Amazons — 2,176 Opening Moves
Play Game of the Amazons against the computer, and see why a game with a hundred times chess's opening width is still over in 92 moves.
Click one of your amazons, then where it should go, then where it should shoot. Both the move and the shot travel like a queen. A burnt square is gone for good, and whoever runs out of moves loses.
2,176 legal opening moves
A move is three decisions at once — which amazon, where it slides, where it shoots — and every combination is legal. Counting them all on the standard opening:
| Game | Legal first moves | |
|---|---|---|
| Amazons (10×10) | 2,176 | |
| Amazons (8×8) | 1,232 | |
| Amazons (6×6) | 386 | |
| Go (19×19) | 361 | |
| Chess | 20 | |
| Draughts | 7 |
That is 109 times chess and six times go, and it is the practical reason Amazons stayed hard for computers long after chess had fallen. You cannot search a tree you cannot even enumerate quickly.
The total splits as 4 × 544 — each amazon offering exactly the same number, which looks like a coincidence. It is not. All eight symmetries of the square leave the opening position unchanged, and the group is transitive on the eight starting squares, so every amazon on the board is looking at the same geometry. Move any one of them a single square and the counts scatter immediately.
It stays wide for a long time
A large opening would not matter much if it collapsed straight away. Average legal moves at each stage of a game:
| Moves played | Choices available | |
|---|---|---|
| 0 | 2,176 | |
| 5 | 1,537 | |
| 10 | 1,171 | |
| 20 | 519 | |
| 40 | 128 | |
| 60 | 24 | |
| 80 | 1 |
Ten moves in it is still offering more than a thousand choices — more than fifty times a typical chess position. It only becomes narrow near the very end, by which point the game is already decided.
And yet it cannot last more than 92 moves
Every move burns exactly one square, permanently, and no square ever comes back. The board has 100 squares and eight hold amazons, so there are 92 squares available to burn and the game cannot possibly run past 92 moves. No clock, no repetition rule, no draw — the game is finite by construction, which is a rarer property than it sounds.
| Average length | Longest seen | |
|---|---|---|
| Random play, 200 games | 71.8 moves | 85 |
| Both sides trying to prolong it | 87.3 moves | 91 |
| The ceiling | — | 92 |
So the bound is nearly tight, but ordinary games fall well short of it — and the reason is not that the board fills up. Games end when someone's amazons are walled into a pocket with nowhere to go. Often both sides get walled in at once: in random play about one game in seven ends with neither side able to move, stranding around twenty squares that nobody could ever have reached. Those squares never get burnt, and that is the whole gap between 71.8 and 92.
Whether a full 92 is actually attainable is a separate question, and one I did not settle. The longest game found here is 91, with both sides cooperating to drag it out.
How to use
- Click one of your amazons, then the square it should move to.
- Then click where it should shoot — both travel like a queen.
- A burnt square is gone permanently and blocks everything.
- Whoever runs out of legal moves loses; there are no draws.
Frequently asked questions
How many opening moves does Amazons have?
Exactly 2,176 on the standard ten by ten board. A move is three decisions at once — which of your four amazons, where it slides, and where it shoots — and every combination is legal. Chess opens with 20 moves and go with 361.
Why is Amazons hard for computers?
The branching factor. It is roughly a hundred times chess at the start, and it does not collapse quickly: ten moves in a position still offers over a thousand choices. You cannot search a tree you cannot enumerate quickly, which is why strong Amazons programs arrived long after strong chess programs.
Why does each amazon have exactly the same number of moves?
Because of symmetry, not coincidence. All eight symmetries of the square leave the opening position unchanged, and the group is transitive on the eight starting squares, so every amazon sees identical geometry — 544 moves each, four of them, giving 2,176. Shift one amazon by a single square and the counts scatter at once.
How long can a game of Amazons last?
At most 92 moves. Every move burns exactly one square permanently, the board has 100 squares, and eight of them hold amazons — so there are only 92 squares available to burn. The game is finite by construction, with no clock, no repetition rule and no draws.
Do games actually reach 92 moves?
No. Random play averages about 72 moves and the longest game found here was 91, with both sides deliberately trying to drag it out. Games stop short because amazons get walled into pockets rather than because the board fills.
Can both players run out of moves at once?
Yes, and it happens surprisingly often — roughly one random game in seven ends with neither side able to move, leaving about twenty squares that nobody could ever have reached. Those squares never get burnt, which is most of the gap between a typical game and the 92-move ceiling.
How does a game of Amazons end?
The player who cannot move loses. Since every move removes a square and no square ever returns, the space runs out and someone is eventually sealed in. There is no other ending and no way to draw.
Does this send anything anywhere?
No. The game and the opponent both run entirely in your browser.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.