Very interesting and extensive guide on mutual benefit theories. It's become second nature for myself in hyper to play with the sole objective of maximizing my own point total irrespective who is 2nd or 3rd. A lot of newer players often fail to see the whole picture and will automatically take 2nd in a position like you showed above (as green)
In some situations in Chaturaji, it's like if the ranking was done but in reality, if remaining players have a chance to upgrade their ranking but that chance is depending on how the other player will play and it's the same for both, they probably can take advantage of this fact to get what they want.
For example, in this situation, green needs 2 rooks + yellow's king to get first and yellow needs 2 rooks + the knight to win :
Here, it can seem hard for them to get first and second but it still possible.
Firstly, yellow could theoretically put himself in check because green have a chance to get first so he shouldn't take yellow's king now but it still more safe to don't take this risk if it isn't necessary.
So, here, yellow e pawn is locked and h pawn's promotion case is cover, the best for yellow to start is probably to bring his king at his h pawn to promote and trade with a rook.
Now, imagine this series of moves : -Kb2 Bd7 -Kb3 Bc8 -Kc4 Bxa6 -Kd5 Bb7+ -Ke5 c2 -Kf4 b2 -Kg3 2xa3=R -Kg2 Ra1 -Kg3 Bc6 -Kg2 Ng4.
This series can seem pretty strange but for green, king, knight and e3 pawn are well placed and until yellow's king is far away d2 pawn, push it is possible but it's easier if you can push it without pay attention to his security. Moreover, yellow haves to wait until the knight don't cover the promotion case to be sure to trade with the rook. We are now in this situation :
Yellow haves just to make a rook and trade with -h1=R Rxh1 -Kxh1.
Now, green needs a rook and the king and yellow needs the knight and a rook or a bishop.
In this situtation, there are two possibilities, the first one is if yellow don't eat the pawn.
We can imagine this series of moves : ...d3 -Kg2 c3 -Kg3 Ne5 -Kf4 Nc4 -Kf5 b3 -Kf4 a3=R -Kf5 Kd2 -Kf4 Kc3 -e3 Ra1 -e2 Nd2 -Ke3 Nc4+ -Kf2 Rb1.
We are now in this situation :
TAKE CARE ! If yellow promote now, after the trade, green can win by repetition and isn't forced to sacrifice his knight. The best to do is to wait until the promotion case won't be cover, even if green is a good player he can take a bit of time to understand what yellow want he do but in each cases green don't want to get second so he won't do a repetition or take yellow's king.
After some moves, the objective of yellow is to get this kind of situation :
As you can see, yellow is in check but Dorami no care because what green want is... THE ROOOOOOOOOOK ! So now, yellow can play Rf3+ and after Rd3+, Rxd3+ and Kxd3, there is Kxc4+ ! (and then Kxc4#S or Bxc4#S) So, after a lot of adventures, green finally get first and yellow second, youhou~ !
The second situation I was talking about earlier is if yellow take the pawn :
In this situation, green can also get first and yellow second, an advantage for green is that the promotion case is white so can be covered by the bishop. This way is the fastest to win but we never know, green could be afraid by this move and take the king... but green is Botbeg and he haves 20 seconds, he is not enough stupid to do that. Take the pawn is possible because a pawn + a bishop + a drawn = 8 points, just enough to win and for green, a rook + a drawn is also enough to win.
Now, a logical series would be : ...Kd2 -Kg2 Bxb5 -Kg3 Ne5 -Kf2 Ba4 -Kf1 Kc3 -d2 Nf3 -Ke2 Nd4+.
Yellow is in check but balek, d1=R then Bxd1+ then Kxd1 and after green can sacrifice his knight or win by repetition.
As you see, even if some situations can seem hard to win, if you need the help of your enemy to win and he needs yours, by taking in consideration both objectives, you can potentially get what you want.
Below, I wanna show you another situation where with cooperation, the two remaining players can help themself to get first and second place. I won't give a lot of details.
Here, yellow needs at least a rook to get first but red needs yellow's rook + yellow's king. He haves no reason to continue to play if he can't get at least a tie in second place so if he can't get that, he could resign (that's what happened in the real game) before that yellow get first place. Red is dependent on yellow and yellow is dependent on red so they have to help themself. Here, if yellow take both pawns he wanna be first but with a tie, it would be stupid cause he can get first. If yellow take one pawn, red still can get second place with tie but if yellow take a protected pawn with his rook, red could just take the rook and yellow wouldn't be first. That's why let red promotes should be good but in this situation, isn't easy.
Firstly, we have to get this kind of position :
The idea for yellow is firstly to trade a rook to then attack the remaining pawn, he just haves to take care that it's possible.
A possible series here is : ...Rg8 -c8=R Rxc8 -Kxc8 Ke6 -c6 Kd6 -Kb7 Ke7 -c7 Rf5.
And now, you see that yellow won't get first but first with a tie because after Rb8, Rxc7+ is forced to don't finish second with a tie. BUT ! If yellow didn't let red do what he want to do, yellow wouldn't be first with a tie but second and be first with a tie still better than be second so it still advantageous for yellow. Because if yellow take a pawn there is the possibility that red take the rook and it wouldn't be good at all for yellow. Moreover, yellow can hope a situation like below.
Here, red just blundered and so after the trade, yellow take the pawn and finish first.
What you have to retain from this lesson is that in Chaturaji, sometimes, your opponents can become your friends, what is really nice lol. If you know what want your enemy from you, maybe you can use it to get what you want, because you have no reason to give him what he wants if he doesn't give you what you want and he doesn't have reason to don't give you what you want if it allows him to get what he wants.
The real problem with this strategy is that a lot of people won't think like that and so you can try it mostly with professionals but it still good to know that because it could save some of your games.
Thanks for reading, signed : [CGM] Botbeg