Teaming and Courtesy in Chaturaji

TEAMING:

Many newcomers to 4-Player Chess are misled by the "FFA rules". The name "Free-For-All" and the rules against cooperation in chat and prearranged cooperation make people think that teaming is not allowed. But every strong standard 4PC knows that teaming with the opposite to checkmate one is the best strategy. The reason that opposite cooperation is so effective lies in the glicko2 rating system, which will play a large part in many things that I will discuss in this post. This is how glicko2 works for FFA (this will not account for glicko rd, the value that represents how accurate your rating is and controls how much your rating goes up or down):

At the start of the game, a value correlating to the relation between your rating and the average rating of the other players is computed (if your rating is higher, this value will be lower. If the opponents' average rating is higher, this value will be higher).  Let's call this x.

1st place: you gain 3x points of rating

2nd place: you gain xy points of rating

3rd place: you lose xy points of rating

4th place: you lose 3x points of rating

where y is a constant which gets lower as the average rating of all players gets higher. In other words, for high-rated games, 2nd and 3rd will both basically not have any changes.

As you can see, eliminating someone and preventing yourself from getting 4th is pretty advantageous. However, this has been about standard 4-Player Chess, where you and your opposite can easily and quickly destroy a flank if they do not cooperate as well. In chaturaji, cooperation almost never means directly removing someone from the game; usually, one player helps another get points or preserve pieces that would otherwise be captured. I will now discuss the topic of when teaming in chaturaji is correct. First of all, let's introduce a concept: when you play a move that has little or no benefit to yourself, but highly inconveniences another player. Let's call this a spite move, as they are often made just based on emotions. The First Law of Chaturaji Dynamics states that advantages and disadvantages can be transformed and transferred to other players, but they can never be destroyed. Therefore, all spite moves must also help another player and are therefore cooperation moves to an extent. Now without further ado, time to discuss teaming!

The 4-Player Stage:

There are two ways to view teaming: 1. Minimize your chances of getting last. 2. Maximize your chances of getting 1st. Personally, I think 1. is boring and stupid; it often involves "playing for 2nd" and blatantly helping the opposite. Let me refer again to the laws of Chaturaji Dynamics: each chaturaji game starts out with an equilibrium of advantage - that is, no one has an advantage. Trading rooks or knights does not disrupt the equilibrium, because the traders lost valuable pieces in exchange for the points. Trading bishops gives an edge to the traders and a disadvantage to the ones not trading. If you are trying to minimize your chances of getting last, you try to put as much distance from yourself to the player with the most disadvantage. Play spite moves against them and team on them and essentially skew the equilibrium as much as possible while maintaining your middling position (there will be one player who benefits greatly from your targeting, and one who suffers greatly, and you and the other player will not have advantages or disadvantages). If you play to maximize your winning chances, you try to preserve the equilibrium as much as possible unless you are benefiting yourself most (if you are the player who is benefiting greatly). This means targeting the player with the most advantage and playing spite moves against them; if no one has a big advantage, you just play chess. No need to sabotage anyone unless it benefits you. As I mentioned, I prefer and recommend maximizing winning chances; I believe it works better, and people will definitely get mad at you less if you play only for yourself. Let's apply these strategies to the following example:

red to move (note: this position is not actually red to move, I skipped a move for green to make it more instructive)

First of all, assume red takes Bxg7. Should blue team and take the rook?

Obviously yes, since it benefits him. Yellow will capture the bishop and blue will have gotten free rook. Both ways of playing support this. Now let's move on to a more complicated thought experiment:

What should red do? He can take the bishop, teaming on yellow, or play Nc5+, teaming on blue, or a waiting move like Kb1, or he can completely stop teaming with d4.

Let's analyze the options. If red wants to minimize chances of being last, teaming on yellow makes a lot of sense. Teaming on blue is rather silly; interference from green will prevent red from taking the bishop and possibly make him lose the knight as well. Note that green should definitely check red; he must limit everyone's points if he wants to stay in the game. He can also push his 1st rank pawn, which puts red in the same position that yellow is now - getting teamed on. So what do you play if you want to maximize winning chances? The threat of d1 from green pretty much rules out Kb1 as well; after Kb1 Rxh8 Bxh8 (if Bxb2, it's just a worse version of teaming on yellow in the first place) d1 Bxh8 Kb8 f6 1xc2, and now green basically takes all of red's pawns. d4 does preserve equilibrium, but it's clearly not worth it. d2 followed by d1 for green (with ideas like Be4) is very annoying for red, and you waste two moves giving green a pawn if you want to trade bishops. This is a trick question you should also take the bishop to maximize winning chances; tempi are very significant in chaturaji (you might be wondering how red and yellow, who move before blue and green, are in such a bad spot. Red pushed his rook pawn, even though his knight was going to block it anyway. Yellow spent two moves moving the knight for no reason and blocking his rook pawn. These are by no means useless moves, but red and yellow are in pretty bad positions here; yellow dropping a piece and red's pawn structure getting destroyed), and wasting time preventing blue from getting a rook is not a good idea.

