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)
+1.13    (207 / 31) 27.2 %
Old Hnefatafl 11x11 +1.33    (1016 / 307) 29.1 %
Historical Hnefatafl 15x15
(Damian Walker setup)
-1.19    (56 / 17) 26.9 %
Sea battle tafl 15x15
(Damian Walker setup)
+1.13    (40 / 14) 25.0 %
Sea battle 9x9 (Imperial Contest) +1.55    (91 / 25) 31.2 %
Copenhagen Hnefatafl 11x11 +1.51    (4976 / 258) 34.4 %
Fetlar Hnefatafl 11x11 +1.41    (1065 / 171) 38.6 %
Simple Tafl 11x11
Tawlbwrdd throneless Lewis cross 11x11
+1.10    (144 / 31) 38.2 %
Sea battle diamond 11x11 -1.26    (57 / 13) 36.1 %
Historical Hnefatafl 11x11 (Welsh Tawlbwrdd)
Tawlbwrdd Bell 11x11
-1.13    (529 / 57) 42.3 %
Berserk Hnefatafl 11x11 +1.22    (656 / 91) 43.3 %
Historical Hnefatafl 7x7 (Irish Brandubh)
Brandubh cross 7x7
+1.32    (934 / 69) 45.2 %
Sea battle circle 11x11 (Nielsen) +1.23    (51 / 17) 43.6 %
Historical Hnefatafl 13x13
(Parlett setup)
+1.30    (95 / 24) 43.7 %
Historical Hnefatafl 9x9 (Saami Tablut) -1.13    (876 / 78) 47.1 %
Historical Hnefatafl 7x7 (Scottish Ard Ri)
Tawlbwrdd throneless 7x7
+1.64   (121 / 27) 48.0 %
Sea battle tafl 11x11
Sea battle cross 11x11 (Dardell)
+1.19    (115 / 29) 47.9 %
Sea battle T 9x9 +1.55    (295 / 51) 52.2 %
Magpie cross 7x7 -1.28    (76 / 15) 55.4 %
Tawlbwrdd Lewis cross 11x11 -1.13    (78 / 15) 62.1 %
Foteviken tablut 9x9 +1.67    (65 / 18) 64.2 %
Sea battle circle 9x9 +1.46    (38 / 8) 66.7 %

( Old Hnefatafl: Identical to Fetlar Hnefatafl 11x11, except that the king can be captured on the board edge.
Skalk Hnefatafl: Identical to Tawlbwrdd, except that corners are added (king wins in corner).
Foteviken Tablut: Rules.
Magpie 7x7: Rules. )

The table data cells contain
game balance    ( number of games / number of players ) *2

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 22.2.2018
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