Solved. A draw with optimal play from both players.
Thank you for that news report on the state of the art. When was the massive research effort concluded?
This game is mentioned in several DonaldNorman
, he describes a game in which alternating players select numbers from 1 to 9, and the winner is the first to get three numbers that add up to 15. It certainly takes a lot of thought to play effectively. Unless, of course, you use this handy little visual aid:
8 1 6
3 5 7
4 9 2
Presumably, there was also a rule to prevent reselection of any number during a game.
version of TicTacToe
on the FoxproWiki?
Equally useless, I started writing a learning tic-tac-toe game with my kids. We never got it to play optimally, but with some very simple rules and a lot of trial games it did learn something. One interesting aspect of the project was that I wrote a cgi script to browse memory dumps from the program. These are board configurations with counts towards wins. The browser lets you compare the amount of learning that is represented by various dumps. Have a look. -- WardCunningham
Any learning algorithm that does not take account of symmetries in the domain will learn vastly slower than otherwise, since it must learn each symmetry group item separately rather than generalizing one solution to all.
On the other hand, adding the ability to learn symmetries makes any such project a much larger conceptual challenge. Yet simply hardwiring the appropriate symmetries is cheating, isn't it? Which of course brings up DanielHillis
' MIT AI Lab koan:
In the days when Sussman was a novice, Minsky once came to him
as he sat hacking at the PDP-6.
"What are you doing?", asked Minsky.
"I am training a randomly wired neural net to play Tic-Tac-Toe",
"Why is the net wired randomly?", asked Minsky.
"I do not want it to have any preconceptions of how to play",
Minsky then shut his eyes.
"Why do you close your eyes?", Sussman asked his teacher.
"So that the room will be empty."
At that moment, Sussman was enlightened.
...which, aside from being silly, really does make a serious point. I wrote some somewhat related notes on TicTacToe
on the GeneticAlgorithm
page. -- DougMerritt
If you wanted to (and it would serve no purpose, probably upset others, but might be fun), two WikiZens
could play each other on this page by edit and save, edit and save....
X's turn: (I found a bug in this program).
The 3-dimensional (4x4x4) version (called Qubic) is more fun. See http://www.wylliedraughts.com/Qubic.htm
for some details and a program.