Vn110.1 Tic TacToe 10/30/77 & 11/12/77
10/30 When Robby and Miriam agreed to play tic-tac-toe together (intending to use Miriam’s ‘magic slate’ which would have left no record of their play), I suggested they play on the chalkboard in the reading alcove. Miriam was granted first move (letters).
| D | 2 3 | A | C B | 4 | 1
Game 2: When Robby moved first (numbers), he chose the corner opening
1 | | a c | b | 3 | 4 | 2
At his move 2 Miriam said, “Oh oh,” apparently sensing the fork’s distant threat, and attempted to circumvent it by moving twice. Her attempt was met by Robby’s loud and justifiable complaint. The game proceeded to Miriam’s defeat.
Game 3: Miriam moves first
A | D | C 2 | 3 | B | | 1
In her turn as aggressor, Miriam first complained “Wah!” when Robby moved 1, then went on to defeat him with an expert win. Her conversation highlights her sense of the situation. While Robby, still confident that he had blocked the corner offensive, walked away, Miriam said somewhat gleefully, “Robby, you’re gonna kill me for this,” and then moved B. She then went on to promise him a million dollars in reparations if she should move between A and B. Robby then moved 2; with his move in place, she added, “I wasn’t going there anyway.” When I asked Miriam if she could beat Robby now, she replied, “Yeah, I think so,” and then she did. Robby was not accustomed to being beaten fairly by Miriam, and he was angry. Miriam offered to let him turn the table on her.
Game 4: Robby first
c | | a 4 | 1 | 3 2 | | b
After this game, Miriam was surprised that Robby didn’t know how to turn the tables. I agreed that he did not have so specific an idea as we did of what we meant by “turning the tables.” I interpret Miriam’s failure to block row 3 – 1 – 4 as a gift to Robby, so he wouldn’t “kill her” for her prior victory. Although she also achieved her preferred three-corner configuration, Miriam appeared not very interested in winning the game.
At this point, I was called outside the house on peripheral matters. I told the children I would return shortly and asked them not to play with each other while I was gone. Miriam, true to her word, played a game against herself on her magic slate (game 5).
A | D | C | a | g b | | B
Miriam explained on my return that she had been playing tic-tac-toe against herself, making “smart moves” for both herself and “the other guy.”
11/12 This evening, when I stopped videotape transcription, a quiz show override signal from channel 4 displayed a tic-tac-toe board with this configuration:
X | | | O | | | X
I shut off theTV, then called Miriam and asked if she had figured out yet how to block a corner opening. She said, “Give me some chalk,” thus volunteering to show me. I reached to the chalk supply, drew a game frame, and placed the corner opening. Once she controlled the chalk, Miriam made moves for both players.
1 | D | C b | g | B | | a
Miriam claimed she could block the corner opening thus: “Go in the opposite corner.” After response a, Miriam knew the next move would be B. She made that move, the forced b, and moved C — at which point she realized she was forked! Miriam then claimed “he” would not go there. I replied, “Yes, he would.” Miriam responded, “Yes, he would try hard to win. So I block him there [moving g] and he wins there [moving D].
Two points stand out in these data. As aggressor, Miriam is unquestionably able to defeat an opponent with an opening game (first two moves) as in game 3. The last two games show a major new capability as the culmination of Miriam’s development: she can now play both sides of the game simultaneously. I consider such an accomplishment the ultimate decentration in any domain, which, when achieved, renders competition-engaged analysis possible.