Tafl, meaning 'table', is a war game for two players originating in Scandanavia and migrating through the Germanic lands and anywhere else the Vikings/Norse went. A great many forms of the board are documented or reliably speculated and versions of the game were played throughout period and are still played in the present century. If your persona is western European, it's likely they might have encountered some variation of Tafl. Hneftafl is simply a change of name, adding hnef (king) to tafl, likely because of the games known as 'tables' brought through Europe by the Romans and altered through the years. Different board and army sizes also carried different names, from the giant Alea Evangeli (19x19) to the relatively small Tablut (7x7).
Tafl and its variants are played on a square board marked with places to put pieces. In their original form, the points of intersecting lines were used; more modern variants, and indeed modern players, seem to prefer playing in the squares. The hard rule is that each grid needs to have an odd number of rows and columns, since there must be a center point or square upon which to place the king at the beginning of play.
Two armies are needed, traditionally dark defending the king and light attacking. The exact number of each side is determined by board size though the attacking army is larger than the defending side. The king piece is bigger than his defenders. For the form of pieces and other board sizes and layouts, refer to the sites listed in Sources or contact me. I'm always delighted to discuss games.
The rules vary from source to source. I'm presenting here a standardized set of rules plus a few variants. With agreement between the players, plausible variants can easily be decided upon and played. Which side begins play is unclear in period sources, so the players should decide this before the game starts. In Tafl it seems it is customary for the defending side to move first.
1. All pieces move orthographically in any direction - along the lines/squares, never diagonally. They may move any number of spaces but may not jump over any other piece.
2. Only the king may occupy the center square, but other pieces may pass over it.
3. Captures of regular men are made by enemy pieces occupying spaces adjacent to it along one row or column of the board. XOX is a capture of O by two X pieces. The same arrangement works 'vertically'. A piece may be moved between enemy men safely without being captured. Captured pieces are removed from the board.
4. The king is captured by being flanked on all four sides by enemy pieces.
5. The attacking player wins by capturing the king.
6. The defending player wins by moving the king to the outside rank of the board where he cannot be surrounded. When there is a clear path from he king to and edge space, the defending player must call "Raichi" to warn his opponent. If two such routes exist, the defending player calls "Taichi" and wins, since the attacking player cannot block two escape routes in a single move.
Some variants, each to be considered individually and used or ignored by mutual agreement (some work best on larger boards and hamper play on smaller ones):
1. Only the defender's pieces may pass over the center space, never the attackers'.
2. The king may not assist in captures.
3. Spaces occupied by pieces at the beginning of the game belong to their respective armies and no enemy piece may occupy them (or in other variants, even pass over them).
4. The center space may make the place of a second piece for purposes of capture; sandwiching an enemy piece between one of your pieces and the center space constitutes a capture.
There are other variants, I only included the most common ones here.