5
$\begingroup$

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?

$\endgroup$
10
  • $\begingroup$ 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
  • 1
    $\begingroup$ @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
  • 1
    $\begingroup$ 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

6
$\begingroup$

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

$\endgroup$
1

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.