Variant of Connect Four

The Game Room
1

I just discovered this game (Giiko Smart Four) today. There’s a video to show how to play. It’s obviously a variant of Connect Four, but this game adds a dimension to it.

The rules for this one:

  • 2 players, one with 32 black disks, one with 32 white disks
  • a 5x5 board
  • Players take turns adding one disk per turn to the board
  • Players may place a disk on top of another disk of either color, thus creating another level for placing disks
  • A win is achieved when a player’s disks are in a 4-in-a-row configuration without a gap
  • The 4-in-row may be horizonally on one level, vertically on one level, diagonally on one level, or ascending (straight line ascending one level at a time through four levels)

So, question time!

  1. Now, I know Connect Four is a solved game. Does this game seem like it, too, should be a solved game?
  2. Is a tie possible?
  3. What are the best strategies for each player?
  4. What if you decide there’s an endless supply of disks for each player; will that change the strategy?
2

It’s certainly a solvable game, at least in principle. Though it’d probably be harder than regular Connect 4, since there are 25 possible options at every move, instead of at most 7. And of course, no matter how easy a game is to solve, it won’t be unless someone puts in the effort, which is more likely the more popular the game is, and this game is surely much less popular than regular Connect 4.

A tie is certainly possible, in that there exist arrangements of 32 disks of each color that don’t result in a win for either side. For a trivial example, you could have a tower of 16 pieces on each corner of alternate colors. The more interesting question, which you might have meant to ask, is whether it’s possible for either or both players to force a tie.

My suspicion is that it’s either very easy for Player 1 to force a win, or it’s very easy for either player to force a tie.

Oh, and for clarification: Is an “ascending four in a row” only straight up, or are diagonals allowed that way, too? If ascending diagonals are allowed, then it’d be nontrivial to design the playing area in such a way that both players can easily see the relevant game state.

3

Yes, ascending 4-in-a-row can go in any direction, without gaps of course.

4

On thinking about it some more, I think I must be missing something, because by my current understanding of the rules, it is in fact trivially easy for player 1 to win. A sample game:

1
,.,.,
.,.,.
,.X.,
.,.,.
,.,.,

2
,.,.,
.,.,.
,.XO,
.,.,.
,.,.,

3
,.,.,
.,.,.
,.XO,
.X.,.
,.,.,

4
,.,.,
.,.O.
,.XO,
.X.,.
,.,.,

5
,.,.,
.,.O.
,.XO,
.X.X.
,.,.,

6
,.,.,
.,.O.
,.XO,
.XOX.
,.,.,


7
,.,.,
.X.O.
,.XO,
.XOX.
,.,.,

8
,.,.,
.X.O.
,.XO,
.XOX.
,.,.O

9
X.,.,
.X.O.
,.XO,
.XOX.
,.,.O

The second layer isn’t even needed (any move by O on the second layer would only speed up the win). And other responses by O are possible, of course, but I think any of them just lead to even quicker wins by X.

5

Connect Four may be solved, but how about Connect Four Million?

6

Pretty sneaky sis.

7

That would be “bro”, actually.

8
9

OK, here’s the parody. (Note, if you never watched LOST, this will be “lost” on you.)
https://www.youtube.com/watch?v=pGeASXjd0UU

10

I think that, if you remove the constraint that no column can have more than six pieces in it, all such games are solved to be draws.