Vn71.1 Tic Tac Toe (7) 8/25/77

This material provides Miriam with an opportunity to exhibit what she retained of instruction in the previous tic-tac-toe session (cf. vignette 61, 8/10/77). Where Miriam fails to elect a winning strategy (game 3), I subsequently demonstrate how she should have played, then provide the opportunity for her to turn the tables on me. (These data were recorded in Home Session 17.)

Game 1: Miriam moves first (letters)

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

After my first move, I ask Miriam:

Bob

Can you beat me if I move here?
Miriam

I think so [moves B].
Bob

Oh ho. I’ve got a forced move. I bet you’ve got me already [moves 2]. Do you?
Miriam

[shaking head ‘yes’, smiles and moves C]
Bob

You do. You’ve got two ways to win already.
Miriam

[laughing] I did the forced move and two ways to win.
Bob

That’s absolutely perfect, Miriam. You got it.

Game 2: Bob moves first (numbers)

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

This dull game is of interest only in Miriam’s avoiding the middle of the row response to a center opening.

Games 3, 4, and 5 —

Game 3: Miriam first (letters) Game 4: Bob first (numbers)

	  
	 A | 4  | D 
	 1 |    | 4    
	 C | 2  | 1 

	 B | 3  | A    
	 3 | 5  | B	
         2 |    | C   

Upon my response (1) to Miriam’s corner opening, she had the opportunity to beat me directly and failed to do so. When she made her second move (B), I informed her of her oversight. She was angry and had to be cajoled to play game 4 with roles reversed. When she moved A in game 4, I review her move of game 3 (B) comparable to the one I then made (2).

Bob

You went down here, where the B is, next to the 1.
If you had gone over here, where my 2 is now —
Miriam

Yeah?
Bob

You could have beat me. You know why?
Miriam

Why?
Bob

‘Cause you’ve got a forced move between the 1 and 2.
Miriam

Oh [she move B].
Bob

Now, what chances to win do I have? From the 2 across
the bottom; from the 1 across the top; from the 1, down through the middle;
from the 2 up through the middle. And I have to go in the middle because
you have one way to win. Now look at this —
Miriam

I get it.
Bob

I take my forced move —
Miriam

I get it.
Bob

Two ways to win. . . .

Miriam became very angry upon suffering this defeat. She cried a little, wanted to quit, and generally made me feel like a bad guy. When she was convinced to turn the tables on me, she played game 5 and beat me directly. With her compensatory victory achieved, she no longer wanted to quit.

Game 6: Bob moves first (numbers)

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

My opening gambit (1) I characterize for Miriam as “probably a pretty dumb move. I’ve never seen anyone go first here before.”

Game 7: Miriam moves first (letters)

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

I check at first to make sure we have not played this corner opening response in this session; then upon moving (1), ask Miriam:

Bob

Do you remember how to beat me?
Miriam

Unh-huh [then she laughs and moves B].
Bob

Oh, you’ve got me now.
Miriam

[gestures toward moving next in the center]
Bob

[stopping her] Show me your chances to win.
Miriam

[gestures along the top and from B up through the center square]
Bob

If you want two ways to win, you have to move where the chances to win come together.
Miriam

[gestures to move in the center square]
Bob

That’s wrong.
Miriam

It is?
Bob

Where do the two chances come together?
Miriam

Here [along the top], here [up through the middle]. Here [the intersection corner].
If I go here, you can block here [the center square], but I’ll go here.
Bob

O. K.

Miriam makes move C, getting her two ways to win.

Relevance
This vignette continues the documentation of Miriam’s tic-tac-toe experiences. Her preferences suggest that she has begun to think of appropriate strategies selected by response to the opening move, and show she can think in terms of intersecting chances to win even though her first inclination is to move in an empty center square. (I myself played so before analyzing the game in the course of this work with Miriam.)

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