The winning opening and variants of Connect6

Just discovered here. About opening for Connect6, it's strange that nobody has been doing this part of the work, so I finished it. In fact, the vast majority of White 2 has already been ended.

Joseki: https://1drv.ms/u/s!AsM50c0N2CKHgVf4cz3j5oSrilGo
(open with Connect6Lib: http://www.connect6.org/Connect6Lib.zip)

====================

About variants of Connect6:

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“Noncollinear Connect5”

The rules are the same as in Connect6 with two differences:

1. It is necessary to place FIVE or more pieces in a solid row vertically, horizontally or diagonally.

2. It is prohibited for each players during the same move to put both pieces at the same line (vertical, horizontal or diagonal).

https://brainking.com/en/Profile?u=37872

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“Collinear Connect6”

There are two additional rules on Connect6:

1. Each player places the two pieces on the same line (- | \ /) in the same move.

2. Each player places one of the two pieces on the same line as one of the two pieces from the opponent's previous move.

(This is a new variant rule that I invented last year, and other players have responded well after trying it out.)

Here are some matches:

https://trmph.com/connect6/board#19,j10j8l10k9l8n6h12h9k12i9k7i10j11l13f7l6h10g11f10j14k13l12j12l9l7l4m5m8k10k11k3k8j9e9d8c7i13o7p8

https://trmph.com/connect6/board#19,j10g7f8h10i10e9d10c11h6l10f10g11i9f9f12f11e11d11d9i11i8i7i13j8j11h11j9k9l8b9f5f6c9c10e10e15h12

https://trmph.com/connect6/board#19,j10i9j8i10h10f10l10k9k8k7l8l6j6k6l7j5k5m7i7j7l9i6i5i4j4j2h4i3m3h2h6h11h12h9h5h3h8h13g12g13g3f3f14l3l4l5j3n7n4m4m8n8n9n6n2n11p9p4p1o2o5i2g2f2l2f11f15f12n12

https://trmph.com/connect6/board#19,j10i9k9h9h10i10h11i8k8j8j7h6f8g9g7g6f6j6j9h8e8g8h7f7e6k7g11g10f11d13d6d9c8b11h5f3a8a18e14a10a6l6l7i7b7

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“Toroidal Connect6”

Like Toroidal Go (https://docs.littlegolem.net/games/go19/),
but use 15x15 board (13x13 draw 17x17 win) and show 25x25.

(This variant can improve boring in the mid to late Connect6 match.)

matches: (richu333 vs me)

https://trmph.com/connect6/board#19,j10i9k8i10h10h9k10k9l8l9i11j7j11j9m7l13m12k12n11m10j15m13k14k15l15l16i15k16j17l17i3k3f9i14i16i13i17f10k5j4j3j5j14h16g15f14l5h14f16e17j12h15h13h12h17g13f13d13j13g14g12g10g16f15d15

https://trmph.com/connect6/board#19,j10i9k9j9i7j7k10k8h8g9l7h11i12g10g12g11i13j11h9i8g8f8l8l9f9f10e10d10e11f11i15d9c9e7d6c5h10c7q8q9p9e9o9d7e6c8p8e8o8q6e12d13p5q7n10m11c6q5h13i14q4m9k7j6o11n8n7o7f12h14n9n11n6q11d12o12p13m10p10o10m7c15f4e5o14o13k14k11n15q12p11l4k3m5k5m16l17

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It's a shame that the administrator doesn't activate another variant of Connect6. I've asked him a few times for a bigger board.

I also asked the administrator to add Noncollinear Connect5 last year, and his response was “It looks interesting. I'll add it to LittleGolem. But I don't know exactly when. ”.

Actually, those variants can be played directly on the Connect6 board as long as the players agree on the rules. For Toroidal Connect6, the location can be mapped using Excel. I have created a VBA version that can be used for analysis. (ToroidalBoard)

==========

However, about the size of Connect6 board, 19x19 is perfect. For a bigger board of 21x21 and above, black is likely to sure win. You can download the Joseki on the top floor link. I have already completed the proof of black winning except for the six openings.

