Board Game Arena

Ceaseless wrote: ↑25 August 2026, 22:27 The previous notes are for when columns are even, regardless of how many there are, even if there are an even number or an odd number of them. However, when the columns are odd, things get a bit messier. As previously mentioned, in an odd column if both players played up the same empty column, whoever started the column would also finish it, meaning a new player would begin the next column. With this the players are exchanging the initiative through this parity change.

If the board only had 1 odd row column, red would play all of the odds, and yellow would play all of the evens, meaning red wins odd row threats, and yellow wins even row threats. However, if there are 2 columns, this is reversed, red’s even row threats wins and yellow’s odd row threats win. This flip flop happens each time a column is added, meaning that if the starting board has an odd number of columns, red’s odds win, and yellow’s evens win, while if the starting board has an even number of columns, red’s evens win, and yellow’s odds win.

However, the parity rules for odd columns and threats are unchanged regardless of how many columns there are. An odd row column functionally deletes an even number of disks from the column, so there is no parity change for an odd row threat on an odd column. For example, a threat on row 3 on a column of 7 slots functionally removes slots 2-7, or 6 slots (an even number), from play. On the other hand, even row threats functionally delete an odd number of disks from the column, so there is a parity change for an even row threat on an odd column. For example, a threat on row 4 on a column of 7 slots functionally removes slots 3-7, or 5 slots (an odd number), from play.

The rules of parity conflict remain similar. Red’s winning row 4 threat (meaning an even number of odd row columns) will trump yellow having row 3 threats on every other column. Take a starting board with 8 columns 7 disks tall and replace our typical 4 in a row concerns with the hypothetical Connect 4 board where only key disks matter. If red had a major threat on A4, and yellow had major threats on B3, C3, D3, E3, F3, G3, and H3, red can play on B1, and after that if yellow played in row 1 of any column besides column A, red would just play in another row 1 besides A1. As there were 6 such row slots remaining, this is possible. Any other disk yellow plays red can play on top of yellow. Meaning A1 is met with A2, any row 2 play yellow makes is met with the row 3 slots above them, any row 4 play yellow makes is met with row 5 above them, any row 6 play yellow makes is met with row 7 above them… Yellow inevitably has to play in A3, where red takes A4 for the win. Note that this only worked because there were also an even number of total columns, so red had their winning column, a spare column for 1 disk, and the even number of other columns cancelled out. Had there been an odd number of total starting columns, red would not have that spare column to slip a move in. This is why yellow would win the row 4 threat in such a situation instead.

The same cancellation rules apply for the parity changing even row threats in odd column games as they did back when the parity changer was odd row threats in even column games, if yellow has an even row threat, it can cancel out red’s even row threat. If yellow has an even number of major even row threats they can win with one. As for the non-parity changing threats, they follow the same lack of cancellation rules. Whoever has them as a win condition can fill them in easily, keeping in mind that the starting board’s number of odd columns (or more specifically the parity of said number) dictates who begins with that favor.