Support ChatGPT

[calcitem]

1.    d6    d2
 2.    f4    b4
 3.    f6    f2
 4.    b6xf2    f2
 5.    b2    c5
 6.    c4    e5
 7.    d5    d7
 8.    g4    e4
 9.    e3    g1
10.    e3-d3    e4-e3
11.    c4-c3    c5-c4
12.    f4-e4    f2-f4
13.    d5-c5    e5-d5
14.    e4-e5    e3-e4
15.    d3-e3    g1-d1
16.    g4-g7    d1-a1
17.    c3-d3    a1-a4xg7
18.    d3-c3    d2-d3
19.    b2-d2    a4-a1
20.    d2-b2    a1-a4xb2

You are a Nine Men's Morris engine playing a Nine Men's Morris match against the user and trying to win.

The phase is placing phase.

white has 2 piece on board and 7 pieces in hand.

black has 1 piece on board and 8 pieces in hand.

Now black to move. No opponent's piece(s) need to remove.

The current board is:

  a b c d e f g
7 * --- * --- * 7
  |     |     |
6 | * - @ - * | 6
  | |   |   | | 
5 | | *-o-* | | 5
4 *-*-*   *-o-* 4
3 | | *-*-* | | 3
  | |   |   | | 
2 | * - * - * | 2
  |     |     | 
1 * --- * --- * 1
  a b c d e f g

In this board, "*" represents an empty position, "O" represents a white piece, "@" represents a black piece, and "-" and "|" represent lines on the board. The coordinates on this board start at a1 in the lower left corner and end at g7 in the upper right corner.

Pick a move from the legal moves that maximizes your chance of winning and provide an explanation of why you picked in the following example format. Even if you think you can't win still pick a valid move.

Print the new board after you make move.

[calcitem]

You are a Nine Men's Morris engine playing a Nine Men's Morris match against the user and trying to win.

The phase is placing phase.

white has 2 piece on board and 7 pieces in hand.

black has 1 piece on board and 8 pieces in hand.

Now black to move. No opponent's piece(s) need to remove.

The current board is:

  a b c d e f g
7 * --- * --- * 7
  |     |     |
6 | * - @ - * | 6
  | |   |   | | 
5 | | *-o-* | | 5
4 *-*-*   *-o-* 4
3 | | *-*-* | | 3
  | |   |   | | 
2 | * - * - * | 2
  |     |     | 
1 * --- * --- * 1
  a b c d e f g

In this board, "*" represents an empty position and no piece on it, "O" represents a white piece, "@" represents a black piece, and "-" and "|" represent lines on the board. The coordinates on this board start at a1 in the lower left corner and end at g7 in the upper right corner.

There are no empty points on these coordinates, so please never place pieces on these locations: b1/c1/e1/f1/a2/c2/e2/g2/d4/a5/b5/f5/g5/a6/c6/e6/g6/b7/c7/e7/f7

Pick a move from the legal moves that maximizes your chance of winning. Even if you think you can't win still pick a valid move.

Just give your move only and do not say more.

[calcitem]

Hard.

[calcitem]

Nine Men's Morris 棋盘上有24个点：

Point	方位	相邻点数量 (相邻点越多价值越大)
a7	外圈，左上角	2
d7	外圈，上方	3
g7	外圈，右上角	2
g4	外圈，右方	3
g1	外圈，右下角	2
d1	外圈，下方	3
a1	外圈，左下角	2
a4	外圈，左方	3
b6	中圈，左上角	2
d6	中圈，上方	4
f6	中圈，右上角	2
f4	中圈，右中	4
f2	中圈，右下角	2
d2	中圈，下方	4
b2	中圈，左下角	2
b4	中圈，左中	4
c5	内圈，左上角	2
d5	内圈，上方	3
e5	内圈，右上角	2
e4	内圈，右方	3
e3	内圈，右下角	2
d3	内圈，下方	3
c3	内圈，左下角	2
c4	内圈，左方	3

以下是各个 Point 之间的关系表：

---

邻接关系

Point	Adjacent 1	Adjacent 2	Adjacent 3	Adjacent 4
d5	d6	e5	c5
e5	e4	d5
e4	f4	e3	e5
e3	d3	e4
d3	d2	c3	e3
c3	c4	d3
c4	b4	c5	c3
c5	d5	c4
d6	d5	d7	f6	b6
f6	f4	d6
f4	e4	g4	f2	f6
f2	d2	f4
d2	d3	d1	b2	f2
b2	b4	d2
b4	c4	a4	b6	b2
b6	d6	b4
d7	d6	g7	a7
g7	g4	d7
g4	f4	g1	g7
g1	d1	g4
d1	d2	a1	g1
a1	a4	d1
a4	b4	a7	a1
a7	d7	a4

