This looks like a fabulous game that would seldom be dull. I don't know if one side can force a win or even a significant advantage straight from the opening, but as long as this is a mystery it adds to the charm of the variant. The 2 games between the author and Joe Joyce, circa 2011, were illuminating for me. These were played using the non-rule enforcing preset "4-Handed Chaturanga" that is still currently used to handle any 4 army (though 2 player) Chaturanga variant on Game Courier, it seems.

My tentative estimates for the piece values of this variant would be: S=0.625; P=1; N=3.5; R=5.5 and the fighting value of K=4 (though naturally it cannot be traded). Bear in mind that years ago ZoG estimated the value of an alfil [an S in this variant] on an 8x8 board to be about 1.16, or almost twice what I have it as. I reached that value by taking an initial value for S of (N-1)/8 - for being thrice binded - and then multiplying that by 2 (as a bonus for usually being a speedier short-range leaper than the otherwise somewhat similar N) to get my final value for S.

[edit: some implications of the rules of this particular variant are not totally obvious to me, though I believe I understand them: Firstly, I asked myself, can a player ever capture one of his own pieces (aside from under the special case of the meeting of the 4 ships rule)? That is, can a piece that belongs to his army of the other colour be captured by a piece of the colour that he is moving, e.g. can, say, a yellow king ever capture a red pawn? The answer seems to be clearly 'no'. For in the rules there is stated: "The black armies pieces and pawns can be captured by the yellow and red pieces". Nothing is mentioned about green being able to capture black's pawns and pieces. That said, a similar question I had about the rules was whether, say, a yellow piece can ever be giving check to the player's other (red) king, and the answer again seems to be clearly 'no' (just as a yellow piece or pawn cannot capture a red one). Lastly, perhaps the most vexing question I had was if, say, the red & yellow kings could ever legally be on adjacent squares. In the rules there is stated: "A king also cannot move to a square that is being attacked by an enemy piece, even if that enemy piece's king is in checkmate". There is nothing stated about a king moving to a square attacked by a friendly king (the quoted statement also in a similar way reinforces my conclusion in the previous paragraph). Thus it seems clear that indeed the red & yellow kings could legally be on adjacent squares.]