Fuseki (game)

How to b fails  

Most likely optimality rankings for square boards

1. 4x4 - optimal 2; 2nd 1, 3
2. 5x5 - optimal 2, 3; 2nd 1, 4
3. 6x6 - optimal 3; 2nd 2, 4; 3rd 1, 5
4. 7x7 - optimal 3, 4; 2nd 2, 5; 3rd 1, 6
5. 8x8 - optimal 4; 2nd 3, 5; 3rd 2, 6; 4th 1, 7
6. 9x9 - optimal 4, 5; 2nd 3, 6; 3rd 2, 7; 4th 1, 8
7. 10x10 - optimal 5; 2nd 4, 6; 3rd 2, 7; 4th 2, 8; 5th 1, 9
8. 11x11 - optimal 5, 6; 2nd 4, 7; 3rd 3, 8; 4th 2, 9; 5th 1, 10
9. 12x12 - optimal 6; 2nd 5, 7; 3rd 4, 8; 4th 3, 9; 5th 2, 10; 6th 1, 11
10. 13x13 - optimal 6, 7; 2nd 5, 8; 3rd 4, 9; 4th 3, 10; 5th 2, 11; 6th 1, 12
11. 14x14 - optimal 7; 2nd 6, 8; 3rd 5, 9; 4th 4, 10; …; 7th 1, 13
12. 15x15 - optimal 7, 8; 2nd 6, 9; 3rd 5, 10; 4th 4, 11; …; 7th 1, 14
13. 16x16 - optimal 8; 2nd 7, 9; 3rd 6, 10; 4th 5, 11; …; 8th 1, 15
14. 17x17 - optimal 8, 9; 2nd 7, 10; 3rd 6, 11; 4th 5, 12; …; 8th 1, 16
15. 18x18 - optimal 9; 2nd 8, 10; 3rd 7, 11; 4th 6, 12; 5th 5,13; …; 9th 1, 17
16. 19x19 - optimal 9, 10; 2nd 8, 11; 3rd 7, 12; 4th 6, 13; …; 9th 1, 18
17. 20x20 - optimal 10; 2nd 9, 11; 3rd 8, 12; 4th 7, 13; 5th 6, 14; …; 10th 1, 19
18. 21x21 - optimal 10, 11; 2nd 9, 12; 3rd 8, 13; 4th 7, 14; …; 10th 1, 20
19. 22x22 - optimal 11; 2nd 10, 12; 3rd 9, 13; 4th 8, 14; 5th 7, 15; …; 11th 1, 21
20. 23x23 - optimal 11, 12; 2nd 10, 13; 3rd 9, 14; 4th 8, 15; 5th 7, 16; …; 11th 1, 22
21. 24x24 - optimal 12; 2nd 11, 13; 3rd 10, 14; 4th 9, 15; 5th 8, 16; …; 12th 1, 23
22. 25x25 - optimal 12, 13; 2nd 11, 14; 3rd 10, 15; 4th 9, 16; 5th 8, 17; …; 12th 1, 24
23. 26x26 - optimal 13; 2nd 12, 14; 3rd 11, 15; 4th 10, 16; 5th 9, 17; 6th 8, 18 …; 13th 1, 25
24. 27x27 - optimal 13, 14; 2nd 12, 15; 3rd 11, 16; 4th 10, 17; 5th 9, 18; …; 13th 1, 26
25. 28x28 - optimal 14; 2nd 13, 15; 3rd 12, 16; 4th 11, 17; 5th 10, 18; 6th 9, 19; …; 14th 1, 27
26. 29x29 - optimal 14, 15; 2nd 13, 16; 3rd 12, 17; 4th 11, 18; 5th 10, 19; 6th 9, 20; …; 14th 1, 28
27. 30x30 - optimal 15; 2nd 14, 16; 3rd 13, 17; 4th 12, 18; 5th 11, 19; 6th 10, 20; …; 15th 1, 29

Special Tactics 1a and 1b : Dango and Empty Triangles

Contrary to Go, dango and empty triangles are not so bad shape in the movement phase of Fuseki due to the de-emphasis of eyes. Dango are always defensive. However, the necessary intermediate step of empty triangles creates linear attacks to the opposite side of the empty triangle.

Dango and empty triangles example

Special Tactic 2 : Attacking From Underneath (Undermining)

Inspired by Go, a chain may be attacked from underneath, on the axis where a stone is already above, by moving another stone along this axis towards this stone. This will capture the stone immediately adjacent to the newly occupied intersection along this axis. A chain attacked orthogonally must be sandwiched along the opposite axis for a capture to occur.

Attack from underneath example

Special Tactic 3: Push Through

Friendly stones may push each other through opposing stones to crush them against the edge or corner of the board or a third friendly stone. In this case, horizontals and verticals only matter when they are the route of attack. Any number of opposing stones may be crushed in this way, but only the one at the far end of the chain is removed. Note: Two of three possible nominal push throughs to a corner can be called push throughs to an edge without loss of clarity.

Push through to third friendly stone

Special Strategy 1: Wedge

Inspired by the basic instinct of connecting against a peep, the counterintuitive looking wedge allows friendly stones to push each other through perpendicular to an opposing jump or push opposing stones through perpendicular to a friendly jump. Being like the push through, the wedge may use the edge or corner of the board to capture stones.

Wedge perpendicular to friendly jump

Special Strategy 2: Cross-Cut

If the cross-cut looks as counterintuitive as the wedge, there is a good reason for this appearance: It is more obliquely explained as a wedge perpendicular to a kosumi. The exceptional nature of the cross-cut is the moving stone can be pushing itself through to capture the opposing stones. Due to the exceptional nature of the cross-cut, a player must capture every opposing stone to win by capture.

Single-Handed Cross-Cut  

Postscript

The next two links progressively remove the off-axis stones from the requirements for capturing orthogonally. They also cease to enforce captures made during placement, instead removing them after the last placement if at all. Interestingly enough, optimal Go play on a 5x5 board is proven to lead to a (nearly) balanced number of and at endgame with prisoners taken only once for each side for at least the off-center openings input into Erik van der Werf's MIGOS program and no proven solution nor current best guess gives a ratio of : more than one stone worse than 2:1 (6x6 yields 17 v. 12 or 14 v. 13 for Black and strangely 7*7 appears to yield an ideal endgame distribution with less than 17 on either side). Seega gives “Black” and “White” matching numbers of ‘’kelb’’ to set up as they please. Petteia basically removes the incomplete line of soldiers from this game. From the undermining tactic, it is now a simple step of removing the requirement of the opposite friendly stone to the approach capture of Fanorona.