---

Mill 组合 （标明了 Point 可和哪些 Point 组成 Mill，Mill 就是三个棋子连成一条线）

Point	Mill Combo 1	Mill Combo 2	Mill Combo 3
d5	d6 – d7	e5 – c5
e5		c5 – d5	e4 – e3
e4	f4 – g4	e3 – e5
e3		e5 – e4	d3 – c3
d3	d2 – d1	c3 – e3
c3		e3 – d3	c4 – c5
c4	b4 – a4	c5 – c3
c5		c3 – c4	d5 – e5
d6	d5 – d7	f6 – b6
f6		b6 – d6	f4 – f2
f4	e4 – g4	f2 – f6
f2		f6 – f4	d2 – b2
d2	d3 – d1	b2 – f2
b2		f2 – d2	b4 – b6
b4	c4 – a4	b6 – b2
b6		b2 – b4	d6 – f6
d7	d5 – d6	g7 – a7
g7		a7 – d7	g4 – g1
g4	e4 – f4	g1 – g7
g1		g7 – g4	d1 – a1
d1	d3 – d2	a1 – g1
a1		g1 – d1	a4 – a7
a4	c4 – b4	a7 – a1
a7		a1 – a4	d7 – g7

---

横线

Point 1	Point 2	Point 3
a7	d7	g7
b6	d6	f6
c5	d5	e5
a4	b4	c4
e4	f4	g4
c3	d3	e3
b2	d2	f2
a1	d1	g1

---

竖线

Point 1	Point 2	Point 3
a7	a4	a1
b6	b4	b2
c5	c4	c3
d7	d6	d5
d3	d2	d1
e5	e4	e3
f6	f4	f2
g7	g4	g1

---

环（Ring）

Ring	1	2	3	4	5	6	7	8
Outer Ring	d7	g7	g4	g1	d1	a1	a4	a7
Middle Ring	d6	f6	f4	f2	d2	b2	b4	b6
Inner Ring	d5	e5	e4	e3	d3	c3	c4	c5

---

备注： d6、f4、d2、b4 为 Middle Ring 上的四个十字交叉点，位置最为重要。

请点评如下的 Nine Men's Morris Move List，在每一步棋后面通过 {} 添加注释，发表你自己的见解：

 1.    d6    d2
 2.    f4    b4
 3.    f6    f2
 4.    b6xf2    f2
 5.    b2    c5
 6.    c4    e5
 7.    d5    d7
 8.    g4    e4
 9.    e3    g1
10.    e3-d3    e4-e3
11.    c4-c3    c5-c4
12.    f4-e4    f2-f4
13.    d5-c5    e5-d5
14.    e4-e5    e3-e4
15.    d3-e3    g1-d1
16.    g4-g7    d1-a1
17.    c3-d3    a1-a4xg7
18.    d3-c3    d2-d3
19.    b2-d2    a4-a1
20.    d2-b2    a1-a4xb2

请直接输出修改后的 Move List

格式形如：

 1.    d6 {Blabla}   d2 {Blabla}
 2.    f4 {Blabla}   b4 {Blabla}

[calcitem]

Nine Men's Morris:

---

1. Points Overview

There are 24 positions, arranged on three rings (outer, middle, inner). Each point belongs to one ring and has a specific location:

• Outer Ring (8 points)

  • a7 (corner, 2 neighbors)
  • d7 (top edge, 3 neighbors)
  • g7 (corner, 2 neighbors)
  • g4 (right edge, 3 neighbors)
  • g1 (corner, 2 neighbors)
  • d1 (bottom edge, 3 neighbors)
  • a1 (corner, 2 neighbors)
  • a4 (left edge, 3 neighbors)

• Middle Ring (8 points)

  • b6 (corner, 2 neighbors)
  • d6 (top edge, 4 neighbors)
  • f6 (corner, 2 neighbors)
  • f4 (right edge, 4 neighbors)
  • f2 (corner, 2 neighbors)
  • d2 (bottom edge, 4 neighbors)
  • b2 (corner, 2 neighbors)
  • b4 (left edge, 4 neighbors)

• Inner Ring (8 points)

  • c5 (corner, 2 neighbors)
  • d5 (top edge, 3 neighbors)
  • e5 (corner, 2 neighbors)
  • e4 (right edge, 3 neighbors)
  • e3 (corner, 2 neighbors)
  • d3 (bottom edge, 3 neighbors)
  • c3 (corner, 2 neighbors)
  • c4 (left edge, 3 neighbors)

---

2. Adjacency (Who Connects to Whom)

Each point is connected directly to certain neighbors. Example notation:

d7 → d6, g7, a7

Use these lists to see legal single-step moves:

• Outer Ring

  • a7 → d7, a4
  • d7 → d6, g7, a7
  • g7 → g4, d7
  • g4 → f4, g1, g7
  • g1 → d1, g4
  • d1 → d2, a1, g1
  • a1 → a4, d1
  • a4 → b4, a7, a1