These six White 2 openings:
I9K8 is almost close to Black win;
J9L11/J9K10/J9K11 is a big advantage and is likely to win in theory;
I9K9 is an advantage, but it is uncertain whether it is a win or a draw in theory;
I9L10 is very fair, theoretically it should be a draw;
but I9L10 on the 21x21 board, there is a way to play that happens to be on the edge of the board with an extra line of space to win.

Therefore, for a board of 21x21 or more, the advantage of black is too great to include switch rules in order to ensure fairness. This is also the reason why Toroidal Connect6 require a 15x15 board.

Thanks for doing this work.

I believe you've missed a critical opening, one that I found some success with playing in the last two years. Please try working out j7g10 (https://trmph.com/connect6/board#19,j10j7g10). I discovered that it can confuse experienced players and gets white on the offensive immediately. I suspect there is some easy workaround as black, but I haven't actually been able to find it.

Is the link on the top floor invalid?
Try this: https://drive.google.com/drive/folders/1XIq-LEkugHwST3KfsiLQ11Dc-vDqhzK2

@metzgerism :

Yes, you are very careful.
I did intentionally omit a few useful openings, such as 2.I8J7. Its black 3 is easy to make mistakes, only at 3.K11L10 is it easier to win. Others are more difficult, you can refer to this match: https://trmph.com/connect6/game/lg-2097432.
The reason for omitting is because these openings already have same shape, such as @2.H9I8 in Joseki.

These two are only different in order.
https://trmph.com/connect6/board#19,j10h9i8k11j12j8k8l10m9n8i13l9l8j7g10f11k6
https://trmph.com/connect6/board#19,j10g10j7k11j12h9i8k6f11j8k8l10m9n8i13l9l8

На самом деле, слишком велико преимущество черных, есть только один дебют за белых, хоть , как то дающий возможность продолжать борьбу, и это печально. Надо менять правила и начинать ходить не из центра, или , по аналогии с гомоку, применять правила swap2

实际上，对于bot只有一种白2.I9L10开局，但对于人类，诸如I9K9/J9K11开局黑棋仅有较小优势，因为人类的计算力不足以完美下出如此复杂的优势局面。而且对于唯一的白2，bot可能有10+种黑3公平开局，而人类至少能有30+种黑3开局可选。因此把黑3当成真正的开局起始就行了，这样虽然黑棋有主动权，但并不具有明显优势。

但尽管如此，开局丰富性不足的问题依然存在，黑3并不容易选择不熟悉的开局，即使开放黑1，黑方同样也会主动选择中央。我的建议是在中央9*9区域随机黑1位置来开局，这种形式更简单也更符合LittleGolem。用gomoku的swap2规则不但失去了connect6原有规则的简洁，而且会扩大提前研究古怪开局带来的巨大优势，如果真的需要专业比赛规则，renju的RIF规则可能更合适（类似黑1在中央，白2在中央5*5区域，黑3可以被交换）。

不过当前更紧要的问题是connect6也逐渐有人用软件下棋了，这样不仅对人类棋手而言很没意思，而且也不能有效提高棋手的棋力。因为相对于Go，gomoku和connect6是更注重逻辑计算的棋种。我制作必胜定式谱的时候，完成大部分开局甚至都还没接触到AI软件，仅依靠这种纯粹的进攻和防守训练，我已经能战胜大部分选手了。因此我才把定式谱拿来分享，目的是有助于新手作为攻杀练习，这些多数是符合人类思维的下法，而不是仅仅依靠AI直觉。

当然如果是完全不想接触bot，那么还可以试试变体，像toroidal connect6就是一种很好的替代版本，或许可以通过开设User tournament来进行。

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Translated:

Actually, for bot, there is only one White 2.I9L10 opening, but for humans, like the opening I9K9/J9K11 only gives a slight advantage because human computational power isn't sufficient to perfectly play out such complex advantageous positions. Additionally, for the lone White 2, bot might have 10+ fair Black 3 openings, whereas humans could have at least 30+ Black 3 openings to choose from. So it's enough to treat Black 3 as a real opening start, so that although Black has the initiative, it doesn't have a significant advantage.

