Balance

I let the TeamTerminator engine think on each starting position for about 8 hours.

For original setup:  eval is +2.59 for RY

For omatamix setup:  eval is +0.42 for RY

i think to decrease r/y opening advantage also good some 960 positions , for ex. if just to switch Q with queenside N

That's interesting. I ran the current position with my AI.

Current setup: 52% RY | 7 % Draw | 41% BG

That's the stats for the original start.

including the standard and omatamix setup, there are a total of 16 different starting positions with different king and queen places. has anyone tried to test the other 14 setups on the computer? it seems that even if swipe all the kings relative to the standard position, then the estimate will not be equivalent to the standard

Out of 16 setups, based on letting TeamTerminator analyze each one for 30 minutes, here is how they rank from most balanced to least balanced. Only 2 out of 16 were slightly favoring BG, and the rest favored RY. The engine thinks the standard 4PC setup is the least balanced out of all of them.

thank you, Tony! a very interesting result! can you please add specific estimates to the table so that it is clear how they relate to each other in more detail?

Added eval column, but it can be misleading. Recent versions of this engine tend to have more exaggerated evals. Its eval is tuned only to win more games, not to give better analysis. If we had a 3700 rating 4pc engine it might tell a different story.

in fact, it is interesting to understand what contributes to the assessment of the starting position and why exactly such a relationship between these 16 positions

here is an attempt to make a model which explain the results

what affects the rating in descending order:

1. move order. quite an obvious point, on average for 16 positions R/Y have an advantage of +1.88

2. the ability to play the king's pawn on 1st move. Terminator and top players use h3 or h4 opening for R/Y in a standard position. statistics also for the h3 move. in games with an omatamix setup, Terminator used this move for B/G, as the setup itself allows it. I think the situation is similar here as in 2pc with e4, which gives +0.5 for White, when other openings give an advantage less or closer to zero. most likely this is due to the fact that this is the only move that activates two pieces at once and creating threats

in the standard setup, only R and Y can play the king's pawn (conditionally, can assume that this is 2:0 in favor of R/Y). in the omatamix setup, this move can be made by everyone (2:2). in the setup that gives the highest score for B/G (3rd position), the king's pawn can be played by R, B, G (1:2 in favor of B/G). in model by default, it was considered that one cannot make a move with a king's pawn if the bishop or queen of the color that makes the move earlier can trade the bishop or queen, and then the move is made with the queen's pawn (also not always possible)

3. kingside R next to G or B. not too obvious point. if look at the position with the inverted standard (all the kings are changed relative to the standard position) and compare with the standard, then is the difference in +0.8. the only thing that has changed is that the R kingside is now next to B. perhaps this is due to the proximity of the R kingside, which can be quickly developed after the king's pawn move and faster connected to the attack, especially if the B or G kingside is nearby. but B has a one move head start in front of Y, i.e. B is better prepared to attack from R/Y than G, i.e. this in turn gives a small advantage to the B/G position. perhaps this rule is a consequence of something else, or it can be formulated differently, but in general it works or does not affect the position

this table is a continuation of the table in the comment above, here is the same order:

1st column shows the colors in which the king is inverted relative to the standard (a separate mark for pairs of inverted positions, where all 4 kings are inverted relative to each other). in 2nd column, the colors "possessing" the ability to play the king's pawn are marked, and the score is conditionally recorded. 3rd column shows the difference in estimates for inverted positions relative to non-inverted ones. 4th column of grades from the original table above, added for readability

now let's go directly to the results. the model explains them pretty well

point 1 explains the general prevalence of R/Y over B/G, as indicated above. if look at the omatamix setup (and its inversion), where points 2 and 3 should not affect the evaluation of positions, i.e. only the move order affects, then the advantage of the first move can be estimated at + 1.14

point 2 of the model explains the order of positions from the most favorable for B/G (3rd in the list) to the most favorable for R/Y (standard). as can see, this can either compensate for the advantage of 1 point, or strengthen it

