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

Measured tafl game balances.

Tafl variant Game balance
Overall Full matches Strong players Strong players full matches Average
Rachunek tafl 9x9 +1.95*    (28 / 8) +3.50*    (18 / 5) +1.71*    (23 / 5) +2.50*    (14 / 3) +3.00*
Alea Berserk 19x19 (Bartley) +1.75*    (22 / 9) +1.86*    (20 / 7) +2.00*    (21 / 7) 1.86*    (20 / 7) +1.86
Foteviken tablut 9x9 +1.59    (66 / 19) +1.77    (54 / 10) +1.52    (29 / 9) +1.59*    (22 / 5) +1.71
Haphaz. 67%
Sea battle T 9x9 +1.42    (314 / 54) +1.53    (248 / 28) +1.48    (202 / 19) +1.57    (172 / 15) +1.61
Haphaz. 52%
Sea battle tafl 9x9 (Imperial Contest) +1.91    (109 / 27) +1.68    (98 / 19) +2.30    (61 / 13) +2.14    (58 / 13) +1.61
History Craft Hnefatafl 11x11 +1.63    (67 / 17) +1.57    (54 / 11) +1.40    (36 / 7) +1.56    (32 / 6) +1.57
Historical Hnefatafl 7x7 (Scottish Ard Ri)
Ard Ri throneless 7x7
+1.47    (195 / 39) +1.41    (166 / 29) +2.00    (111 / 22) +1.69    (94 / 20) +1.50
Copenhagen Hnefatafl 11x11 +1.41    (6278 / 305) +1.46    (5222 / 201) +1.40    (2478 / 40) +1.47    (2146 / 39) +1.46
Sea battle circle 9x9 (Nielsen) +1.38    (38 / 8) +1.38    (38 / 8) 1.55   (28 / 7) 1.55    (28 / 7) +1.44
Haphaz. 67%
Fetlar Hnefatafl 11x11 +1.26    (1354 / 211) +1.39    (984 / 128) +1.35    (405 / 32) +1.41    (332 / 30) +1.39
Historical Hnefatafl 7x7 (Irish Brandubh)
Brandubh cross 7x7
+1.87    (1052 / 80) +1.24    (726 / 59) +2.16    (545 / 29) +1.40    (376 / 26) +1.30
Sea battle circle 11x11 (Nielsen) +1.30    (53 / 17) +1.19    (46 / 13) +1.39    (43 / 12) +1.22    (40 / 11) +1.21
Haphaz. 55%
Berserk Hnefatafl 11x11 +1.33    (908 / 105) +1.26    (776 / 60) +1.08    (377 / 27) +1.09    (340 / 22) +1.20
Chess (roughly 52% - 56% white wins)
(balance +1.08 to +1.27)
+1.17
Old Hnefatafl 11x11 +1.08    (1279 / 359) +1.21    (712 / 152) -1.13    (233 / 25) -1.25    (152 / 22) +1.12
Sea battle tafl 13x13
(modif. Parlett setup)
+1.25    (231 / 33) +1.10    (190 / 25) +1.11    (140 / 16) +1.08    (128 / 15) +1.09
Sea battle tafl 11x11
Sea battle cross 11x11 (Dardell setup)
+1.13    (175 / 37) +1.08    (162 / 28) -1.02    (81 / 15) +1.05    (78 / 13) +1.07
Simple Tafl 11x11
Tawlbwrdd throneless Lewis cross 11x11
+1.11    (186 / 41) +1.05    (168 / 29) +1.08    (79 / 15) +1.11    (78 / 15) +1.07
David Brown Hnefatafl 11x11 +1.28    (66 / 16) +1.15    (56 / 8) 1.00    (22 / 6) -1.22*    (20 / 5) +1.05
Historical Hnefatafl 11x11 (Welsh Tawlbwrdd)
Tawlbwrdd Bell 11x11
-1.07    (632 / 67) -1.05    (554 / 56) -1.14    (332 / 29) -1.15    (290 / 27) -1.08
Historical Hnefatafl 9x9 (Saami Tablut) -1.05    (1018 / 87) -1.08    (930 / 64) -1.12    (595 / 31) -1.12    (464 / 30) -1.09
Magpie 7x7
(Magpie cross 7x7)
+1.04    (104 / 23) -1.04    (98 / 20) -1.13    (51 / 16) -1.30    (46 / 14) -1.12
Haphaz. 64%
Tawlbwrdd Lewis cross 11x11 -1.07    (85 / 15) -1.10    (84 / 15) -1.14    (60 / 12) -1.14    (60 / 12) -1.12
Haphaz. 62%
Historical Hnefatafl 13x13
(Parlett setup)
-1.05    (250 / 39) -1.14    (220 / 28) -1.08    (127 / 19) -1.11    (116 / 17) -1.13
Historical Hnefatafl 15x15
(Damian Walker setup)
-1.21    (115 / 27) -1.26    (106 / 20) -1.21    (53 / 13) -1.17    (50 / 12) -1.23
Sea battle tafl 15x15
(Damian Walker setup)
1.00    (74 / 16) -1.13    (68 / 14) -1.22    (40 / 9) -1.40    (36 / 9) -1.21
Sea battle diamond 11x11 -1.19    (59 / 13) -1.24    (56 / 12) -1.33    (28 / 8) -1.36    (26 / 8) -1.28
Sea battle tafl 13x13 (Nielsen) 1.00    (22 / 8) -1.22*    (20 / 7) -2.00*    (12 / 5) -2.00*    (12 / 5) -1.46
Old Hnefatafl 13x13 (Viking Siege) -1.40    (103 / 25) -1.39    (98 / 19) -2.36    (37 / 11) -2.27    (36 / 10) -1.58
Skalk Hnefatafl 9x9 (ExpoMedia) -1.38    (162 / 40) -1.60    (122 / 16) -1.80    (98 / 10) -1.90    (84 / 8) -1.71
Skalk Hnefatafl 11x11 -1.58    (178 / 60) -2.49    (124 / 24) -4.64    (79 / 14) -4.85    (76 / 12) -3.12
Ashton Tablut 9x9 -4.87    (91 / 14) -4.55    (86 / 10) -4.52    (58 / 9) -4.33    (56 / 8) -4.46