Nonetheless, the issue of limited opening diversity still exists. Choosing an unfamiliar opening for Black 3 isn't easy. Even if Black 1 is opened up, Black would still likely choose the center. My suggestion is to randomly choose the Black 1 position in the central 9x9 area to start, which is simpler and more in line with LittleGolem. Using gomoku's swap2 rule not only loses the simplicity of the original connect6 rules but also amplifies the huge advantage brought by pre-studying unusual openings. If professional competition rules are really needed, renju's RIF rules might be more suitable (similar to Black 1 in the center, White 2 in the center 5x5 area, Black 3 can be swapped).

However, the more pressing issue currently is that people are gradually using program to play connect6. This is not only uninteresting for human players but also doesn't effectively improve their skills because compared to Go, gomoku and connect6 are more logic-based games. When I made the winning opening joseki, I had completed most of the openings before I even encountered the AI program, and I was able to beat most of the players just by this purely offensive and defensive training. Therefore, I shared the joseki to help beginners practice attacking and killing moves, most of which are in line with human thinking rather than relying solely on AI intuition.

Of course, if one completely wants to avoid bots, they can try variants. Toroidal connect6 is a good alternative version. Perhaps it can be conducted through a User tournament.

@Anatolij

Hi,my friend Anatoli! Nice to see you here!

I totally agreed with you. For center opening, black is way too better.

If we play connect 6 like swap_1 or swap_2 in gomoku, its must be very interesting!

Maybe someday this kind of new rule will introduce here.

:D

:). Я тебя так же приветствую !

@Andrew_Marshall

You mean this way? https://www.littlegolem.net/jsp/game/game.jsp?gid=2442302
It's indeed quite possible. Looking forward to you ending it.

And yet, by the time you want to play on your own, you can't even execute such a simple winning move. It's indeed called too better.
https://www.littlegolem.net/jsp/game/game.jsp?gid=2440573&nmove=6

Yeah I mess up in some easy position lol.

Its seems that the strategy of connect 6 has a lot of different compare to gomoku.

i'm still trying to figure it out!

No, it means that AI can't effectively help beginners actually improve their skills, and AI's balance can't be applied to humans.

Yeah, This game is very logistical. Let's play and enjoy it!

Thanks for this, very interesting!
Is this you feel also playing with other top-level players or it's just AI calculated? Are there some statistics from LG at different Elo levels maybe?
What I mean is that it could still be theoretically a win (and very likely it is), but maybe it's still fun to play for humans without need to adding swap or other protocols. Are there papers about this? I thought there were some AI tournaments going on for some time.
Thanks for any info!

@Frasco

At first, I was able to solve about 60% of the openings in Connect6 using human brainpower. Later on, @Azusa informed me of several possible key moves, which allowed me to solve about 20% of the stronger openings. At last, with the help of a strong AI, I managed to handle the most challenging 10% of openings. The remaining 10% cannot be won through continuous direct attacks, so I relied on the AI's win rate to determine the advantage. Until recently, with the assistance of human brains in selecting moves for the AI, I found the solution to the only defensive move, White 2, that the AI considered balanced. This finally allowed the black player to enter a phase where theoretical victory is possible.

From this, it can be seen that relying solely on human thinking and some opening experience can give Black a significant advantage in most openings. Personally, I believe that only 6 openings are playable at the highest level of human play, and it is difficult for anyone playing as White to win against me in any other opening. As for the advantageous moves played by the AI, there are at least three types of openings that are almost impossible for humans to master, so even though there may be theoretical advantages, the practical difference is limited. I have examined many Connect6 platforms, and LG has the highest average skill level. However, even in the current highest-level tournaments (unfortunately, the strongest players have almost all retired), most players still haven't mastered powerful attacking techniques (possibly due to insufficient calculation time), which leads to them quickly missing opportunities and returning from an advantageous position to a balanced one (there is a window of opportunity for a quick wins in the opening phase of Connect6).

This is the main reason for the different determination of advantages between AI and humans. Taking the opening as an example, in White 2.J9K10, human experts usually prefer Black 3.I8L9. This is a control configuration, aiming to allow White to break through the siege. If theoretically White has no good breakthrough method, then the calculation pressure is often on White, making it easier for Black to complete the blockade and thus gain an advantage. However, AI suggests Black 3.I8H8, which is a strong attacking configuration (since I am very good at attacking, I naturally liked to choose this even before knowing about AI). It requires continuous offensive pressure, with a substantial amount of computation involved, which also means that the potential for mistakes increases. Therefore, if one's ability is not at a certain level, this theoretical advantage may actually turn into a disadvantage. The same situation applies to the White 2.J9L11. Black 3.I10K10 and 3.K10L9 can both be close to a sure win theoretically, but the former is more of a mutual attack type that makes it easier for one side to win, while the latter is a defensive type that is more likely to prevent one side from creating opportunities. Humans often choose the latter. However, relying solely on the latter is insufficient to fully leverage the theoretical advantages present in all scenarios.

