Historical Hnefatafl 7x7 initial setup.
At the moment we use these setups for the Hist. Hnef. 7x7:
Brandubh (forbidden throne and corners):
Ard Ri (no forbidden squares):
Although the two setups are playable, the balances are not too good:
Brandubh balance +1.44
Ard Ri balance +1.47
The setups of game pieces for the two variants are the same, only some rule details differ, and it's interesting that the two balances end up practically the same.
Could setting the game pieces in another way result in better game balances?
An algorithm found all setups for the 7x7 board; there are 78 possible setups.
Ignoring setups where one party wins immediately or kills opponent pieces immediately, left are 9 setups.
Code: Select all
27.
- - - b - - -
- - - b - - -
- - - w - - -
b b w K w b b
- - - w - - -
- - - b - - -
- - - b - - -
Brandubh balance known +1.44
28 .
b - - b - - b
- - - - - - -
- - - w - - -
b - w K w - b
- - - w - - -
- - - - - - -
b - - b - - b
29.
- - - b - - -
- b - - - b -
- - - w - - -
b - w K w - b
- - - w - - -
- b - - - b -
- - - b - - -
Brandubh balance known +1.47
31 .
b - - - - - b
- - - b - - -
- - - w - - -
- b w K w b -
- - - w - - -
- - - b - - -
b - - - - - b
32.
- - - - - - -
- b - b - b -
- - - w - - -
- b w K w b -
- - - w - - -
- b - b - b -
- - - - - - -
34 .
b - - - - - b
- b - - - b -
- - - w - - -
- - w K w - -
- - - w - - -
- b - - - b -
b - - - - - b
37.
- b - - - b -
b - - - - - b
- - - w - - -
- - w K w - -
- - - w - - -
b - - - - - b
- b - - - b -
Not usable for Brandubh
38.
- - b - b - -
- - - - - - -
b - - w - - b
- - w K w - -
b - - w - - b
- - - - - - -
- - b - b - -
Brandubh balance known +1.82
39.
- - - - - - -
- - b - b - -
- b - w - b -
- - w K w - -
- b - w - b -
- - b - b - -
- - - - - - -
Hypothesis:
One or more of these setups could result in better 7x7 game balances.
And while we're at it: The Ard Ri should have a throne if possible, since the Buckquoy board clearly has a marked throne.