And here's James Irwin's original implementation, auto-set to a Monte-Carlo AI and with a rules variation that (to my knowledge) prevents Perfect Bot from winning. Play with the config variables at the top for some other AIs and 2-player games and whatnot. https://www.khanacademy.org/cs/in-tic-tac-toe-ception/167633...
TLDR: you're wrong.
C/C, C/SW, C/S, [opponent takes C], C/SE, NE/SW, NE/S...
after C/SE, your opponent has control and can go anywhere that is available in the center board they've already won, so you can't assume you're next play will be NE.
More importantly after you've sent them to the SW board with NE/SW they can go anywhere except the middle and so they then have the initiative.
Hmm, It looks like you switched notation halfway through? I was assuming board/position and only showing player 1 moves but that doesn't after losing the center board
Regardless you lose the initiative after 5 moves.
The initial idea (extending Orwin Gambit) should still be leverageable into a much better position. This might fall short of a certain win though, if the opponent plays a proper response strategy -- which we should probably assume if the contestants are peer mathematicians. :)
| The very first move in the game must not be in the center board (or more specifically CC)
So player has to pick some other board. If they choose C in that board, then they're fucked, the next player will end up playing the Orwin Gambit. So both players will avoid C like the plague until they're sure the Orwin Gambit is no more applicable.
Even if I start with some board (say NE), and in the first move itself I play a C and thereby giving the other player an option of taking the Orwin Gambit, it still can't be effectively used. Because I can later play NE again in the C table, thereby outplaying the gambit (since the C inside NE is already used).
Edit: Formatting
The standard strategy (without optimization) seems to work perfectly. You gain control by forcing the oponent to fill out the miniboards. The last move on the second exhausted miniboard will allow you to choose any miniboard, so it's an easy win.
EDIT: like 3pt14159 pointed out, O might cause you problems if he immediately picks the center in the NW miniboard. This needs further testing...
This would be the general strategy, although I am now no longer sure you can force a win through. The options for moves for O starts to grow past what I can work through in Paint right now.
I don't think you can force that. When you have the nine center squares of each square and he has the 8 non-center squares of the center square, it is your opponent's move.
The 'force-fill the center square' only works because, in your first move, you occupied the center square. That move prevents your opponent from ever picking the center of the center, thus forcing you to move in the center square.
- Force opponent to fill center miniboard, as he describes.
- Force opponent to fill (e.g.) northeast corner in the same way. Opponent now has taken two miniboards, and you have none, but you are one turn away from taking each of the remaining seven.
- Pick SW corner of SW corner. You have taken SW corner miniboard. Opponent is forced to play in same SW miniboard, already won by you.
- Pick SW corner of S. You have taken S miniboard. Opponent is forced to play in SW corner again, already won by you.
- Pick SW corner of SE corner. You have taken SE corner miniboard.
- Done. You win.
Like regular tictactoe, there is an advantage to going first. Unlike regular tictactoe, the advantage can't be compensated for. Otoh, the second player can use the same strategy with a little more carefulness, as long as they start early.
So either player can force the other into a protracted certain loss, unless there's an agreement or a rule against it. That's no fun.
EDIT: actually, you can win every time, in far fewer moves, and not using the Orwin gambit at all. It's not necessary to force your opponent to fill any of the miniboards, not even the center.
I think this will win in ten moves and never lose driver control (excuse the notation): C/C, C/SW, C/S, [opponent takes C], C/SE, NE/SW, NE/S, NE/SE, [opponent takes NE], SW/SW [you take SW], SW/S [you take S], SW/SE [you take SE, and win]. A variation can be used by either player early in the game, but whoever starts with control would be foolish to lose it.
If this is a game played by mathematicians, either I'm wrong, or there are additional rules. :)
EDIT2: C/C (first move above) is unnecessary. Nine moves. Perfect inning.