"but the extent players will go out of their way to protect their opposite sometimes seems a little silly and pointless to me." I'll get to some other reasons in a minute, but part of it is simply social expectations....helping your opposite is what you're "Supposed" to do regardless of whether it is helpful in the specific game or not.
"However, in my very limited experience, the player that gets eliminated first generally has little bearing on which remaining color ends up winning the game." While you can definitely win in the middle, it becomes harder because A. you have less space and room to operate, and B. may, depending on how the game went, be at a severe point deficit. For these reasons, it's harder to get a good position and harder to win from a bad position (because on average you may be behind on points, potentially severely), and so while winning from the middle is certainly possible (especially against bad players), it is not ideal.
The other thing to keep in mind is that mutual cooperation is the best strategy for opposites in the four player stage, simply because 2>1. I hope that makes sense. And so if you aren't supporting your opposite, you're probably going to get fourth more than you would otherwise because you and your opposite are automatically losing the four-player stage (assuming optimal play from sides).
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With all that said, I think there is an argument to be had for the specific situational decision, if your opposite is guaranteed to die without intervention, to let them die. That's not how I play out of principle, and so I don't know how to weigh that versus the downsides (points & position, eventual societal lack of trust etc.), but I wouldn't call that a terrible idea per se.
Unless you're my opposite
Hope that helps a little
I've recently started playing 4PC, and something that has continually confused me is opposite cooperation, so I had a few questions. I understand the basic premise behind cooperating with your opposite in the initial 4 player stage (at least I think I do)--your opposite is farther from you and cannot immediately attack you, whereas the players on your flanks can immediately create threats, but the extent players will go out of their way to protect their opposite sometimes seems a little silly and pointless to me.
From my understanding--and maybe this is completely wrong--the goal of the 4 player stage is simply to eliminate one of the players, and this is why teaming up with your opposite can be incredibly useful. However, in my very limited experience, the player that gets eliminated first generally has little bearing on which remaining color ends up winning the game. Theoretically, this assumption makes sense, because once in the 3 player stage, the fundamental strategy is to maintain a balance of power between the players. If on player becomes too powerful, the other two will coordinate attacks to weaken that player, and this will constantly repeat.
The main benefit of eliminating the first player is to increase your own chances of getting first, and this increase in winning chances is completely independent from whether the eliminated player is your opposite or not, so why is it that opposites in the 4 player stage will sometimes blindingly cooperate? For example, I have seen many instances where a player is about to be checkmated, and their opposite saves them with a check, sometimes sacrificing a bishop or even a queen. Why are moves like these that save one's opposite at all necessary? What substantial difference is there if your opposite is checkmated vs one of your other opponents? To me it simply seems incredibly pointless. From my understanding, checkmating a player is almost always necessary to meaningfully progress in the game, essentially eliminating the weakest link, so why is it that players will team to directly prevent checkmate?
Here are a couple of games to illustrate my point. In this game, played 12. Qxh13+, setting up a mate on yellow if red plays 13. Qxg12#. However red declines to play this, and it seems to me like this was mostly based on the sole fact that yellow is red's opposite.
https://www.chess.com/variants/4-player-chess/game/79427307/306/4
In this game, blue could have played 8. Qxn9+, allowing yellow to play 8. Qxn6#. This seems counter intuitive, because generally opposites cooperate, but this seems like a perfectly valid move for blue to play. If blue could set up this same mate on either red or yellow, they would play it without so much as batting an eye, so what is the difference that makes checkmating an opposite so horrible.
https://www.chess.com/variants/4-player-chess/game/74495770/30/1
Obviously I understand the frustration that comes when an opposite or opponent doesn't play a move that I expect or think is best, but I believe that it is simply naive to ALWAYS trust and play for your opposite. In these aforementioned games, there are clear checkmate opportunities, so why are they ignored? Sometimes, it seems completely beneficial to play against your opposite, so why is that viewed with such a negative connotation of an unforgivable "betrayal"? On what basis can any player fully trust their opposite to save them than general custom and accepted play? I simply don't see how letting your opposite get checkmated or even actively checkmating them is any different than letting one of your other opponents get checkmated or actively checkmating them.
Obviously my 4pc experience is incredibly limited, so I am genuinely curious about the answers.