### Vn72.1 Tic Tac Toe with Robby 8/25/77

Having seen Miriam play tic-tac-toe with me and feeling a little left out, Robby asked to play with me after Miriam went to bed.

Game 1: Robby moves first (numbers)

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

Robby originally made move 3 in the middle of the top row, belatedly recognizing his error, and asked to move instead in the middle of the bottom row. Such oversights appear to be characteristic. When I mentioned, before placing C, that I had a forced move, Robby noted, “This is probably going to turn out to be a draw.”

Game 2: Bob moves first (letters)

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

After Robby’s first move (1), I asked:

 Bob Do you believe I can beat you? Robby No. Bob You don’t believe that? I’ll prove you wrong. Robby All right. Bob Watch. I put a B in that corner. Do you have a forced move? Robby Arggh. Bob How many chances to win do I have? Robby [gesturing across the top and up through the center from B] This way and this way. Bob Two chances to win, right? Robby Yeah. Bob Do they come together? Robby Yeah. In that corner. Bob So I put my letter C up there and what do I have? Robby Two ways.

I had not in the past described play in such a manner with Robby. His finding it immediately natural is a sign he thinks of the game in such terms himself.

Game 3: Robby moves first (letters)

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

After Robby’s corner opening, I brag that I’m not so easy to beat as the computers at the Children’s Museum. He responds:

 Robby I also have a different technique if you do that [unclear referent; perhaps: respond with center move to his corner opening as the computer did]. Bob You think I’ll do that? Well, suppose I go over here. You think you can beat me if I go there? . . . Son of a gun, you got me. Do you believe you have me? Robby [a less than absolutely confident smile] Bob You’re right. You know why? Robby Yeah. You’re forced to go there (2) and I can go there (C), then I have two ways to win.

I congratulate Robby on being “pretty good at this” and inquire how he learned to be so good at tic-tac-toe. Robby explained that the 3 times we were at the Children’s Museum he played tic-tac-toe with the computer “quite a bit.” He suggested as many as 26 games.

At this point in recording Home Session 17 the tape recorder malfunctioned and the remainder of the conversation was lost.

Game 4: Bob moves first (letters)

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

This game exhibits use of the block I developed to counter the strategy Robby first employed against the computer at the Children’s Museum (cf. Vignette 5).

The remaining three games we played this evening were all center openings by Robby. When I responded with corner moves twice, we tied. When I responded with a middle row move, he beat me.

At the end of the games, we discussed the game generally. Robby, in response to a question of how many ways one could start out, explained that there were possible only 3 opening moves (center, side, and corner). He also knew that when responding to a center opening, a move in the middle of a row invariably led to defeat, whereas a corner move would guarantee a tie unless you made a mistake.

Relevance
These data are collected for comparison and contrast with the more extensive collection of Miriam’s games. My general impression is that there are two main differences between the children’s grasp of the game. Robby appears to conceive of an entire game as a single entity, the sort of game it is being determined by the first 2 moves. I infer this from his being able to describe and discuss the games in a relatively abstract way: there are only three opening moves; there are only two responses to a center opening. This is a different way of thinking of the game’s symmetry from the way it is manifest in Miriam’s thought: she will recognize one game as equivalent to a second when both appear for judgment in that respect. Her response to such questions needs further probing.