Hnefatafl
Play Hnefatafl (Brandubh) with the disputed rules as switches, plus measured win rates showing one rule swings the game 80 points.
Everything moves like a rook — any distance along a rank or file, nothing jumping. Capture by sandwiching an enemy between two of your pieces. Only the king may stand on the throne or a corner, and those squares help either side make a capture. Attackers move first. Everything runs in your browser; nothing is uploaded.
One disputed rule swings the game eighty points
Nobody knows exactly how tafl was played, so modern sets pick their own answers to three questions: where the king must reach, whether he can help capture, and what it takes to capture him. Those look like three comparable choices. They are not remotely comparable.
| King escapes to | King captured by | Attackers win | Defenders win | Mean length |
|---|---|---|---|---|
| a corner | surrounding on four sides | 4.9% | 95.1% | 46.1 plies |
| a corner | an ordinary sandwich | 85.0% | 15.0% | 20.1 plies |
| any edge | surrounding on four sides | 0.5% | 99.5% | 12.4 plies |
| any edge | an ordinary sandwich | 26.6% | 73.4% | 11.4 plies |
Change nothing but how the king is captured and a game the defenders win 95 times in 100 becomes one the attackers win 85 times in 100 — a swing of 80 points. That is not a tweak, it is a different game with the same pieces. The escape target matters too, though less violently.
Worth noting what the piece count does not tell you. The attackers outnumber the defenders two to one, which reads as decisive, and under the classic rules it is simply wrong: the defenders take better than nine random games in ten. Being outnumbered is not being behind when your win condition is to run away.
And another, argued over just as hard, decides nothing
Whether the king may act as one jaw of a sandwich is the rule reconstructions fight over most. Across all four other settings it moves the result by at most 0.37 of a point — and under corner escape with an ordinary sandwich it changed nothing at all, 2551–449 either way. Set against 80 points for the capture rule, the two arguments are not the same size.
The tempting explanation is that the rule never comes up. It does. Resolving every position twice — once with the king armed, once not — finds 121 of 1,500 games containing a capture that happens only because the king is armed, 129 such captures out of 2,983. So the rule fires perfectly often and still decides nothing, which is a different and more interesting claim than "it never applies".
24,000 games, all of which reached a real ending. These are random players, so the table describes which way each rule set leans rather than what strong play looks like — the opponent on this page is one ply of lookahead and no more. The table is frozen; a fresh sample of 200 games per rule runs on every build, coming out at 4.5% and 82.0%.
How to use
- Everything moves like a rook — any distance along a rank or file, nothing jumping.
- Capture by sandwiching an enemy piece between two of yours.
- Only the king may stand on the throne or a corner, and those squares help either side capture.
- Defenders win by getting the king out; attackers win by capturing him.
- Switch the escape and king-capture rules to see the balance move.
Frequently asked questions
Which side is Hnefatafl balanced towards?
It depends entirely on which rules you use, which is the whole problem with the question. Under the classic set — king escapes to a corner, captured only by being surrounded on all four sides — the defenders win about 95 per cent of random games. Change only the capture rule to an ordinary two-piece sandwich and the attackers win about 85 per cent.
Do the attackers not have an advantage with twice the pieces?
No, and the piece count is misleading. The attackers start with 8 against 4 plus the king, which reads as decisive, but the defenders only need to run away. Under the classic rules the outnumbered side takes better than nine random games in ten.
Which disputed rule matters most?
How the king is captured, by a very long way. Surrounding on four sides versus an ordinary sandwich moves the result by about 80 percentage points. The escape target matters too — corner versus any edge — though less violently.
Does it matter whether the king can help capture?
Almost not at all, which is striking because it is the rule reconstructions argue over most. Across every other setting it moves the result by at most a third of a percentage point, and in one case by literally nothing.
Is that because the armed-king rule never comes up?
No, and that is worth separating. Resolving every position twice, once with the king armed and once not, finds a capture that depends on it in 121 of 1,500 games — 129 captures out of 2,983. The rule fires perfectly often and simply does not change who wins, which is a different claim from it never applying.
Does this send anything anywhere?
No. The game and the rule study both run entirely in your browser and nothing is uploaded.
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