Is Hnefatafl Solved? No Tafl Game Has Been Yet

No. As of 2026, no tafl game has been solved: not Copenhagen Hnefatafl on 11×11, not Tablut, and not even Brandubh on 7×7, the smallest common variant. Nobody has proven which side wins with perfect play. What does exist is a handful of research papers estimating how hard solving would be, plus large sets of results from online games that show how the sides fare in practice.

What “solved” means

A game is solved when someone proves the result of perfect play from the starting position: first player wins, second player wins, or draw. Usually that takes a computer checking an enormous number of positions.

Checkers is the famous example. A University of Alberta team led by Jonathan Schaeffer finished solving it in 2007 after about 18 and a half years of computing, working through roughly 500 billion billion positions (5 followed by 20 zeros). The answer: a draw. Connect Four was solved back in 1988 (the first player can force a win). Chess is not solved.

For hnefatafl, a solution would settle the question players argue about most: does the king escape, or get caught, when neither side makes a mistake?

The closest anyone has come: Brandubh

Brandubh is the obvious first target, because it’s tiny: a 7x7 board, a king, 4 defenders, and 8 attackers. In a paper posted in 2021, Kiernan Compy, Alana Evey, Hunter McCullough, Lindsay Allen, and Aaron Crandall counted how many positions the game could possibly have. Their upper bound is around 10¹⁴ states, which puts Brandubh between Connect Four and checkers. The authors said this should make the game tractable for a full solution and named solving it as their goal.

That paper measured the size of the problem. It didn’t solve it. We found no later publication reporting a solution to Brandubh, and Wikipedia’s list of solved games doesn’t mention any tafl variant.

Tablut got the same treatment. Andrea Galassi’s 2021 paper describes it as a game that “has not been solved nor properly studied yet” and puts its complexity in the same range as checkers. Checkers took more than 18 years of computing, so that comparison isn’t encouraging.

Why the big boards resist solving

The Brandubh paper cites a rough estimate by Slater that 11×11 hnefatafl has about 10⁴³ possible positions. Standard comparison tables put chess around 10⁴⁴ and checkers around 10²⁰. So the game most people play online is, by that measure, in the same weight class as chess, and roughly 10²³ times bigger than checkers.

Why so big? The move count, the piece count, and the rules all push the numbers up:

• Long moves. Every piece slides any distance, like a rook. In Copenhagen the attackers have 116 legal first moves, counted with this site’s rules engine. Brandubh has 40.
• Lots of pieces on a big board. Copenhagen starts with 37 pieces on 121 squares, and they can be arranged in a huge number of ways as captures thin them out.
• Games that loop. Pieces can shuffle back and forth, so a solver has to handle repetition instead of assuming every game ends.

There’s a theory result too. In 2023, Kyle Burke and Craig Tennenhouse showed that a variant where captures are compulsory is PSPACE-hard when played on boards of any size. In plain terms, it belongs to a class of problems for which no efficient general method is known. That’s a result about a modified game, but it points the same way: bigger tafl boards get hard fast.

What we know about balance instead

Without a proof, the best evidence is results. The site aagenielsen.dk keeps balance statistics from full pairs of online games, where each player takes both sides. The figures below were checked in September 2026:

• Copenhagen Hnefatafl: across 13,640 games, defenders won about 1.36 games for every attacker win. Among the strongest players (rating above 1900, 1,418 games) the ratio falls to 1.07, close to even.
• Brandubh: across 2,318 games, defenders won about 1.62 games for every attacker win. Among the strongest players the lean gets bigger, not smaller, though that sample is only 364 games.

That’s evidence about how humans play, not proof about perfect play. It’s still useful: Copenhagen gets closer to even as players improve, and Brandubh doesn’t. The is hnefatafl balanced page covers what that means for choosing a variant.

Engines add another angle. Hobby projects have trained AlphaZero-style programs for 11x11 hnefatafl purely by self-play, the approach DeepMind used for chess and Go. However strong such an engine gets, it isn’t a solution. It can still be wrong about who wins a position.

So which side wins with perfect play?

Nobody knows, for any variant. If you want a practical answer, play pairs of games with sides swapped, which is how serious players already handle it. You can try that against the computer on the homepage, and the strategy guide covers how to play each side.