Going first, you should be able to force a win.
Using @kaine's terminology:
- box - an area on the board that can be made into a square
- square - a box of 4 lines
- three - a box of three lines which can be made into a square on the next turn
- safe - a move that doesn't result in a three
Moves are enumerated as follows:
* 1 * 2 *
3 4 5
* 6 * 7 *
8 9 10
*11 * 12*
After 5 moves, the board is split down the middle into 2 1x2 half boards. One half contains 2 connected boxes with no threes and no safe moves, and the other contains 2 separate boxes with no threes and no safe moves. For example, the following boards are split down the middle into left and right half boards. Any move on either board will concede a square or two:
o o---o o o---o o o o o o o
| | | | | |
o---o o o---o o o---o o o---o o
| | | | | |
o o o o o---o o o o o o---o
If you can make any of these boards, or rotations/flips of them, you will win.
Note that there are three sections, one with 2 boxes (on the right in these examples), and 2 with 1 box (on the left). Your opponent goes first, and must concede two of these sections to you. Since you will have a choice of which to concede, you never have to concede the right half (with 2 squares). Thus, you will win 3-1 every time.
If a board can be divided in such a way after 6 turns that you are forced to concede a single square, but the other 3 squares are connected and will be conceded to you, then you will win.
Below are some examples of such boards.
o o o o---o---o o---o---o
| | c | c c |
o o---o o o o o o o
| | |
o---o---o o---o---o o---o---o
For all three boards, concede the box 'c' in the upper right, and your opponent will be forced to concede the other 3 to you.
Corner Boards have the following properties:
- the corner box has two out of four sides completed
- there are no threes
- the corner box is isolated so that making a square in it does not make a three elsewhere, but results in all boxes having 2 out of three sides completed
The general strategy to be used is as follows:
- If presented with a three, take the square and play again
- If no squares can be taken, play safe
- If you can't play safe, concede a single square
This strategy is used in a number of situations and is referenced simply as "General Strategy" for the following scenarios.
On your first move, you must take an outside edge.
Note: If you don't and take one of the lines touching the middle dot, then your opponent can force a draw simply by splitting the board with their first move and then mirroring every move you make on the other half of the board. When you are forced to make a three, he will take the square and make the same three on the other half board. Repeat until the end of the game for a tie.
So, here is an example of taking an outside edge:
o o o
o o o
Your goal will be to create the split board, but failing that, work towards the corner board. Your opponent can now either take an interior line, or an edge.
If your opponent takes an interior line (4/6/7/9), then you can take another interior line 90 degrees to it without setting up a three. Here are the moves you would make based on his move:
4 --> 6
6 --> 4
7 --> 9
9 --> 7
Thus, there are two possible boards (since either 4/6 and 7/9 result in the same board):
Board 1 Board 2
o o---o o o---o
o---o o o o---o
o o o o o o
Your opponent has a few choices.
- Moves 1/3/5/7: All concede a square, which you take on your first turn, and then make move 11. Proceed with the General Strategy for the win.
- Moves 9/10/12: In one move, you can create a Split Board for a win.
- Move 8/11: Play safe with 10, and he will be forced to either concede a square, or make a Corner Board with move 12. If he concedes, play the General Strategy for the win.
There are the following options for your opponent:
- Moves 1/3/6: You can make a Split Board on your next move.
- Moves 4/5/10/12: Take the square and make move 8. General Strategy results in a win.
- Move 8/11: Play safe with move 3. He will be force to make a Corner Board with move 1 or concede a square. General Strategy results in a win either way.
If your opponent takes an exterior line, then you can try to aim for a Split Board or Corner Board, if available.
Split Board Candidates
The following boards should be attempted to be made into a Split Board.
Board 1 Board 2 Board 3
o o o o o---o o o---o
o o o o o o o o o
o o o o o o o o---o
If the flipping/rotating the board matches any of these, then you can try for a Split Board by attempting to split the board vertically. So, make move 4. To complete the Split Board, your opponent must make either 6 or 9, and when they do, you make the other for the guaranteed victory.
If they make a different move, then your goal is now to make a Corner Board. Here are the break downs for each board above after you make move 4:
Boards 1 and 2
o o o o o---o
| | |
o o o o o o
o o o o o o
The only safe moves (other than 6/9 which can be made into a Split Board) are 1/3/8/11/12.
- Move 2/7: He is conceding the upper right square early. Take it and then play safe with move 11. General Strategy wins the day.
- Move 8/11/12: If you make move 6 (the bottom of the top left corner square) the only remaining safe move is 12 or 11, which makes a Corner Board. If your opponent instead concedes a square, General Strategy wins.
- Move 1/3: Make move 11. Your opponent can now complete the Corner Board by making move 12, or make the only other safe move - move 8. By making move 12 your self, the next move by your opponent will concede all 4 squares to you.
o o o
The only safe moves are 1/3/8/10/11.
- Move 5/7: Similar to the previous case, you can take the square and then force a victory by making move 11 and using the General Strategy.
- Move 8/11/10: If you make move 6, the only remaining safe move is 10 or 11 which makes a Corner Board. Anything else, and General Strategy will win for you.
- Move 1/3: Concede the upper right square immediately by making move 7! If your opponent takes the square, they will only have 2 possible safe moves for their second move - 8 or 11. You take the other, and they will be forced to concede the other three squares. Alternatively, your opponent may concede the one of the other squares, so take it, and then make move 11. They will then be forced to concede the other two squares.
Corner Board Candidates
After eliminating the Split Board candidates, and any rotations/flips, the following three boards remain:
o o---o o o---o o o---o
o o o o o o o o o
o o o o---o o o o o
None of these are split board candidates. So, you will aim for a Corner Board instead.
On your move, for the first and second boards, make move 8. For the third, make move 11. All three boards are now rotations/flips of one another, so they are all the same scenario. Thus, without loss of generality, we can use the following board for your opponents move:
o o o
Your opponent can either play safe or concede the square.
- Move 4/7: Take the square on your first move of the turn and then make move 8. General Strategy takes over from here.
- Moves 3/8/12: Try to make a Corner Board with the top right corner as the corner box. Thus, you can play move 8 (or 3/12 is 8 is already taken), leaving your opponent move 12 or 3 as the only safe move, which results in a Corner Board. If instead, they concede a square earlier, General Strategy can be used to win.
- Moves 1/10: Make move 8 and the board is now a rotation/flip of the previous case except the corner is the lower left. Flip the board and use the same strategy.
- Move 6/9: Make move 10. The only safe move left is 1 or 3, and if they take it, you have a Corner Board. If they don't use General Strategy to win.