are calculated:
Opening:
Let us name each players opponents as A, B, and C. Our player gains points as follows:
(Points against A PLUS Points against B PLUS points against C) PLUS (Points against A TIMES Points against B TIMES Points against C)
Middle:
(Points against A PLUS Points against B ) PLUS (Points against A TIMES Points against B )
End:
(Points against A ) PLUS (Points against A SQUARED)
What does this do, you naive mathematicians ask? Well... watch how it affects teaming...
Our hero teams up with C, and beats up on A and B in the opening, checkmating B but giving the queen and a bishop to C. Our hero's points would be:
(20+0+0) + (20 * 0 * 0) = 20
C's points:
(12 + 0 + 0) + (12 * 0 * 0) = 12
Along the way B managed to eat two pawns and a bishop from both of them, plus he ate red's knight. His points are:
B's points:
(4 + 4 + 3) + (4 * 4 * 3) = (11) + (48) = 59
I could work out more examples but the end conclusion is this: taking and checkmating are good, but if you do so in a lopsided fashion, you don't get many points. In order to really score you have to do so in a balanced fashion.
(Someone may ask why the phases of the game. Good game theorists will have already figured that out. I will leave it out there until/unless it becomes really confusing. It is very necessary to prevent teaming, however.)