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).

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.

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 

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.