- 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.
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).
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.
First heard about it in a column in Scientific American by A. K. Dewdney. The rules are simple and it is rather fun. In one of his columns he talked about playing a toroidal version where a line going off one edge of a rectangular page comes back in on the opposite side.
• the board is first built by each player alternating in drawing an oval lightly (as with pencil) until 5 ovals are placed; each oval after the first must intersect another in at least one place, such as a tangent, but usually more
• every intersection gets a dot to emphasize its role as a vertex; the oval segments between them are edges
• after the board is built, one player starts by picking any vertex, and tracing (heavily or with a unique pen color) an edge from that point to a new vertex, and then to another vertex, and then to another (3 segments end-to-end per turn)
• the next player starts from the vertex where the previous player ended; if for any of their 3 segments (including the 1st) there is no legal move, their turn ends and the other player has choice of vertex to begin their next move
• if a player's move completes a loop, they capture it (adding their initials inside); first to capture 3 loops wins
So for example, the 5-rings olympic logo is a legal board (though one which allows the 1st player to immediately capture a 2-segment oval on either end).
Anyone else play this? Do I remember the name right?
I brute-forced this with a little lunchbreak program and the visualisation output from graphviz was ... 340 MEGAPIXELS!
I blogged about it: http://williamedwardscoder.tumblr.com/post/35858593837/tic-t...
The first two moves have no constraint, so you can just start with an X and O already on the board. And after a few moves there might be only one implied board possible, after which it reduces to the normal game. But I always thought it was an interesting twist.
(To see why no torus version exists: on a '3x3' torus, all squares are identical, so you have must four ways to get three in a row from each starting number. Also, the row/column/diagonal sum must be 15. However, starting with 9, there are only two ways to get 15 with: 1 and 5 and 2 and 4)
The variant with nine words, where selecting three words that share a letter wins the game, IMO is even better.
What I remember clearly is that the game was equivalent of tic tac toe on a torus -- one could win with a "diagonal" of the form
as well as any of the traditional tic tac toe win conditions.
The way to play is to "warp" each side of the board to the side opposite of it. For instance, playing on a 6x6 board with a win condition of length 5:
I can't find any material about this on the net, I just played it in school on boring lessons (but more commonly we played for 5 in a row on an infinite board, I personally prefer the Torus)
And what about the dual of this game, where whichever board you pick determines the square he plays next?
I am amazed by the fact that Gomoku can be so hard to master with rules so simple you can explain to a five year old. And unlike Chess where there are a hundred year of theories to learn from before you can get going, Gomoku is still new. After a few weeks studying the standard surewin openings, you can expect to see things in a very different light and the game will get much more interesting.
Perhaps Gomoku is best known for programmers as a problem to solve. But it is nowhere near being solved. In fact, the best software are weaker than many top players.
I find Gomoku hits the sweet spot when it comes to my desire to play board games. It doesn't consume much of my time. I am always excited to find those long and obscure wins. I think the game needs more love from programmers like me.
Facebook page: https://www.facebook.com/GomokuWorld
Play here: http://www.playok.com/en/gomoku/
Or here: http://fumind.com
We have to remember, however, that this proof is computer search based. There was never an algorithm to find the best move given a random position. In other words, it only proves that these certain openings will guarantee black a win.
Those who loved the game came up with new opening rules. The world championships in 1989 and 1991 used the pro rule. After some evolutions, swap2 now became the standard. Under Gomoku swap2, the first player puts two black stones and one white stone on the board, and the second player can either pick one color, or puts two more stones and gives back the power to choose color to the first player.
I know about Connect6, and also a branch called Renju. But I find Gomoku more attractive. You should totally try it sometimes.
Later someone complained with university administrators that my dad was "playing games" in the computer lab, and he got banned from it :/
But I guess this version might be even more interesting to make a AI test or something!
Randall Munroe could do a "small" update to this based on these rules... although it would take some time.
I'm not sure what you mean by this?
BTW are you aware that despite it has only one type of stone and simpler rules, checkers is in fact the more complex game, to write an AI for?
The usual caveat with checkers is that you are probably not good at it. Even if it is simpler and smaller than chess, being a good chess player gives you no advantage and the game is still sufficiently complex that you can't quickly brute force it without years of practice. A chess master will get their ass handed to them by a skilled yokel.
Much harder to program an AI for than chess, certainly. The computer never managed to beat the world champion in a match last year.
I'm almost certain that's false. Checkers is weakly solved (There are AI's that will never lose, only win or draw)
I assume you meant Go, not checkers. And that's mainly harder for AI because the board is 5 times bigger.
Edit: I meant chess is harder to write an AI for of course, not checkers. Fixed.
A quick hack while avoiding doing actual work.
The code is on github, We might implement multiplayer soon
A similar situation arises in the game 'hex', except in that game there is no draw, so it has to be a p1 win!
Please do so, as I do not see that this is trivially true. I see two tricky cases:
- your opponent must play on the board where p1 is placed, and that board would have room iff p1 weren't present => Addition of p1 gives him a 'move anywhere' move.
- you must play on the board where p1 is placed, and that board would have room iff p1 weren't present. The normal argument 'move anywhere and assume that that 'anywhere' is where your first move went, and you just played p1' does not help here, as changing the first move may change where your opponent's first move could have gone.
Except from an exhaustive search, I do not see how to prove that you can prevent either case.
Actually, the fact you force your opponent isn't the problem (I don't think) but the fact that the presence of that piece might later give p2 a free move, where previously they wouldn't means it doesn't work.
Sorry, that's what I get for thinking I didn't need to figure out all the details carefully!
Harder to draw a lot on napkins though, but then again, a single game takes much longer.
Anyone care for a game?
level 1 level 2 level 3 level 4
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Start on an edge-center container [N,E,S,W], marking it with it's corresponding sub-board space. Employ the Orwin gambit to fill the initial edge container. When your opponent selects the last space in the first container, wherever you are sent: pick it's corresponding sub-board space and then employ the Orwin gambit again and then repeat the routine until the game is finished. Your opponent gets to pick your next moves but because they eventually must send you to a filled square on the second and third rounds, you have the ability to control the game's end.
Starting in the center gives you a tactical disadvantage because it only leaves you 4 paths to victory compared to your opponents 8 with him/her in a position affecting 4 lines, whereas by starting on a side piece, you have 7 paths to victory and your opponents position only benefits him on 2 lines.
If the corner is not attached to a board, you roll the board around as though the ends are connected (or as though it's an infinitely repeating tiling of the same game). For example, the bottom right square on the bottom right board makes the next board the top left.
The center-right square on the center-right board would result in the next board being the center-left board, and so on.
Would there be a gambit in this ruleset?
So, it looks like the same gambit applies, instead of selecting the center piece you just pick the one pointing toward the center every time.
My quick implementation of this game
Edit: For anyone who arrived 10 seconds after i posted that link, The board resembled the ultimate tic tac toe, and then quickly degraded into a paint fight
This creates a means of alternating who goes first.
I'm not sure whether this gives too much advantage to the other player or not.
There is a bag of numbers 1-9. Players take turns moving numbers from the central bag to their own private bags, removing that number from play. Whenever a player has a subset of exactly 3 numbers that sums to 15, they win.
This is isomorphic to tic-tac-toe since the magic square for a 3x3 board has rows/columns/diagonals that sum to 15.