Triangles Strategy

Triangles looks like a game of luck at first: everyone draws lines and hopes the other player slips. But just like its square cousin, dots and boxes, it has a real backbone of strategy. Most games are decided in the last few minutes, when the safe lines run out and the board breaks into chains. This guide walks through the ideas in the order you'll need them. If you're new to the game, read the rules first.

1. The Golden Rule: Watch the Second Side

A triangle belongs to whoever draws its third side. So the line to avoid is the second side of any triangle. Before you draw, look at the one or two small triangles your line touches. If either of them already has a side drawn, your line will leave it with two sides, and your opponent will take it.

A line is safe when every triangle it touches has no sides yet. At the start of the game almost every line is safe. As the board fills, safe lines get scarce. The single most useful habit is to check, every time, that your line is safe. Our Easy computer does little more than this, and it already beats most people who don't.

2. Take What You're Given

When a triangle has two sides, close it. You score, and you draw again. If your opponent leaves you a whole run, take them all, one after another. There is one important exception at the very end of a run, which is the clever part of the game; see section 5.

Remember that after taking, you must still draw one more line. If there's a safe line left, use it. If not, that extra line will give something back, so pick it carefully.

3. Chains: How the Endgame Works

After a while every remaining line will touch a triangle that already has a side. Now there are no safe lines left, and whoever has to move must give something away. Look at the board at this point and you'll see the untaken triangles linked together in chains: rows of triangles where each one's open sides are shared with the next. Draw any line in a chain, and your opponent can close the triangles in that chain one after another.

• A short chain is one or two triangles. Giving one away costs little.
• A long chain is three or more. Giving one away usually costs a lot.
• Sometimes a chain joins up with itself to make a loop. Opening a loop gives away all of it, since it can be taken from both ends.

4. When You Must Give Something, Give the Least

If every line gives something away, count before you choose. Opening a single triangle on the edge costs one; opening a long chain might cost six. Give the smallest piece first, and save the long chains for later. Our Normal computer always does this, and the Hint button will show you which line costs the fewest triangles.

Also check where your line falls inside a chain. A line in the middle of a chain opens it in two directions at once; the result is usually the same number of triangles, but it gives your opponent more choice.

5. Leaving Two Behind: Keeping Control

Here is the trick that separates good players from beginners. Suppose your opponent opens a chain of five triangles for you, and after it there are still two more long chains on the board. If you take all five, you then have to draw an extra line, and that line opens the next long chain for your opponent. You'd win five and lose the next one.

Instead, take the first three, then stop before the last two. Draw the line at the far end of the chain instead of the one between the last two triangles. Now those last two triangles both wait for one shared line. Your opponent takes them both with that one line, but then must draw an extra line, and every line left opens a long chain for you. You gave away two triangles to win the whole of the next chain. Players call this "double-dealing", or simply keeping control.

With a loop, the same idea means leaving the last four triangles (two pairs), which is more expensive, so it pays less often.

6. Who Runs Out of Safe Lines First?

Since the endgame favors the player who is not forced to open the first long chain, the middle of the game is really a fight over who runs out of safe lines first. Each safe line you draw uses one up. Strong players count the safe lines left and try to arrange things so that their opponent is the one left without one.

You don't have to count perfectly to benefit. Two simple habits help:

• Notice when safe lines are getting scarce. When only three or four are left, slow down and count them. If the number is odd and it's your move, you'll take the last one, which is what you want. If it's even, look for a line that changes the count, such as one that uses up two safe lines at once by touching two empty triangles.
• A small sacrifice can turn the tables. Giving away a single triangle early, on purpose, hands the move to your opponent. If it means they are the one who must open the first long chain, it can be well worth one triangle.

When our Hard computer says "I counted ahead: it should leave you the first one with no safe line", this is the fight it is talking about.

7. Practical Tips

• Edges of the board are a good place for early safe lines: an edge line touches only one triangle.
• Lines in the middle touch two triangles, so they "use up" more safety. Use them when you want to change the count of safe lines.
• Keep an eye on the score line. If you're well ahead, there's no need for tricks: take everything and give away the smallest pieces.
• Use Hint and Why? as a teacher. Each explains its reason in one sentence, the same ideas as on this page.
• Try the Small board to practice the endgame quickly, then move up to Medium and Large.

The Ideas at a Glance

If you enjoy thinking ahead like this, you may also like Reversi, another game where the count near the end decides everything, or the logic of Minesweeper. The variations page explains the house rules and board sizes.