# Is "Connect 4 is Excellent, Connect 3 is Great" a solved game?

Connect 4 is known to be a solved game.

I am introducing the Connect 4 is Excellent, Connect 3 is Great, variant of Connect 4.

Both players play like connect 4 and fill the grid i.e. they don't stop when 4 or more of a color is connected in a row, as contrary to classic connect 4.

When the grid is filled. For all 4 colors or more connected a player gets, he scores 3 points and for all 3 colors exactly a player gets, he scores 1 point.

Here is a example:

| X | O | X | X | O | O | X |
| X | O | O | X | O | X | X |
| X | X | O | O | O | O | X |
| O | X | O | X | X | X | O |
| X | O | O | O | X | O | X |
| X | O | X | O | O | X | O |

In this example,

X scores $$0\times 3$$ points (it doesn't have any 4 connected X) + $$5\times 1$$ points = $$5$$ points
O scores $$3\times 3$$ points (it has one vertical 4 connected, one horizontal and one diagonal) + $$5\times 1$$ points = $$14$$ points

This is a large victory for O!

The puzzle asks: is Connect 4 is Excellent, Connect 3 is Great a solved game? Can you prove your answer?

• I am a bit disappointed that a connect 5 or connect 6 doesn't bring 5 or 8 points... Commented Nov 8, 2022 at 13:56
• @Evargalo haha, I did think about it. My plan is to wait for an answer for this puzzle then give a more advance one where connect 2 gives 1 point, connect 3, 2 points, connect 4, 4 points, connect 5, 6 points, connect 6, 10 points, connect 7 is infinite number of points but should probably not happen :)
– JKHA
Commented Nov 8, 2022 at 15:00
• What do you mean "solved?" Do you mean, can the players optimize their play? Commented Nov 9, 2022 at 17:06
• Before I put too much thought into this, do you know if this has an answer? Or is it an open question? Commented Nov 10, 2022 at 0:27
• OK. It took a long time on a computer to solve the basic problem, so this will likely take a similar effort and not be possible to explain on this forum easily. However, I could be wrong and it might be that this added rule actually makes it simpler to solve. Commented Nov 10, 2022 at 1:08

Here is one idea to consider. In classic connect 4, you can always win if you go first. In this version of connect 4, the

second player can always force a tie.

The strategy is simple.

Drop a piece in the same slot that player 1 drops a piece.

This results in a board where

player 1 owns all the places in the first row, player 2 owns the entire second row, player 1 the third, etc.

While this strategy trivializes the game, there might be a more complex strategy that

guarantees a win for player 2