### Vignette 25.1 TicTacToe (4) 6/3/77

Miriam wanted to play a few games of tic-tac-toe before going to bed this evening. After vignette 15’s instruction in the proper ordering of three rules,

1. Look for a way to win (complete a row of three)
2. Look for a way to lose (make all forced moves)
3. Look for two ways to win (fork your opponent)

I wanted to document how well or ill Miriam could absorb those notions. Thus the game was recorded (on the tape of Home Session 6) but not transcribed in detail.

Miriam moves first (her moves are letters, mine are numbers) in this game where I make the sure-to-lose response of a non-corner move after she takes the center square:

```	  C  |  1  |  2
---------------
D  |  A  |
---------------
B  |     |  3
```

Miriam recognized my second move and her ‘C’ as forced moves and knew she had two ways to win before my third move.

After my defeat, I move first in this tied game:

```	  B  |  4  |  5
---------------
3  |  1  |  C
---------------
A  |  D  |  2
```

Miriam asked if I were going to try my ‘good old trick’ (a corner opening); instead I took the center. She replied “Not usually” to my question of whether she ever moved ‘in these side places’ (as I had just been defeated doing). When I asked “How come?”, she simply said, “I don’t know.” Then she revealed her plan of going on both sides of my center move, and also a third corner, thereby getting two ways to win. Such is a terribly unrealistic plan as it neither recognizes the importance of being one move ahead of the opponent nor makes allowance for the opponent’s possible moves to block such a plan. I made move 2, telling Miriam I would not let her complete such a plan. She said, “Then I won’t do it. I’m thinking of something else.” She made her forced moves.

We had been taking turns drawing the grids in which our games were played out. I introduced the word frame to Miriam as a label for the grid with our third game.

 B I get to write the frame. I will call this the frame, O. K.? M Alright. B And that’s just the little tic-tac-toe thing but we will call it the frame. M Me first. B ‘Cause the frame tells us where to go and what to do.

Miriam begins with a corner move.

```	  3  |  C  | B
--------------
E  |  1  | 4
--------------
A  |  2  | D
```

After Miriam’s first two moves, I asked her advice. “Go anywhere.” She said then, “Oh, shucks, I’ve got a forced move,” and she followed all her forced moves appropriately. I requested her to draw the next from and she did so.

In game four, as I went first, I attempted the three corner strategy to see if Miriam was able to block it yet.

```	 3   |  C  |  2
---------------
4   |  B  |
---------------
1   |     |  A
```

After my move at 2:

 M Oh, no. B What did I do? M You’ve got some plan. B Does this look like a familiar plan? M Unh-uh. B Two ways to win [making move 3]. M [move C] B That was a nice gambit, Miriam. You really did good work there. That was a good idea: trying a different way to beat me.

This is interesting in showing an attempt to block the corner opening on the first move.

```	  3  |  C  |  B
---------------
E  |  2  |  4
---------------
A  |  1  |  D
```

Noting her last attempt at a non-center response to a corner opening and its failure, I moved 1. Her attempt to continue the three corner strategy failed with her forced move 'C' and its sequels. Miriam drew the next frame.

In game 6, I refer back to Miriam's earlier statement that she had a plan to get on both sides of a middle move. The center opening again:

```	  5  |  C  |  2
---------------
4  |  1  |  D
---------------
A  |  3  |  B
```

Since I have no forced move at 4, I discuss with Miriam whether I should put it in the corner (which can never win) or at the side (where I get 1 way to win). Miriam is happy to block it.

Miriam begins game seven with a center move.

```	 2   |  4  |  E
---------------
C   |  A  |  3
---------------
1   |  D  |  B
```

I note how every time I go on the side, I end up losing, so I move 1. When Miriam remarks she has no forced move D, I note it was like the game we just played. I ask Miriam where she can go to win and not win; can she tell the difference. She moves D.

I note how every time I go on the side, I end up losing, so I move 1. When Miriam remarks she has no forced move D, I note it was like the game we just played. I ask Miriam where she can go to win and not win; can she tell the difference. She moves D.

```	 C   |  B  |  4
---------------
D   |  1  |
---------------
A   |  2  |  3
```

Move 3 forces Miriam's C. I remark on having a forced move at 4. Miriam responds to a 'forced' move between 3 and 4. We both discover together that she has overlooked the A - C win. Miriam changes her move to D.

 B Oh well. You had two ways to win and didn't even know it. How did that happen? M I went here [I had a forced move 'B'] so I have a move here ['C'] also. Then I couldn't see that because I was trying to keep my eye on if you were going to win. B Hum. O. K.

In game 9, I request that we play the last game again because it was so tricky. Instead Miriam starts with a corner move.

```	 D  |     |  1
---------------
|  B  |  2
---------------
A  |  3  |  C
```

I play out this game in such a way as to duplicate the lesson, though not the form, of the last game. By move 2, Miriam is forced to move 'C' which also gives her two ways to win.

We stopped playing as it was near bedtime, and Miriam wanted to show Gretchen the videotape of the plays she and Meg had made at Logo today (Logo Session 19).

RELEVANCE
One clear conclusion is that Miriam now subordinates her strategy of finding two ways to win to that of making all forced moves. Game 8 shows an instance of her failing to make a winning move while responding to a forced move. I value game 4 for showing specifically how far advanced from its initial rigidity (cf. vignette 5) is her response to the three corner strategy employed by an opponent. Games 8 and 4 exhibit for Miriam how one can be forced into a series of moves that forks the opponent.

The word frame is introduced to Miriam to name the grid upon which the game is played. The idea is that it is a structure with implications for action.