### Vn96.1 Tic Tac Toe 9/19/77

After the final arithmetic session of this date, Miriam wanted to play some tic-tac-toe. (Her purpose was to get the material over with so she could have a friend come play with her on the morrow; her assumption that such was necessary was an error.) These games began with a discussion of Miriam’s play with Glenn Iba (cf. vignette 86).

 Bob I remember a funny thing happened the last time we were at Logo. Miriam What? Bob We were there and you ended up playing tic-tac-toe with Glenn. Miriam Yeah. Bob Was he surprised when you beat him that time? Miriam Yeah. Bob What did he say to you? Did he say, “How did that happen?” Miriam I told him how I was going to beat him in the first time and he spoiled it. Bob In the very first game? Miriam I went here [a corner response]. Bob Yeah. You had a corner opening. Miriam And he went here [center]. I went here [opposite corner], and said if you go here [adjacent corner], I’ll go here and get two ways to win. And he went here [side move] and I had to go here [forced move]. Bob He spoiled your game. Miriam Yeah. Bob That’s why you didn’t beat him in the first game. Do you remember that other game you did beat him in though?… Miriam [no response]

After Miriam selects a pen (by applying the chant “Engine, engine number 9, going down Chicago line. . .”), we try to discuss the possible responses to Miriam’s opening corner move. Miriam shows no inclination to reduce her count of possible responses based on symmetry arguments.

Game 1: Miriam moves first (letters)

```	 A | 1 | B1->D
2 | C |
B |   | 3
```

Miriam’s initial counter-move (B1) to my opening response was not optimal (for a game of the form classed as Game VII in Learning: Tic-tac-toe ). Together we worked through the recorded game above.

 Bob Let’s see if you can beat me when I move right close here to you. Do you know whether you can beat me or not? Miriam Unh-uh. Rats. This red pen [moves on opposite side of my markers]. Bob That’s where you want to go? Miriam, I’m really surprised. Why do you want to go there? Miriam ‘Cause then if I go here [opposite adjacent corner], I can beat you. Bob Now hold on. You’re trying to move there. So then you’ll get two ways to win? … Let me show you’ve got a bug. Miriam, I get to go next, and I’m planning on going there [center]. Miriam Go here. Bob Oh no. The good trick to beat me there is you have to force me to go someplace else. Miriam How? Bob Like, if you crossed out that move and moved in a different corner, like down there. Miriam Yeah? Bob Would it work then? Miriam Maybe. Would it? Bob What do you think? You force me to move over there. Then the center will be free. You think that’ll make it? O. K. Go ahead. Miriam I did. Bob Great. Well, Miriam, I am forced to move here, in the side place. . . . Your chance to win do what? Miriam Come together, this way and this way [moves C]. Bob I will go down there with my 3 then. Miriam I will make this. I win, I win. Bob Why don’t you put a big M over the top for Miriam. . . . But if you fail to force my move, the next time around, my number 2 — I could have put my number 2 right in the middle and that would have screwed your strategy all up.

Games 2 and 3:

After a replaying of the game situation in which Glenn beat Miriam (cf. vignette 86) — at her request — in which I beat her (the opening game, of form X, is determinate), Miriam spontaneously turns the tables on me in game 3.

```	numbers first	letters first
A  |    | 2 	 1  |    | B
C  | 3 | 1

3  | C | A
4  |    | B 	 D  |    | 2
```
 Bob I remember when you were playing with Glenn, you did a lot of playing on the side. He started on the side a lot. Is that because you told him to every time? Or just because he wanted to after the first time? Miriam Will you go over here [the far side from upper left corner]. Bob Over here? What were you going to do? Miriam Here [upper left corner move]. Bob Who do you think will win? Miriam Me? Bob Let’s see. Ah. You’re the letters, I’m the numbers. Miriam Unh-uh. Bob Now you think you’re going to beat me by going up in the corner? Miriam [moves A] Bob That’s a bug, Miriam. Shall I show you why? . . . Do you think you’re going to win, or do you think I’m going to win? Miriam I think you’re going to win. Bob How come? Miriam You just told me. Bob You want to see how I do it? Miriam Yeah. Bob I put my 2 right up here, over top of the 1. Now you have a forced move…. My good trick is that your second move (B) comes right under my 1. Now, tell me, what I’ve got [3 in center square], where my chances to win intersect. Miriam Two ways to win. Bob How did I do that to you? . . . Miriam I’m going to go here. Bob So you block my 1 – 3 and I go there. O. K. One for Bob. . . . Where do you want to start? Miriam [moves A where my 1 had been in last frame] Bob You’re going to go where I went last time? Miriam Yeah. Bob Oh. . . . Is this “turning the tables”? Miriam [laughing] Yeah. Bob Well, that means I have to go up where you went last time, right? Miriam Yeah. Bob O. K. So you’re turning the tables on me. You’re going to be able to beat me now? . . . Miriam Yeah. Bob I will put my 2 down here. Miriam Here? [i. e. is move C in right location?] Bob Uh-huh. Miriam C. Bob Oh. You put it there because you’ve got one chance from the B through the center and one chance from the A across. Miriam [unclear comment] Bob Well, I’ll go here. 3. So you turned the tables on me all right. You like turning the tables on me? Is that a good way to do tic-tac-toe? Miriam Yeah. Bob Here. I go first again? Shall we do another side one? Miriam Let’s stop. I’ll do some more after a while.

We leave tic-tac-toe for a game of frisbee in the courtyard and do not return to it.

Relevance
Miriam’s play in game 1 shows the residual dominance of the three-corner configuration and an imperfect integration of the idea of a forcing chain (we have not explicitly discussed this idea). Miriam requests we replay the game in which she was defeated in vignette 86, the re-executes it of her own volition in ‘table-turning’ mode. I cite this event as evidence that Miriam has adopted this procedure as a powerful learning tool.