Rasmus Holbroe vikings
Artist: Copyright © Rasmus Holbroe (Jan. 2016).

Measured tafl game haphazardness.

Tafl variant Game balance Game haphazardness
Sea battle tafl 13x13
(modif. Parlett setup)
+1.09 32.3 %
Simple Tafl 11x11
Tawlbwrdd throneless Lewis cross 11x11
+1.07 49.7 %
Historical Hnefatafl 7x7 (Scottish Ard Ri)
Tawlbwrdd throneless 7x7
+1.50 46.0 %
Copenhagen Hnefatafl 11x11 +1.46 41.4 %
Fetlar Hnefatafl 11x11 +1.39 42.7 %
Magpie cross 7x7 -1.12 63.6 %
Berserk Hnefatafl 11x11 +1.20 46.8 %
Sea battle tafl 11x11
Sea battle cross 11x11 (Dardell)
+1.07 38.5 %
Old Hnefatafl 11x11 +1.12 34.0 %
Sea battle diamond 11x11 -1.28 32.8 %
Sea battle 9x9 (Imperial Contest) +1.61 37.7 %
Historical Hnefatafl 9x9 (Saami Tablut) -1.09 51.0 %
Historical Hnefatafl 7x7 (Irish Brandubh)
Brandubh cross 7x7
+1.30 42.8 %
Historical Hnefatafl 13x13
(Parlett setup)
-1.13 50.0 %
Tawlbwrdd Lewis cross 11x11 -1.12 62.1 %
Historical Hnefatafl 11x11 (Welsh Tawlbwrdd)
Tawlbwrdd Bell 11x11
-1.08 49.4 %
Sea battle T 9x9 +1.61 52.2 %
Sea battle circle 11x11 (Nielsen) +1.21 54.5 %
Sea battle circle 9x9 +1.44 66.7 %
Foteviken tablut 9x9 +1.71 67.2 %

( Skalk Hnefatafl: Identical to Tawlbwrdd, except that corners are added (king wins in corner).
Foteviken Tablut: Rules.
)

The tafl game haphazardness is calculated as:
(number of games where, after adjusting for game balance, a lower rated player wins against a higher rated player) divided by (number of games) and *2. Draws are counted as half wins.
The game haphazardness is the percentage of games where a weaker player beats a stronger player *2.

Example:
In Skalk Hnefatafl 11x11 (game balance -3.77) a white player rated 1740 against a black player rated 1500 both have the same chance of winning.
Thus if a white player rated 1600 beats the black player rated 1500, then the outcome is unexpected and counted.

Imagine some completely uncontrollable game, where the outcome is like throwing a dice. The higher rated player would win half the games and lose half the games, and the game haphazardness would be 100%.
In a completely controllable game, where the higher rated player always wins, the game haphazardness would be 0 %.


Updated 23.8.2018
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