the only exception that does not fit into the model is the most balanced position (1st in the list), which, according to 2 point, should be at the end of the list (approximately 13th). but I think this can be explained by the fact that the model did not consider sharp positions, where B/G is played with a king's pawn, despite the possibility of exchanging a queen or bishop on the 2nd move. it is possible that in the most balanced one there will be a tense 2:2 (not 2:0) with a slight advantage of B/G (additional analysis of the position is needed)

point 3 of the model explains the difference between pairs of positions inverted relative to each other. as can see, this is true for pairs of positions 2 and 3, 4 and 8, 15 and 16, does not affect for pairs 5 and 6, 9 and 10, 11 and 12, it is strongly noticeable for pairs 1 and 13 (in the 13th position, a similar sharp variant 2:2 as for the 1st ends with the loss of the queen for B/G), where the difference is increased by the influence of point 2. the only exception is pair 7 and 14, where the inverted position is less beneficial for B/G, but this is easily explained if take into account the prevailing influence of point 2 over 3

point 3 is actually more difficult. in positions 8, 13, and 16, it can be additionally noted that the R kingside  is close to the G kingside, and this geometry creates additional tension. although the 9th position with similar geometry does not differ much from the inverted one

can try to draw some conclusions, although in an amicable way, in order to draw them, for each position need a base of games commensurate with the one that is available for the standard

for Team, any of these positions will most likely be playable. the experience of tournaments shows that B/G can stand up for themselves quite well in the most unbalanced starting position. it is even possible to create a variant of 4pc 16 (as in 2pc 960), where one of 16 positions will be given randomly

it works harder for FFA. deficiencies in certain positions for certain colors can be exacerbated by passive cooperation with opp. statistics for the standard FFA position shows this. therefore, the best option should be symmetrical without discrimination of individual colors. if you use point 2, then the best and only options are the omatamix and the inverted omatamix setup

Wow, fascinating. Sadly, it does not seem to me chess.com implements any real changes to 4pc. So many suggestions have come about across different realms and nothing happens. 

Is this the most balanced position that is symmetrical? If so I suggest changing to this, for both teams and FFA (which plays like teams..)

there are 8 symmetrical positions in total, the 3 most balanced of them have fairly close estimates within 0.2 (this is a relatively small difference that can be neglected), it make sense to evaluate and compare these 3 positions separately with more time for analysis. also, if we want to have a single position for Team and FFA, then a balance must be observed between all colors separately

Well then please hurry up and make up your minds

I can provide 10 self-play games for each symmetrical position with Phoenix, will that help with your answer?

it would be coo!

Here is the stats phoenix thinks on each symmetrical position.

Similar to terminators estimates. I find the second one weird as its favoring BG.

I am at work, when I get home I’ll start running self-play games. Also the PGN’s I send might be invalid due to castling. Because castling does not work when the kings are switched.

Ok so top engines say that the current starting position is 2+ advantage for RY, meanwhile there are alternatives that reduce it quite a bit by simply swapping King and Queen square. What is holding back from implementing this clearly good change?
Perhaps a fundamental change to the starting position will just be confusing for the players as everyone is used to the way the game has been. Well, sure, but that's ok. 4PC is still very young, the player base isn't much and currently the game is at a point where there's lots of room for improvement. An argument that some drastic change might be cause for confusion and maybe the players won't take it so well, shouldn't pass. If there's a way to make the game better, do it

I think they are deciding which alternate symmetrical starting position is best. Swapping the blue and yellow king seems to be the best atm.

if we compare the analysis of Terminator and Phoenix, then the 3 most imbalanced symmetric positions coincide (I think they can be excluded from further analysis). also both think that switched RG position is the most favorable for B/G among symmetrical, perhaps it can be chosen

is it score for 10 games? can it be done for 100?

there is also a separate question for FFA. it would be nice to come up with some kind of criterion that can be pulled from the analysis for Team
for example, is it possible to separately see what color the checkmate gets more often in a particular position? for example, R/Y lose 3 out of 10 games in some position, in 2 out of these 3 get mated red, in 1 out of 3 get yellow