• Middle Ring

  • b6 → d6, b4
  • d6 → d5, d7, f6, b6
  • f6 → f4, d6
  • f4 → e4, g4, f2, f6
  • f2 → d2, f4
  • d2 → d3, d1, b2, f2
  • b2 → b4, d2
  • b4 → c4, a4, b6, b2

• Inner Ring

  • c5 → d5, c4
  • d5 → d6, e5, c5
  • e5 → e4, d5
  • e4 → f4, e3, e5
  • e3 → d3, e4
  • d3 → d2, c3, e3
  • c3 → c4, d3
  • c4 → b4, c5, c3

---

3. Mill Combinations (Sets of 3 in a Line)

A “mill” is formed when three pieces of the same color line up on these triplets.

• Inner Ring Mills

  • (c5, d5, e5)
  • (e5, e4, e3)
  • (c3, d3, e3)
  • (c5, c4, c3)

• Middle Ring Mills

  • (b6, d6, f6)
  • (f6, f4, f2)
  • (b2, d2, f2)
  • (b6, b4, b2)

• Outer Ring Mills

  • (a7, d7, g7)
  • (g7, g4, g1)
  • (a1, d1, g1)
  • (a7, a4, a1)

---

4. Key Lines

Horizontal Lines

1. (a7, d7, g7)
2. (b6, d6, f6)
3. (c5, d5, e5)
4. (a4, b4, c4)
5. (e4, f4, g4)
6. (c3, d3, e3)
7. (b2, d2, f2)
8. (a1, d1, g1)

Vertical Lines

1. (a7, a4, a1)
2. (b6, b4, b2)
3. (c5, c4, c3)
4. (d7, d6, d5)
5. (d3, d2, d1)
6. (e5, e4, e3)
7. (f6, f4, f2)
8. (g7, g4, g1)

---

5. Rings (Outer → Middle → Inner)

Points on each ring in a circular sequence:

• Outer Ring:
  d7 → g7 → g4 → g1 → d1 → a1 → a4 → a7 → (back to d7)

• Middle Ring:
  d6 → f6 → f4 → f2 → d2 → b2 → b4 → b6 → (back to d6)

• Inner Ring:
  d5 → e5 → e4 → e3 → d3 → c3 → c4 → c5 → (back to d5)

---

6. Important Cross Points

On the middle ring, these four intersections are most crucial:

• d6, f4, d2, b4

They connect diagonally or vertically/horizontally to many points, increasing strategic value.

---

7. Notes on Board Layout String

A typical boardLayout can be represented by three 8-character segments (one segment per ring), for example:

********/********/********

• First 8 chars: Inner Ring in order (d5, e5, e4, e3, d3, c3, c4, c5).
• Second 8 chars: Middle Ring (d6, f6, f4, f2, d2, b2, b4, b6).
• Third 8 chars: Outer Ring (d7, g7, g4, g1, d1, a1, a4, a7).

'*' = empty, 'O' = white piece, '@' = black piece, etc.

---

请点评如下的 Nine Men's Morris Move List，在每一步棋后面通过 {} 添加注释，发表你自己的见解, 注意先把原来的 {} 清空，然后再填写你自己的，注释全都是要表明意图：

1. d2 { side=white, type=place, boardLayout="/*O/", moveIndex=0, roundIndex=1, } d6 { side=black, type=place, boardLayout="/@O/", moveIndex=1, roundIndex=1, }
2. f4 { side=white, type=place, boardLayout="/@OO/", moveIndex=2, roundIndex=2, } b4 { side=black, type=place, boardLayout="/@OO*@*/***", moveIndex=3, roundIndex=2, }
3. f2 { side=white, type=place, boardLayout="/@OOO@*/", moveIndex=4, roundIndex=3, } g4 { side=black, type=place, boardLayout="*/@OOO@*/@", moveIndex=5, roundIndex=3, }
4. f6 { side=white, type=place, boardLayout="/@oooo*@*/@", moveIndex=6, roundIndex=4, } xd6 { side=white, type=remove, boardLayout="/OOOO@*/@", moveIndex=6, roundIndex=4, } b2 { side=black, type=place, boardLayout="*/OOOO@@/@", moveIndex=7, roundIndex=4, }
5. b6 { side=white, type=place, boardLayout="/*OOOO@@O/@", moveIndex=8, roundIndex=5, } d6 { side=black, type=place, boardLayout="/@oooo@@O/@", moveIndex=9, roundIndex=5, }

请直接输出修改后的 Move List

格式形如：

 1.    d6 {Blabla}   d2 {Blabla}
 2.    f4 {Blabla}   b4 {Blabla}

{Blabla} 的部分不要再出现 side type boardLayout 之类的标记了！