Lesson 4 of 4
Threats
4 min

Zugzwang in Connect Four: The Hole Under a Threat

In Connect Four you can't pass. Late in a game that matters more than anything: the player who runs out of safe holes has to drop a disc where it loses. Chess players call this zugzwang, and so do Connect Four players.

Step 1 of 4

The poison hole
Yellow's diagonal climbs from the bottom of column 7 to row 3 of column 5. The hole that would complete it is on row 4 of column 4, and column 4 holds two discs. So a Red disc in column 4 would land on row 3, right under Yellow's threat, and Yellow would drop on top of it and win.

The hole right under an opponent's threat is poison. Stay out of it, even when it looks like your best move.
Stay out of it
You are Red, on the same board. Column 4 is tempting: your disc there would join your discs on row 3 of columns 1 and 2, and the gap on row 3 of column 3 would become a threat on an odd row. But column 4 is poison. Make that threat another way.
Your move
Make a threat on row 3 or row 5 without dropping into the poison hole.
Find the poison
Red to move. Yellow has one threat on this board, and it isn't easy to see. Which column must Red stay out of?
Question
Make Yellow run out
An endgame, with you as Red. Your threat is the starred hole on row 3 of column 1, an odd row. Yellow's threat is on row 4 of column 7. The holes under both are empty. The only other free holes are at the top of column 2 and the top two of column 5.

Count it out. You, Yellow and you fill those three holes, and then Yellow has to drop under one of the two threats. Play only safe discs: not under Yellow's threat, not under your own, and block Yellow whenever Yellow can connect four next.

If Yellow drops under Yellow's own threat, block it. The two holes above it then go Yellow, then you, and Yellow is out of safe holes again. A Red threat on an odd row beats a Yellow threat on an even row in another column: Yellow runs out first.
Your move
Play safe discs until Yellow has to drop under your threat, then connect four.

What you learned

The hole right under an opponent's threat is poison: drop there and they win on top of your disc.
Don't fill the hole under your own threat either, or your opponent blocks it.
You can't pass, so the player who runs out of safe holes has to give a threat away. That is zugzwang.
Red's odd threat wins by zugzwang, and so does Yellow's even threat, but only if Red has no odd threat.