Peg Links: building a chain the computer cannot cut
Peg Links is a connection strategy game where you place pegs on a grid and link them a knight's move apart, racing to build an unbroken chain from your edge to the opposite side before the computer does the same. The twist is that links can never cross, so every connection you make is also a wall against your opponent.
How the game works
You and the computer take turns placing a single peg on the board. Your pegs go on any free hole except the side columns and the four corners. The computer plays on any free hole except the top and bottom rows and the corners. After each placement, links form automatically between your new peg and any of your existing pegs that sit a knight's move away. A knight's move is two squares in one direction and one square at right angles, the same L-shape as the chess piece.
Your goal is to build an unbroken chain of links from the top row to the bottom row. The computer is trying to chain from the left column to the right column. The first side to complete a connection wins. If a potential link would cross any existing link, whether yours or the computer's, it is not created. Links never cross.
Controls and board layout
Tap or click any free hole to place your peg. The top and bottom rows are your home edges, and the side columns belong to the computer. The four corner holes are dead and belong to nobody. After you place a peg, the computer responds with its own peg, and then it is your turn again.
The scoreboard shows how many pegs each side has placed and how many links you have formed. Three difficulty levels are available. Gentle plays on a ten-by-ten grid with a simple computer. Normal plays on twelve-by-twelve with moderate thinking. Sharp plays on the same twelve-by-twelve grid but with a stronger computer that checks whether your next move would complete your chain and blocks it.
Why links cannot cross
The no-crossing rule is what makes the game strategic rather than a race to place the most pegs. Every link acts as a barrier. If you draw a diagonal link across the middle of the board, the computer cannot create any link that would intersect it. This means your connections actively cut off the computer's options, and the computer's links do the same to you.
The crossing check is a real geometric test on the line segments, not a lookup table. Two links cross when they properly intersect in the interior, not when they share an endpoint at a peg. This means two links meeting at the same peg are fine, but two links that cut through each other in empty space are forbidden.
Strategy: blocking and building at once
Because links cannot cross, a peg placed across the computer's likely path usually earns you links of your own as a side effect. The best moves are ones that do both: extend your chain towards the far edge and block the computer's route at the same time.
Look for spots where the computer's chain is starting to form a clear path from left to right. Placing a peg in the middle of that path often creates links that physically block it while also adding to your own network. Moves that only block, without earning you any useful links, are weaker because they do not advance your own position.
Strategy: building redundant paths
A single chain of links from top to bottom is fragile. It is a single chain of cut points, meaning the computer can sever it by placing one peg that blocks a critical link. Two loosely parallel paths are far harder to stop. Even if the computer blocks one, the other is still alive.
Do not build a straight narrow ladder down the board. Instead, spread your pegs so that your links form a broad front with multiple connections. Think of it as building a net rather than a rope. A net can lose a few strands and still hold together. A rope snaps when one strand breaks.
When two of your pegs sit so that two different knight's moves could connect them, that pair is nearly impossible to cut. Blocking one potential link still leaves the other. Place pegs with this kind of redundancy in mind.
Strategy: using the edges
Your home edges, the top and bottom rows, are where your chain must start and end. You need at least one peg on the top row that connects into your network, and at least one on the bottom row. Getting those anchor pegs placed early gives you something concrete to build towards.
The computer's home edges are the side columns. You cannot place pegs there, but you can place pegs near them to create links that block the computer from connecting to its own edge. A peg one or two squares in from the computer's side column, with links that reach across the column's territory, can shut down an entire side of the board.
The corners are dead, so neither side can use them. This means the very first and last cells of each edge are unavailable. Account for this when planning where your chain will touch the edge.
How the computer thinks
The computer scores every free hole by counting how many links it would gain, measuring how far its chain would spread across the board, and favouring holes near the centre. On Normal difficulty, it also considers how good a hole would be for you, so it sometimes steals a move you were about to make. On Sharp difficulty, it checks whether any hole would let you complete your chain on your next turn and plays there first.
The computer does not look ahead many moves. It makes a greedy choice on each turn, with a small random element so it does not always play the same game. This means it can be outmanoeuvred by long-term planning. If you set up a position where two different moves would both complete your chain, the computer can only block one of them.
Common beginner mistakes
- Building one narrow chain down the middle. A single line is easy to cut. Spread your pegs to create redundant paths.
- Ignoring the computer's progress. A chain at sixty percent across the board is two or three moves from winning. Check their side regularly.
- Playing only on your own home rows. Edge pegs are needed to anchor the chain, but the connection work happens in the middle of the board.
- Forgetting that links form automatically. You cannot choose to decline a link in this version. A link that gets in your own way later cannot be removed, so think about what links a peg will create before you place it.
- Placing pegs far from any of your existing pegs. A peg with no knight-move neighbours earns no links and does nothing for your chain.
- Trying to play on the side columns or corners. Those holes are reserved for the computer's edges or are dead zones.
Difficulty levels explained
Gentle uses a ten-by-ten board. The computer scores each hole based only on how many links it would earn and where the hole sits relative to the centre. It does not consider your moves. This level is forgiving and good for learning the link mechanics.
Normal increases the board to twelve-by-twelve and adds a defensive component. The computer scores each hole for both itself and for you, and partially weights how good the hole would be in your hands. It will sometimes take a hole that would have been strong for you, even if it earns fewer links of its own.
Sharp keeps the twelve-by-twelve board and adds a direct block check. Before scoring holes the normal way, the computer looks at every hole to see if placing your peg there would complete your chain. If so, it takes that hole immediately. This prevents you from winning with a single obvious finishing move and forces you to set up positions where two or more holes would each win the game.
Nothing leaves your browser
The board, the computer's thinking, and your game history all run inside this page. The crossing test, the link detection, and the chain check are all computed on your device. There is no server, no account, and no data sent anywhere. Your best result is saved in local storage on this device and stays there. Once the page has loaded the game works without a network connection.