( Rachunek tafl: Identical to Sea Battle tafl, except that a throne is added. Rules.
David Brown Hnefatafl: Rules.
Skalk Hnefatafl: Identical to Tawlbwrdd, except that corners are added (king wins in corner).
Foteviken Tablut: Rules.
Ashton Tablut: Rules.
Magpie 7x7: Rules. )


The table data cells contain
game balance    ( number of games / number of players )
*    Number unreliable, too few games.

Games selection 1, "Overall".
All games in the games archive.

Games selection 2, "Full matches".
Subset of games selection 1, including only full pairs of games (player A white against player B black and player B white against player A black)

Games selection 3, "Strong players".
Subset of games selection 1, including only strong players.

Games selection 4, "Strong players full matches".
Subset of games selection 3, including only full pairs of games (player A white against player B black and player B white against player A black)

White = defenders. Black = attackers.

The tafl game balance is calculated as:
(number of most winning color's wins) divided by (number of least winning color's wins), the number positive if white is more winning, negative if black is more winning. Draws are counted as half wins.

Examples:
White wins 20 times and black wins 10 times. Balance = +20/10 = +2 (white has twice the chance of winning than black).
White wins 20 times and black wins 30 times. Balance = -30/20 = -1.5 (black has 1.5 times the chance of winning than white).
White wins 10 times and black wins 10 times, and 20 draws. Balance = 20/20 = 1 (perfect balance).

Average is calculated from columns 2 and 4 (full matches) this way:
average of a/b and c/d is (a+c)/(b+d)
Strong players have at least rating 1500 in all games total or in at least one variant, based on at least 32 games.


Updated 23.8.2018
Copyright © 1998-2018 Aage Nielsen, All Rights Reserved;