But should blue take yellow's rook if he wants to maximize winning chances? Of course, he does. Half of the time, yellow takes red and gives him the advantage, which is always good. The other half, red gets an "advantage" but it's not actually an advantage because green demolishes him. This is more of an equilibrium than if blue decided not to take the rook and let red and yellow trade bishops and red take his bishop for his knight. That's the other reason why blue must take the rook; he wants to avoid Nc5+ as soon as he can, and that means Kb8 after the rook trade (or free rook, as the case may be).

Now imagine that green's 2nd and 1st rank pawns are moved back one square. Now, d4 is good for red; the key difference here is that after the rook trade, red can immediately trade his knight for blue's bishop (green cannot interfere in time unless he sacrifices a pawn, which most people will not do). This gives you a slight advantage, which is much more preferable than just killing yellow off in my opinion.

Note that I have analyzed this example as if all players were strong players. Low-rated people like flashy forcing moves, and will check and capture and threaten as much as they can. Always expect inexperienced players to team.

The 3-Player Stage:

This is fairly straightforward. Due to how the rating system works, 2nd = 3rd = basically nothing, and the only thing you should be doing is maximizing your chances of getting 1st. In other words, don't help anyone, and if someone is too strong, team with the other player to balance it out. The 3-player stage is all about balance. Do not liquidate into the 2-Player stage unless you are winning (if you are confident in your skills, equality is a win).

Mate Teaming in The 4-Player Stage:

I have only been talking about "soft teaming", which results in an imbalance of points/pieces and one player having an advantage, and one player having a disadvantage. There is another type of teaming which occurs at the beginning of the game: you cooperate with your opposite to eliminate a flank just like in standard. This only works as red and yellow with a decent opposite. Here are the two main ones:

In both, blue and green played normal openings. In both, the opposite cannot save the one being mated. In both, the cost to red and yellow is minimal, and they have no chance of getting 4th. So this seems great, right?

Theoretically, yes. However, we are not robots. What is objectively the best move is not always the move you should make. Now for the second part of the post: 

ETIQUETTE/COURTESY:

4-Player Chess has been around much longer than the variants server and therefore has more developed ideas of  "dignity" and "courtesy" and "etiquette" and "not being a ****"... etc. Don't betray your opposite before the 3-Player Stage in standard FFA. Don't target people, anywhere (this is not in any of the rules). Follow your higher-rated partner's arrows in teams. Resign, don't abandon games and waste people's time. There are many of these guidelines which aren't often in your best interest, but they keep the game friendly for others. I guess here is a good time to refer back to the stupid rule they teach you in school as an attempt (not a successful attempt lmao) to stop bullying: Treat others the way you want to be treated. This may seem really stupid for a competitive game, but think of it this way: you are about to do X, which would be really inconvenient for an opponent. If someone did X to you, would you objectively think "Wow, well played / Damn, that was silly of me" or "WTF is this degenerate trash? BLOCKED REPORTED... etc." Sure, going for mate on blue and green with your opposite on move 3 will get good results, but everyone will block you and you will have no one left to play with but other people who play like that. Also do not randomly or frequently make spite moves; they are annoying and people will block you (if only you could block people in school xD). I don't care if it's "objectively the best". No one gives a damn about someone's chaturaji blitz rating on the chess.com variants server. It's all for fun, so don't spoil the fun by being a bot.

Of course, there are some grey areas when it comes to courtesy. Imagine you, as red, play b3 - Bb2 on the first two moves, and your opposite, yellow, plays g6 - Bg7 on the first two moves. Now, this may seem a little bit ridiculous, but there's an ongoing debate in 4-Player Chess hyper circles about whether or not you take the free 10 points. After all, if everyone agrees to not take the free bishop, then yellow and green aren't so much worse than red and blue (right now, yellow and green can be forced to play standard based on what the preceding players play (and blue to a lesser extent)), and a more balanced game is better for everyone. I generally think that you should take the free bishop; encouraging bad habits like hanging a bishop will end up costing that player a lot more than just one game if he sees a strong player not taking the bishop and expects everyone else to do the same. Remember that this is a hyper argument; of course, there is no question about this in blitz.

A less extreme argument is mouse slips (this, on the other hand, is only about the slower time controls). I'm not going to tell you what to do about mouse slips; everyone has their own courtesy policies. In general, the more obvious the blunder is, the more likely it is a mouse slip, and the stronger the player is, the more likely it is a mouse slip. I don't like to exercise leniency in mouse slips, because people often like to say "oops my mouse slipped" when they don't want to admit to making a mistake. I would only spare the mouse slip if the blunderer in question was a strong player (use your own judgment on what strong means), and the blunder in question was a hanging piece.

I also will not advocate leniency for anything that was not beyond the control of the blundering player. Again, I don't like encouraging bad habits; if someone blunders, they should be punished. Most 2v1s are easily preventable if you are careful and avoid trading into multiple people at once (early-mate 2v1s are not easy to prevent, which is why I discourage people from using this strategy). If you don't punish people's mistakes, they will never learn.

