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

Measured tafl game haphazardness.

Tafl variant Game balance Game haphazardness
Sea battle tafl 13x13
Sea battle tafl 13x13 (David Parlett)
+1.13    (206 / 30) 27.3 %
Old Hnefatafl 11x11 +1.33    (1016 / 307) 29.1 %
Historical Hnefatafl 15x15
Tablut 15x15 (Damian Walker)
-1.21    (52 / 17) 29.0 %
Sea battle tafl 15x15
Sea battle tafl 15x15 (Damian Walker)
+1.13    (39 / 13) 25.5 %
Sea battle 9x9 (Imperial Contest) +1.55    (79 / 19) 33.3 %
Copenhagen Hnefatafl 11x11 +1.49    (4452 / 236) 35.8 %
Fetlar Hnefatafl 11x11 +1.41    (1013 / 161) 40.3 %
Tawlbwrdd throneless 11x11
Tawlbwrdd throneless Lewis cross 11x11
+1.10    (143 / 30) 38.4 %
Sea battle diamond 11x11 -1.27    (55 / 12) 40.7 %
Historical Hnefatafl 11x11 (Welsh Tawlbwrdd)
Tawlbwrdd Bell 11x11
-1.12    (518 / 53) 42.1 %
Berserk Hnefatafl 11x11 +1.20    (596 / 87) 43.2 %
Historical Hnefatafl 7x7 (Irish Brandubh)
Brandubh cross 7x7
+1.34    (926 / 63) 45.2 %
Sea battle circle 11x11 (Nielsen) +1.24    (49 / 16) 45.3 %
Historical Hnefatafl 13x13
Tablut 13x13 (David Parlett)
+1.32    (94 / 22) 47.5 %
Historical Hnefatafl 9x9 (Saami Tablut) -1.12    (847 / 74) 48.0 %
Historical Hnefatafl 7x7 (Scottish Ard Ri)
Tawlbwrdd throneless 7x7
+1.64   (119 / 25) 48.8 %
Sea battle tafl 11x11
Sea battle cross 11x11 (Dardell)
+1.19    (111 / 27) 49.1 %
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 22.8.2017
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