Lines of Action
Play Lines of Action, plus the measured reason capturing is usually a mistake — and the one rule that flips that answer completely.
Click one of your pieces, then a highlighted square. A piece moves along a rank, file or diagonal exactly as many squares as there are pieces on that whole line, counting both colours. It may leap its own pieces but not enemy ones, and may land on an enemy piece to take it. You win by getting all your pieces into one group, diagonal contact counting. Everything runs in your browser; nothing is uploaded.
Being captured helps you
The goal is to gather your pieces, so every piece you own is another one you have to bring home — and every piece your opponent takes is one fewer. A capture is not a gain; it is a gift. Here is what that costs, varying only how often Black takes a capture when one is offered, against a White who takes them half the time.
| Black takes a capture | Black wins | Median game length | White pieces left at the end |
|---|---|---|---|
| never | 100.0% | 47 plies | 12 |
| a quarter of the time | 95.0% | 54 plies | 7 |
| half the time | 43.5% | 55 plies | 2 |
| three quarters of the time | 7.7% | 43 plies | 1 |
| always | 1.3% | 33 plies | 1 |
From certainty to almost never, on nothing but a willingness to take material. The right-hand column is the mechanism in plain sight: a Black who never captures leaves White all 12 pieces to gather, and a Black who always captures grinds White down to 1 — which is a position White cannot lose.
Except one rule decides whether any of that is true
Whittle someone down to a single piece and that piece is, trivially, all in one group. The usual reading is that they have therefore won. Some play it the other way round. Flip that one choice — the selector at the top of this page does — and the whole table turns over.
| Black takes a capture | Lone piece wins | Lone piece loses |
|---|---|---|
| never | 100.0% | 24.2% |
| a quarter of the time | 95.0% | 27.7% |
| half the time | 43.5% | 53.8% |
| three quarters of the time | 7.7% | 70.3% |
| always | 1.3% | 80.2% |
Under one rule, capturing everything wins 1.3% of games. Under the other it wins 80.2%. That is not a difference of degree — the strategy points in the opposite direction. Advice about captures in this game is worth nothing unless it first says which version is being played, and "take material when it is offered", the reflex every other board game teaches, is the losing move under the commoner rule.
What these numbers are
6,000 games, played by policies that move at random except for how often they take an available capture. So they measure the pull of the rule — which way the game leans if nobody is steering — rather than what strong play looks like. A good player would avoid being reduced to one piece precisely because they can see it coming.
Every one of those games finished inside the move limit, so none of the curve rests on abandoned games — worth stating, because a policy that never captures produces long games and an abandoned-game column is exactly where a bias would hide.
The table is frozen — six thousand playouts take about a minute. To stop it going stale, 30 fresh games at each end of the curve are played on every build: never-capture wins 100% and always-capture wins 0%.
How to use
- Click one of your pieces, then a highlighted square to move it.
- A piece moves along a line exactly as many squares as there are pieces on that whole line, both colours counting.
- You may leap your own pieces but not enemy ones, and you may land on an enemy to capture.
- Win by getting all your pieces into a single group, diagonal contact counting.
- Switch the lone-piece rule to see the strategy reverse.
Frequently asked questions
How does a piece move in Lines of Action?
Along a rank, file or diagonal, exactly as many squares as there are pieces standing on that entire line, counting both colours. So the same piece has four different move distances, and they change every time anything moves anywhere on those lines. It may leap over its own pieces but not over enemy ones, and it may land on an enemy piece to capture it.
Is capturing a good idea?
Usually not, and this is the thing that makes the game strange. You win by gathering your pieces into one group, so every piece your opponent has is another one they must bring home. Taking one shrinks their problem. Measured over 600 random games each: a player who never captures wins 100 per cent, and one who always captures wins 1.3 per cent.
What happens if a player is reduced to one piece?
A single piece is trivially all in one group, so under the usual reading that player has won. Some groups play it as a loss instead. It sounds like an edge case and it is the most important rule in the game.
How much does the lone-piece rule change things?
It reverses the strategy completely. With a lone piece counting as a win, always capturing wins 1.3 per cent of games and never capturing wins 100. With it counting as a loss, always capturing wins 80.2 per cent and never capturing wins 24.2. Not a difference of degree — the advice points the opposite way, so any advice about captures is worthless unless it says which version is meant.
Are these figures from strong play?
No, and that matters. They come from 6,000 games played by policies that move at random except for how often they take an available capture, so they measure which way the game leans when nobody is steering. A good player would avoid being whittled down to one piece precisely because they can see it coming.
Does this send anything anywhere?
No. The game and the playout study both run entirely in your browser and nothing is uploaded.
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