Summary on the Scottish Ard Ri.
The attackers can be set up in two ways, here called cross and circle. (Reuse of diagrams - there are no forbidden corner squares on the Ard Ri board.)
To that comes that the board can contain a hostile throne, a friendly throne, or no throne. (Although a throne does appear on the historical Ard Ri board, we test with no throne also.)
The king can be armed, hammer only or unarmed. (David Brown mentions the choice of a hammer-only king in his rules for the David Brown Hnefatafl 11x11.)
This makes in all 18 possible setups for the Ard Ri 7x7 game. In any case the Ard Ri king is captured from two sides and wins on the edge.
(If necessary, pieces limited to one step per move could also be explored.)
The game balances of the setups are measured through test tournaments:
|Hostile throne||Friendly throne||No throne|
|King armed||1) ?||4) ?||7) ?||10) ?||13) +1.64 (119 games)||16) +inf. (5 games)|
|King hammer only||2) ?||5) ?||8) ?||11) ?||14) ?||17) ?|
|King unarmed||3) +6.33 (22 games)||6) ?||9) +3.40 (22 games)||12) +3.92 (32 games)||15) -3.40 (22 games)||18) ?|
The setups 3), 9) and 12) are heavily unbalanced in favour of white (the defenders). Setups 9) and 12) indicate that circle setup favours white even slightly more than cross; thus 6) is probably also unbalanced in favour of white. All these ( 3), 6), 9) and 12) ) have king unarmed. King hammer only and king armed favour white even more; thus all the setups shown in the table with hostile and friendly throne must be unbalanced in favour of white.
Left are only setups with no throne. We already found a reasonable balance of setup 13) (balance +1.64). 14), 17) and 18) are unknown.
However, the historical Buckquoy board shows, that the historical setup must have a throne square.
So one-step setups were investigated also:
As in Magpie 7x7, the king can only move one step at a time.
So, the result of the Ard Ri tests is that we stick to the one configuration we found balanced:
Ard Ri throneless 7x7, balance +1.64.