So in this situation, it is estimated that 90% of players still find it fun, and fairness is not a serious issue. Recently, I briefly studied Pente, and without understanding the opening at all, I defeated several high-level players on pente.org in my first tournament. I found that in Pente, without the swap rule, it is much easier to achieve a sure win compared to Connect6. But it doesn't significantly affect the participation of general players or create overwhelming advantages (overall Black win rate is around 60%, while top players have a win rate of about 90%). However, as time goes by, the issue of opening move diversity becomes more severe. This might not necessarily be caused by theoretical fairness but rather because lower-level players tend to learn openings from higher-level players instead of developing their own suitable openings. This can be seen when high-level players still manage to win against lower-level players despite using disadvantageous opening moves. General players do not use certain openings is not because they have mastered the advantages of those openings. Therefore, looking at the long-term changes in opening move diversity, the enjoyment might indeed decrease with the development of theoretical advantages. However, for those who are not too concerned about the enjoyment of the opening moves, the mid-game variations are rich enough, which is much better compared to Pente and Gomoku.

I remember promising someone to introduce a new variant.
This variant belongs to a completely new category, similar to random, hidden, and simultaneous categories. I call it the Fair Pace category. Unlike traditional board games, it emphasizes both spatial relationships and time sequences. In this variant, the number of moves each player can make in a round is not fixed and follows a specific rhythm. Pace Connect6 is an excellent representative of this category, and its principles and practical tests indicate that it is essentially the ultimate form of N-in-a-row games. It has the highest level of fairness and simplicity, and at the same time has a level of complexity higher than Connect6 (which may be a shortcoming in modern times, similar to Go). The unique rhythm of offense and defense makes it highly enjoyable for me at least.

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Pace Connect6 ( Thue-Morse Connect6 )

[ Introduction ]

Play Connect6 with alternating order of Thue-Morse sequence
The original ABBAABB... sequence becomes ABBABAAB...
The original 1222222... pace becomes 12112221...
The original 2 pieces per move becomes an average of 1.5 pieces per move
The original 19x19 board becomes 25x25+ board or 19x19 toroidal board
( Optional: In case of a draw, the one with more 5-in-a-row wins )

https://youtu.be/prh72BLNjIk ( The Fairest Sharing Sequence )
https://en.wikipedia.org/wiki/Thue-Morse_sequence#Equitable_sequencing
https://oeis.org/A010060
https://oeis.org/A026465

[ Pace Sequence ]

1 → 121
2 → 12221

1
121
121 12221 121
121 12221 121 121 12221 12221 12221 121 121 12221 121

0000000001111111111222222222233333333334444
1234567890123456789012345678901234567890123
1211222112112112221122211222112112112221121... (43/64)

A → AA•AA
1•1 → 2

1
1 1•1 1 = 121
121 121•121 121 = 12112221121
12112221121 12112221121•12112221121 12112221121

1211222112112112221122211222112112112221121
121122211211211222112221122211211211222112
2211222112112112221122211222112112112221121
1211222112112112221122211222112112112221121... (171/256)

[ Attack Pattern ]

Winning Sequence { Current Pattern } → { Target Pattern }

( Example )
211 { 3" } → 11 { 5 } → 1 { 5' } → { 6 } :
x-ooo → x-ooooo → x-ooooox → xoooooox

211 { 3" } → { 5 } ( Unique method )
112 { 3 / 4'3' } → { 4 / 4'4' } ( Gomoku method )
222 { 3•2' / 3'•2 / 3'•3'3' } → { 44' / 4'4'4' } ( Connect6 method )

(Format issue, details here )

[ Research ]

Thue-Morse Connect6 = Connect(∞, ∞, 6, 1.5, 1)

In Connect(m, n, k, p, q),
two players alternately place p stones on an m × n board in each turn,
except that the first player places q stones for their first move.
The player who first gets k consecutive stones of their own wins.

