Breakthrough

You can't capture straight ahead, and that's everything

Breakthrough gives every pawn two ways to move forward, straight or diagonal, but only one way to capture: diagonally. A pawn can never take the piece directly in front of it. Once that sinks in, the defence almost designs itself. A pawn sitting right in an enemy's path is safe from that pawn; what threatens it are the enemies one step to either side. So you defend a pawn by backing it up diagonally, making sure any capture can be answered with a recapture. Every good habit in this game grows out of that one rule.

The goal is a footrace with walls: be first to land a single pawn on the opponent's home row, or capture every pawn they have. Because one runner reaching the far edge wins outright, the game is a constant tug between shoving forward and keeping your own back rows guarded. It helps to literally count the race. Work out how many moves your fastest pawn needs to reach the far row, then count the same for the most advanced enemy pawn. If your number is smaller and no diagonal can touch your runner on the way, push and never look back. If not, fix your defence before you sprint.

How to break through

• Attack where you outnumber the defender. A local majority (three of your pawns against two of theirs on a couple of files) can force a hole no wall can close.
• Keep pawns connected in a staircase so each one defends the next. Lone pawns get picked off diagonally.
• Don't over-commit a single runner. A pawn that sprints ahead unsupported is usually just a free capture for the computer.
• Trades aren't equal. Sometimes losing a pawn to strip away a key defender opens the exact file you need.
• The outermost columns are worth a look: a pawn on the edge can only ever be captured from one side, so the defence there has half its usual grip.

The standard break is three against two. Line up three pawns facing two defenders and push the middle one straight up between them. Whichever way a defender captures, you recapture with a flank pawn, and the third pawn now has a clear run. Count it out on the board once and you'll never forget it: two defenders cannot cover both diagonals at the same time.

In the opening, advance on a broad front instead of racing one pawn up the board. Move a pawn here, a pawn there, and keep the staircase links forming as you go. You aren't trying to land a blow yet. You're building a wall on one wing and a majority on the other, while giving the computer nothing free to bite. Games between good players are usually decided by whoever creates the first real weakness, so be in no hurry to create one yourself.

Holding your own wall

Defence is mostly patience. Keep your back row at home as long as you can; those pawns are the goalkeepers, and every one you push forward opens a diagonal door behind it. Meet a lone enemy runner early, with a pair of defenders placed so that whichever way it steps, something can take it. And don't chase. A defender lured two squares out of position is often worth more to your opponent than a captured pawn would be. When an enemy pawn crashes into your wall, recapture with the pawn that keeps your remaining defenders connected, not just with the nearest one. A tidy wall bends; a scattered one snaps.

A modern classic

Breakthrough is young by board-game standards. Dan Troyka designed it in 2000, originally on a 7x7 board, and it won the 8x8 Game Design Competition the following year, which is how it settled onto the chessboard-sized grid you see here. It caught on with abstract-strategy players because the rules fit in a sentence yet the play runs deep, and computer scientists still use it to test game-playing programs for exactly that reason: tiny rules, serious tactics. The computer here runs a classic alpha-beta search, and on Hard it will punish a loose pawn the moment you drop one. You move first with the light pawns at the bottom. Choose Easy, Medium or Hard to face the computer, or press 2P to pass the device and play a friend.