TwixT
Play TwixT against the computer, plus the measured crossing geometry: all eight of a peg’s links fit, but each link rules out nine others.
Click an empty point to place a peg. Links to your own pegs a knight's move away form automatically, unless they would cross a link already on the board. You are Red, joining the top edge to the bottom; the computer is Black, joining left to right. Neither may build inside the other's end lines. Everything runs in your browser; nothing is uploaded.
A peg can carry all eight of its links
A peg has eight knight's-move neighbours, and the natural worry is that its own links get in each other's way — that choosing which neighbours to join is part of the skill. It is not. Of the 28 pairs of links leaving a single peg, exactly 0 cross. Links sharing a peg fan out and never meet again, so there is no such thing as a peg that is too connected.
Nor can one enemy link shut a peg down: searched over every link with both ends nearby, the most any single one takes away is 3 of the eight. Cutting a peg off takes several links, which is why blockades in this game are built rather than played in one move.
But each link rules out nine others
The cost is paid by everyone else. Take one link and count the other knight links, of either colour, whose segments it crosses: exactly 9, out of 224 candidates inside a window of 9 points. That is what a link really is — not a connection you made, but nine you took away from the board.
| Direction of the crossing link | How many |
|---|---|
| (2,-1) | 4 |
| (1,-2) | 3 |
| (2,1) | 2 |
Notice which direction is missing from that list: its own. Two parallel links never cross, at any offset anywhere on the board. So a ladder of links all running the same way is always legal however long it gets — which is why TwixT ladders are something you can rely on rather than a pattern you have to check square by square.
And no direction is favoured: each of the eight is crossed by the same 18 placements, so nothing about the geometry rewards building one diagonal over another. The board is as even as it looks.
The opponent here plays a simple forward-and-block heuristic with no search. TwixT is genuinely hard for computers — the crossing rule makes threats non-local — so it is a sparring partner rather than a test.
How to use
- Click an empty point to place a peg.
- Links to your own pegs a knight’s move away form automatically.
- A link is refused if it would cross any link already on the board.
- Red joins the top edge to the bottom; Black joins left to right.
- Neither player may build inside the other’s two end lines.
Frequently asked questions
How many of a peg’s eight links can it actually use?
All eight. Of the 28 pairs of links leaving a single peg, exactly zero cross each other — links sharing an endpoint fan out and never meet again. So there is no such thing as a peg that is too connected, and choosing between a peg’s own links is never something you have to do.
How much does one link block?
Nine other links. Counting every knight link with both ends inside a nine-point window, a single link crosses exactly nine of the 224 candidates. That is what a link really is: not just a connection you made, but nine you removed from the board for both players.
Can two parallel links ever cross?
No, at any offset anywhere on the board. Of the four direction classes a link can be crossed by, its own is missing. That is why a ladder of links all running the same way is always legal however long it gets — you can rely on it rather than checking it point by point.
Does the board favour any direction?
No. Each of the eight knight directions is crossed by exactly the same number of placements, so nothing in the geometry rewards building along one diagonal over another.
Can a single enemy link cut my peg off?
Not close to it. Searching over every enemy link with both ends nearby, the most any one of them takes away is three of your eight. Isolating a peg takes several links, which is why blockades in TwixT are built up over moves rather than played in one.
How strong is the computer opponent?
Not very, and it is better to say so. It plays a simple forward-and-block heuristic with no search at all. TwixT is genuinely hard for computers because the crossing rule makes threats non-local, so treat it as a sparring partner rather than a test.
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