Connect(11, 11, 5, 1, 1) the first player wins
Connect(∞, ∞, 6, 1, 1) the game is likely a draw
Connect(17, 17, 6, 2, 1) the game is likely a draw
Connect(19, 19, 6, 2, 1) the first player advantage
Connect(21, 21, 6, 2, 1) the first player likely wins
Connect(∞, ∞, 6, 2, 1) ≈ Connect(∞, ∞, 6, 2, 2) wins

Connect(∞, ∞, 6, 1.5, 1) draw?
Connect(∞, ∞, 6, 1.5, 2) win?

This is likely the most challenging
"A game that can maintain balance on an infinite board but still easily determine a winner"
(Similar to a harmonic series diverging but very close to converging)

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The following are some game examples. It can be seen that the offensive is quite fierce. Figure 1 shows the winning method attempt when there is a difference of one piece or a distance at the opening; Figure 2 is a general game, and it may win in the 10th move, but it can be seen that the winning method is much more difficult than Connect6.

https://trmph.com/connect6/board#19,j10i7k7j11a1j8b1i11k11g11m11l10h10j12c1h12d1k9h6h8e1g5f1f4i9g7g1i10h1k10l12h9h11h13h7g8i1f7j1k12l13
https://trmph.com/connect6/board#19,j10i7k7j11a1j8b1i11k11h11j7l7l8h10c1l6d1l9h12i9e1h8f1h9i10g8g1k9h1m7g9k12l13m14i8l11i1n11j1f8i14i13m10k10k13k8k1k14l1
https://trmph.com/connect6/board#19,j10j9k10k9a1i11b1j8i8h8i7j6l8k7c1j7d1g9h10h9e1g10f1g11f8f10g1e11h1i10i12i14e10h11k8k6i1l5j1m6g12j13k14l15f9k13k1l14l1j11k11l11k15h13g14l9m1f15n1
https://trmph.com/connect6/board#19,j10j9k10k9a1i11b1i8j8i7h8j6l8k7c1j7d1g9h10f8e1f10f1e11h9g10g1k6h1l5g11g8i10j11m8l9i1k13j1j12n6m7m6m9l10k11k1h11l1m11j14l11l12l13l7h12m1k12n1k14n7h13o1j13p1m5n5i12q1l15r1k8m4m14m10n15k5g12s1g13a19e10d10c10b19f11c19c8i14m13d19m12e19n13o12p11k16o13p13

Maybe you can try manual battles here. https://designer.abstractplay.com

Link display issue...

https://youtu.be/prh72BLNjIk ( The Fairest Sharing Sequence )
https://en.wikipedia.org/wiki/Thue-Morse_sequence#Equitable_sequencing
https://oeis.org/A026465

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https://trmph.com/connect6/board#19,j10i7k7j11a1j8b1i11k11g11m11l10h10j12c1h12d1k9h6h8e1g5f1f4i9g7g1i10h1k10l12h9h11h13h7g8i1f7j1k12l13

https://trmph.com/connect6/board#19,j10i7k7j11a1j8b1i11k11h11j7l7l8h10c1l6d1l9h12i9e1h8f1h9i10g8g1k9h1m7g9k12l13m14i8l11i1n11j1f8i14i13m10k10k13k8k1k14l1

https://trmph.com/connect6/board#19,j10j9k10k9a1i11b1j8i8h8i7j6l8k7c1j7d1g9h10h9e1g10f1g11f8f10g1e11h1i10i12i14e10h11k8k6i1l5j1m6g12j13k14l15f9k13k1l14l1j11k11l11k15h13g14l9m1f15n1

https://trmph.com/connect6/board#19,j10j9k10k9a1i11b1i8j8i7h8j6l8k7c1j7d1g9h10f8e1f10f1e11h9g10g1k6h1l5g11g8i10j11m8l9i1k13j1j12n6m7m6m9l10k11k1h11l1m11j14l11l12l13l7h12m1k12n1k14n7h13o1j13p1m5n5i12q1l15r1k8m4m14m10n15k5g12s1g13a19e10d10c10b19f11c19c8i14m13d19m12e19n13o12p11k16o13p13