The Story
Where it came from, and why it turned out this way.
DesignWalter Zamkauskas · Argentina, 1988 · first published in the magazine El Acertijo
It started in an Argentine puzzle magazine
The Game of the Amazons was designed by Walter Zamkauskas in Argentina in 1988 and first appeared in the Spanish-language puzzle magazine El Acertijo. It had no major publisher and no commercial push, yet it spread rapidly through the 1990s via the internet and academic circles — for a practical reason: the rules are short enough to fit in an email, while the combinatorial complexity was enough to keep researchers busy for years.
Every turn permanently destroys a square
The mechanism is one sentence: move an amazon exactly as a chess queen moves, then fire an arrow from where it landed, and the square the arrow lands on is sealed forever. Nothing is ever captured; the only thing that changes is that usable space monotonically shrinks. This guarantees the game ends in a finite number of moves — one square burns per turn, so a 100-square board lasts at most 92 turns. There are no draws and no infinite loops.
It is really a combinatorial game theory problem
In the endgame the arrows cut the board into disconnected regions, and once a region can only be entered by your amazons it becomes your territory, after which each side simply burns down their own. The result becomes a pure counting question: whose territory yields more complete turns. That is combinatorial game theory in its most characteristic form, and it explains why Amazons is far better known in academia than among casual players.
A territory's square count is not its turn count
This is where players go wrong. How many turns a territory yields is usually fewer than its number of squares: long narrow shapes, pockets you seal off from yourself, and squares you can enter but not leave all waste capacity. Strong players never compare how many squares they enclosed, only how many complete turns they can still play — and whether a particular partitioning arrow is worth it has to be judged by that same measure.
- Because exactly one square burns per turn, Amazons has a hard upper bound on game length, which is quite unusual among abstract games.
- Arrows fired by both players look identical: they are neutral obstacles belonging to nobody and are never removed.
- Amazons has long been a Computer Olympiad event; its opening branching factor is enormous, since one move selects both a destination and an arrow square, making it a classic stress test for search algorithms.
Complete Rules
Start with what a turn allows and how the game is won.
- Board
- 10 × 10, 100 squares
- Pieces
- 4 amazons per side, White moves first
- Winning conditionon a player's turn, if none of their four amazons can complete a full move-and-shoot, that player loses immediately. So the game is not about capturing but about space: every turn permanently seals one square, and whoever gets sealed in first loses.
- White's four amazons start on A4, D1, G1, and J4, and Black's on A7, D10, G10, and J7. White moves first.
- A turn is one indivisible move-and-shoot: choose one of your amazons and slide it any distance along a rank, file, or diagonal, then fire an arrow from the square where it stopped, along those same eight directions. Moving without shooting is not a legal turn and does not pass the turn.
- Neither amazons nor arrows can pass over anything: your own amazons, the opposing amazons, and every arrow already on the board all block the line, and the range stops one square short of the obstacle.
- The arrow may land on any empty square reachable in a straight line from the new position, including the square the amazon just vacated, since that square became empty when the amazon moved.
- The square an arrow lands on is permanently blocked: it can never be removed, passed through, or occupied again. Arrows from both players are the same neutral obstacle and belong to neither side.
- If a player cannot complete a move-and-shoot with any of their four amazons, they lose at once. Amazons are never captured, and standard play has no draws.
Your First Game
Use this order of thought to get through a complete game quickly.
- The interface completes a turn in two clicks: select one of your amazons and pick a highlighted destination, then pick a highlighted arrow square. Nothing is committed until the arrow is fired, and undo cancels an incomplete action.
- As long as one amazon can move at least one square, the turn can always be completed, because the arrow can always be fired back into the square just vacated. So losing really means all four amazons have been sealed in completely.
- Where the arrow lands usually matters more than where the amazon goes. Before committing an arrow, ask two things: which of my opponent's corridors does it close, and does it also close one of my own escape routes?
- Do not fire arrows to the far side of the board in the opening. Use them first to shrink the range of your opponent's most active amazon.
- Keep your four amazons spread out with several exits each, and avoid crowding two of your own pieces into the same small region where they compete for the same squares.
Practical Strategy
Move from knowing the rules to playing with a plan.
- The goal is not to hunt enemy pieces but to partition the board. The arrow that splits the open space into two disconnected regions is usually the most valuable one available.
- Once a region can only be entered by your amazons, it becomes your territory, and from then on every turn you can safely burn one square inside it while your opponent burns theirs.
- Judge who is ahead by comparing how many complete turns each side can still play inside their own territory, not by comparing how many squares each territory contains.
- Territories often yield fewer turns than they have squares: long narrow shapes, pockets you seal off from yourself, and squares you can enter but not leave frequently go unused. Account for these defects before you commit to a partition.
- The classic partitioning technique is to occupy a narrow corridor with an amazon and then seal the other side of the corridor with the arrow, completing the split in one turn.
- In the middlegame, try to keep your amazons where they can enter two different regions, so that whichever side your opponent seals first, you still have a choice.
Winning and Special Rules
Details that are easy to miss but can change the result.
- Every turn converts exactly one empty square into an arrow, so a game ends after at most 92 turns. Infinite games are impossible and there are no draws.
- Arrows from both players look identical because they are neutral obstacles; only the crowned pieces on the board are movable amazons.
- The move and the shot are animated in order, and the turn passes only after the arrow actually lands — before that, the game state has not advanced.
- Once the two territories are completely separated, the result is already determined by how many turns each side has left, and the remaining play is just burning them down square by square.
Common Mistakes
The traps new players fall into most often.
- Mistaking the neutral arrow obstacles for enemy pieces. Arrows fired by both players look identical, belong to nobody, and are never removed from the board.
- Focusing on blocking your opponent without checking whether the arrow also cuts off your own amazon's exit.
- Treating a territory's square count as its turn count and ignoring the waste that its shape causes.
- Assuming the turn is over once the move is made, and forgetting the shooting half — until the arrow lands, nothing has advanced.
- Treating amazons as capturing pieces and trying to move onto a square occupied by an opponent.