Six Stone Chess

The Game Room
1

I recently learned this game. The Chinese name is 六子棋 (liu-zi-qi) which is, unfortunately, also the Chinese name for Connect6. I couldn’t find any online rules, so here’s my translation of the rules that came with the app.

Board: Square board, size is 3 units, giving a board of 4 points by 4 points. The points are connected orthogonally (horizontally and vertically). There are no diagonal connections. For convenience, the boards coordinates will be as follows:

A4 B4 C4 D4
A3 B3 C3 D3
A2 B2 C2 D2
A1 B1 C1 D1

Players: Two. One is termed White, the other Black.

Pieces: Each player begins the game with six stones of their color. The stones are placed as indicated below. White’s pieces begin on the following points: A1, B1, C1, D1, A2, and D2. Black’s pieces begin on: A4, B4, C4, D4, A3, and D3.

Goal: (a) Capture all but one of the opponent’s stones, or (b) block the opponent’s stones so that there is no move available.

Movement: White begins the game and turns alternate. There is no passing. When it is a player’s turn, they must move only one stone orthogonally exactly one point distant from the stone’s current position. There is no diagonal movement and no jumping of either color stones.

Capture: This is done by cooperative capture as follows. Remember that the lines on the boards extend for a total of four points. If, at the end of a player’s move, one point on the line is unoccupied, two adjacent points on the line have the player’s stone, and the remaining point has the opponent’s stone, then the opponent’s stone is captured. Example: There is a white stone on A4, a black stone on A3, a black stone on B2, and A1 is unoccupied. Black moves his stone from B2 to A2, thus capturing the white stone on A4.

I believe that covers all of it. So, what’s the best strategy? It’s a very small board, so I’m guessing it can’t be too hard for the game theorists among us to determine if it’s a solved game and what the solution is.

2

Without doing any analysis, the fact that the opening position is symmetrical and that pieces only move short distances must mean that with perfect play either:

-White has a forced win

  • Black has a forced win
  • it’s a draw

I reckon draw is the most likely.

3

The fact that the opening position is symmetrical and pieces only move a short distance are irrelevant to the conclusion that either one side can force a win or that either side can force a draw.

Can a player self-capture? For instance, if white starts by moving the piece on D2 to C2, that would create a situation where D column would have two adjacent black stones, an empty point, and a white stone. Would that result in the capture of the white stone on D1?

4

There is no self-capture.

5

OK, then what if the opponent makes a move that doesn’t change that capture situation? Is the white piece captured then? Is it possible to make a move that results in multiple captures?

Do you have a link to the app? Playing around with it a bit might make it easier to understand the details.

6

Sounds a lot like Nine Men’s Morris.

7

Yes, you can capture two stones at one time. I don’t see how it would be possible to capture more. But, to capture two stones, each of the opponent’s stones must be the sole opposing stone on the line into which you move your stone. Example:

The game is down to two stones for White and three stones for Black. White stones are on B4 and D3, Black has stones on A3, B2, and C3. Black moves the stone on C3 to B3, thus capturing the white stone on B4 and the white stone on D3, winning the game.

Here is a link to the app on Apple’s App store. I believe you have to change your region to mainland China for this, but maybe not.

I guess there’s some similarity to Nine Men’s Morris, but in this game, the pieces are all already on the board. In Nine Men’s Morris, you take turns introducing your pieces onto the board.

8

After messing around with it some, playing both what I considered the best moves and what I considered incredibly bad moves on my part, with me playing white while the computer played black and also playing against a friend with us switching colors after each game, here’s what I figure is the real result of the game:

Move White Black
1 D2C2 C4C3
2 A2B2 B4C4
3 B2B3 A4B4
4 B1B2+B4 A3A2
5 B3B4 C3B3
6 C2C3 B3A3+A1
7 C1C2+A2C4 D4C4
8 C2D2+D3 C4D4
9 B2/B4B3+A3 LOST

Explanation of notation: Grid coordinates are given as in an earlier post. Piece’s orginial coordinates given first followed by ending coordinate. A plus sign indicates capture. A forwward slash indicates a choice of originating piece for that move. If there are four characters after a plus sign, that indicates two pieces were captured on that move.

So, ISTM that the game is solved as a win for white. That’s for a four by four board. I’m wondering how it would be for a larger board and at what point in the expansion the required line-up of stones to capture would be more than two.