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.|
|Bob||We were there and you ended up playing tic-tac-toe with Glenn.|
|Bob||Was he surprised when you beat him that time?|
|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.|
|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?…|
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].
|Bob||Oh no. The good trick to beat me there is you have to force me to go someplace else.|
|Bob||Like, if you crossed out that move and moved in a different corner, like down there.|
|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.
|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?|
|Bob||Let’s see. Ah. You’re the letters, I’m the numbers.|
|Bob||Now you think you’re going to beat me by going up in the corner?|
|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.|
|Miriam||You just told me.|
|Bob||You want to see how I do it?|
|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?|
|Bob||Oh. . . . Is this “turning the tables”?|
|Bob||Well, that means I have to go up where you went last time, right?|
|Bob||O. K. So you’re turning the tables on me. You’re going to be able to beat me now? . . .|
|Bob||I will put my 2 down here.|
|Miriam||Here? [i. e. is move C in right location?]|
|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.|
|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?
|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.
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.