There are often scenarios where you can choose places: for example, if you have a rook and king against two kings, you can choose who gets 2nd place. If someone is mated with 20 points, another person is mated with 0 points, you have 1 point, and the other player has 16 points, you can choose who is 1st. As I said, this is quite common; there are countless scenarios. Generally, I always try to gift a higher place to higher-rated players, unless they played really badly. Everyone does poorly from time to time (usually as a result of spite moves made by weak players). 

Here's an example:

https://www.chess.com/variants/chaturaji/game/18284969

This is Oyeyif's (hopefully not) last game. I'm not gonna provide in-depth analysis since that isn't the point of this post (I will say though, fun fact: blue could've won sometime from move 40 to 60 by sacrificing his king onto yellow's king. If yellow takes, then green cannot pass blue in points, and yellow cannot run with his king forever. Green had to cut off the two kings with a rook at all times). As you can see, 15.y and 16.y made yellow lose a knight, although this is by no means an obvious blunder; 15.g was a pretty brilliant move (remember what I said earlier, about how weaker players always love forcing moves? props to green for taking advantage of the psychological element of this game), can't blame yellow for not expecting that. And of course, 20.r was silly, allowing a double-check which cost yellow two pawns. And then red decided to play for 3rd and take a rook (yellow's rook essentially) for a king. Basically, yellow got pretty unlucky because red was kinda trolling him and green was playing really well. Yellow didn't play anything terrible and didn't deserve last, so green gifted him 3rd. A really great finishing game; you will be missed, Oyeyif.

These are just my opinions. Unlike my previous post and the teaming half of this post, the courtesy half of this post was pretty much completely subjective. Feel free to disagree .

Questions? Comments? Stories about teaming, degeneracy, and win-gifting?

Hi,

After reading your article I found myself in a position to replicate one of the traps you showed here: https://www.chess.com/variants/chaturaji/game/18380539/5/1

however, yellow declines to eat the king and I am just down a pawn....

https://www.chess.com/variants/chaturaji/game/18255939/108/3 In this game red implodes too soon and blue and green have traded bishops. As yellow I am probably not going to win 1st place after move 23. Things have gone wrong and blue has too many points, green is slightly ahead of me and red is out in 4th. So I change my strategy from try to beat box in a rap battle, to play for 2nd. As is stated in this article this is a lowly poor strategy that barely gains you any points. However as a result I gain 5 rating points instead of lose 15.

Playing for 2nd from move one is clearly not optimal but to be flexible and force an ending where you are 2nd instead of probably 3rd seems okay to me. 

On move 24 Box helps me to gain a knight with his attack on the blue rook which sets up my idea to "claim" 2nd but also sets up the idea of trying to coordinate to take blue down. I perhaps should have played that way but it felt like blue would be first unless we eliminate him immediately and even then Box will probably be first and I'm 2nd or 3rd. So I chose 2nd place now rather than maybe 2nd or 3rd. 

Feel free to share any analysis, suggestions for how I should have played for first etc.

Thank you for your instructive articles!

Kyle

Don't trust bad players to do anything. You can try to predict what they play, but they sometimes do random things. Click on the player's profile, and see how many games they have. That was literally yellow's first game ever.

Maybe you are right. In 4PC standard FFA, where the "decent" players are 2500+ and games are often 2400+, 2500+, and 2600+, 2nd place and 3rd place are literally +0.1 and -0.1. However, in chaturaji variants, most of us are 2200s, so 2nd place and 3rd place has a more significant difference. I'd say playing for 2nd is fine if you have literally no chance to get 1st, or you need to leave or something. I remember doing it myself one time when I had 15 or so points, someone had 10 or so points, and another had 30 or so points. These are subjective topics; just use your own judgment on how likely you are to get 1st if you play for 1st.

I have more than 2700+ in ffa and I like to eliminate a side briefly for 2 reasons, not to be last and to go to a final of 3 much more comfortable. However, when I tried chaturaji for the first time, which was not long ago, the teams question was the first one that I posed at the beginning of the game, I particularly decided to approach it with a "SOLO" mentality, since I don 't usually see good players of opposites who understand the plays still, because there are still very few playing this variant, the thought I use is to prevent others from earning points, is the reason why I would make a temporary team, to prevent another player from earning free points due to the carelessness of another player. I would intervene with a check or a piece threat.

by the way is there the possibility of a 2vs2 teams mode in chaturaji? or is there an imbalance of advantage in the colors? I never played hyperfiesta, so I don't have the experience of testing the meta-game with strong FFA / TEAMS players.

yes, hest created "Chaturaji Alternate Teams", which is red and green against blue and yellow, with CTK. Regular teams with red and yellow against blue and green would be imbalanced; red and yellow would have a substantial advantage. We can only play it on the 4-Player Chess server right now, but once 4PC is integrated into variants, then alternative teams will be playable.

oh I see, it sounds fair and fun, it would help a lot to improve the level of the game if that mode is enabled here, and thanks for all the info I will definitely rethink some ideas.

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