Tawlbwrdd summary

Tawlbwrdd board, Robert ap Ifan 1587.

Summary on the Welsh Tawlbwrdd.

Initial orderings proposed for tawlbwrdd 11x11 have been combinations of

Defenders' ordering:

Diamond or
Cross.

Attackers' ordering:

T-ordering,
```
. . b . .
b b b b b
```
Bell
```
. b .
b . b
b b b
```
or Lewis
```
b b b
b b b
```

These formations can be combined in 5 ways: T diamond, T cross, Bell diamond, Lewis diamond and Lewis cross.
To that comes that the board can contain a throne square or not. The game with a throne will be called Tawlbwrdd, and the game with no throne will be called "Tawlbwrdd throneless" (historical sources indicate that the Welsh tawlbwrdd has a throne, just like the Saami Tablut).

This makes in all 10 possible initial setups for the Tawlbwrdd 11x11 game. In any case the Tawlbwrdd king is armed, is captured from two sides and wins on the edge.

The game balances for the 10 setups were measured through test tournaments:

Board setup	Tawlbwrdd throneless	Tawlbwrdd (throne)
Lewis diamond	+1.67 (b begins)	+1.49 (b begins)
Lewis cross	-1.21 (b begins) -1.23 ? (w begins)	-1.07 (b begins) -1.16 ? (w begins)
T cross	-3.00 (b begins)	-2.10 (b begins)
T diamond	-3.89 (b begins)	-1.88 (b begins)
Bell diamond	-1.57 (b begins)	-1.21 (b begins) +1.08 (w begins)

The measured game balances confirm, that a throne square protects the king and to some degree is a help to the defenders. Though in some setups the throne seems to make very little difference.

The best balanced setups are found to be Tawlbwrdd throneless Lewis cross and Tawlbwrdd Bell, both very well balanced.

Wikipedia says:

This variant was played in Wales. It is described as being played with 8 pieces on the king's side and 16 on the attacker's side. Robert ap Ifan documented it with a drawing in a manuscript dated 1587. His version was played on an 11x11 board with 12 pieces on the king's side and 24 on the opponent's side. His passage states:
The above tawlbwrdd should be played with a king in the centre and twelve men in the places next to him, and twenty-four men seek to capture him. These are placed, six in the centre of each side of the board and in the six central positions. And two move the men in the game, and if one [piece] belonging to the king comes between the attackers, he is dead and is thrown out of the game, and the same if one of the attackers comes between two of the king's men in the same manner. And if the king himself comes between two of the attackers, and if you say 'Watch your king' before he moves to that space, and he is unable to escape, you capture him. If the other says 'I am your liegeman' and goes between two, there is no harm. If the king can go along the [illegible] line, that side wins the game.

In the Robert ap Ifan text, a diagram shows that the Tawlbwrdd game board has a throne.

Furthermore,

twenty-four men seek to capture him. These are placed, six in the centre of each side of the board and in the six central positions

seems to be a good description of the Lewis attackers' setup.

And the

a king in the centre and twelve men in the places next to him

fits with a diamond defenders' setup.

We tested the Tawlbwrdd Lewis cross and Tawlbwrdd Bell setups more thoroughly, and found that the Tawlbwrdd Bell setup results in the more interesting games.

If considering the possibility of the king to win on special corner squares here:
It's much harder for the king to reach a corner than to reach an edge, so the only candidate setup for win in corner is the Lewis diamond.
We know from the Linné Saami Tablut 9x9 board and the Robert ap Ifan Welsh Tawlbwrdd 11x11 board, that both boards have a throne and no special corner squares, indicating win on edge.

So, these test tournaments indicate that the most likely setup for the historical Tawlbwrdd is the Tawlbwrdd Bell 11x11.
(Tawlbwrdd Bell was proposed by Arne Hansen ("arne64") already December 2012.)

Tawlbwrdd Bell

More about the Welsh Tawlbwrdd in our forum.
Test tournament.

Update June 13, 2022:
If in Tawlbwrdd Bell 11x11 white begins, then the game balance becomes +1.08, which is better.
When black begins, the game balance is -1.21.