Six Dots▶Play

The classic pencil-and-paper game Sim. Six dots, fifteen possible lines: you and the AI take turns drawing them, and whoever completes a triangle in their own colour loses. No luck, no draws — just reading the board a few moves ahead.

How to play

Six dots sit at the corners of a hexagon, and every pair of dots can be joined by a line — fifteen lines in all. You draw in orange with solid lines; the AI draws in blue with dashed lines. You always move first.

To draw, tap one dot and then a second dot, or drag your finger from one dot to the other. A line that already exists cannot be drawn again; tapping the dot you picked a second time cancels the choice. Once you pick a dot, every dot that would close a triangle of your own lines is marked with a red ring and an X, and the AI's most recent line glows so you can see what it just did.

A triangle counts only when all three of its sides are the same colour. The first player to complete a triangle of their own colour loses at once, and the triangle flashes. Triangles mixing both colours do not matter, and lines drawn between the corners do not need to avoid crossing each other. The game can never end in a draw: once all fifteen lines are coloured, a one-colour triangle is mathematically certain, so someone always loses before that.

Beat the AI and the next game starts with your win streak growing; your score is that streak. Every win also makes the AI more careful — it makes fewer loose moves the longer your streak runs. Lose once and the streak is over; you can save it to the Hall of Fame from the result card.

Tips & strategy

Think of every line you draw as using up future lines. The moment two of your lines meet at a dot, the line joining their far ends becomes poison for you — drawing it would close your triangle. A dot touched by three of your lines poisons three lines at once. So spread your lines out instead of piling them onto one favourite dot, and before each move count how many safe lines you will have left afterwards.

There is a neat way to never close a triangle: split the six dots into two groups of three and only ever draw lines that cross from one group to the other. A drawing made only of such crossing lines can contain no triangle at all, because a triangle needs two corners in the same group. You will not always get to keep this shape, since the AI takes some of those crossing lines, but steering towards it keeps your options open far longer.

The real battle is the endgame, when only a few lines are left uncoloured. Look at each remaining line and ask which of you it is poison for. Lines that are poison only for the AI are the ones you want left at the end, because it will be forced to take one; lines that are poison for you should be used up by the AI or made harmless early. A line that is poison for both players is neutral — whoever is forced to take it loses.

Sim was invented by the mathematician Gustavus Simmons in 1969 as a playable piece of Ramsey theory: among any six people, three are always mutual friends or three mutual strangers, which is exactly why fifteen coloured lines must contain a one-colour triangle. The game is small enough to solve completely, and the solution says the second player wins with perfect play. This AI does solve it — so as the first player, you win only by exploiting its loose moves, and those become rarer with every game in your streak.