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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?

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  • $\begingroup$ I am a bit disappointed that a connect 5 or connect 6 doesn't bring 5 or 8 points... $\endgroup$
    – Evargalo
    Nov 8, 2022 at 13:56
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    $\begingroup$ @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 :) $\endgroup$
    – JKHA
    Nov 8, 2022 at 15:00
  • $\begingroup$ What do you mean "solved?" Do you mean, can the players optimize their play? $\endgroup$
    – Boba Fit
    Nov 9, 2022 at 17:06
  • $\begingroup$ Before I put too much thought into this, do you know if this has an answer? Or is it an open question? $\endgroup$
    – Trenin
    Nov 10, 2022 at 0:27
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    $\begingroup$ 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. $\endgroup$
    – Trenin
    Nov 10, 2022 at 1:08

1 Answer 1

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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

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