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
Old Hnefatafl 9x9 +2.27    (85 / 16) +2.20    (80 / 16) +2.50    (35 / 10) +2.40    (34 / 10) +2.26
Tyr 9x9 +1.60    (65 / 10) +1.67    (64 / 10) +2.00    (39 / 8) +2.17    (38 / 8) +1.83
Historical Hnefatafl 7x7 (Irish Brandubh 1)
Brandubh cross 7x7
+1.88    (1860 / 92) +1.62    (1528 / 81) +2.02    (1232 / 52) +1.80    (1024 / 46) +1.69
Market Hnefatafl 9x9
(Nielsen setup, Simple Tafl rhombus-w 9x9)
+1.50    (50 / 13) +1.50    (50 / 13) +2.00    (30 / 9) +2.00    (30 / 9) +1.67
Copenhagen Hnefatafl Bell 11x11 +1.41    (169 / 31) +1.43    (168 / 31) +1.40    (125 / 24) +1.43    (124 / 24) +1.43
Fetlar Hnefatafl 11x11 +1.33    (1614 / 117) +1.44    (1322 / 89) +1.35    (691 / 48) +1.39    (606 / 43) +1.42
Copenhagen Hnefatafl 11x11 +1.36    (11153 / 207) +1.41    (9934 / 192) +1.33    (7278 / 79) +1.37    (6634 / 78) +1.40
Historical Hnefatafl 7x7 (Irish Brandubh 2) +1.35    (1281 / 58) +1.39    (1186 / 50) +1.30    (864 / 34) +1.36    (792 / 31) +1.37
Saami Cuhkka 5x5 +1.40    (169/ 22) +1.33    (162 / 20) +1.27    (101 / 15) +1.20    (98 / 15) +1.28
Berserk Hnefatafl 11x11 +1.27    (1228 / 76) +1.27    (1130 / 59) +1.21    (594 / 42) +1.19    (544 / 32) +1.24
Saami Daabloe 11x9 +1.16    (268 / 27) +1.19    (256 / 25) +1.26    (165 / 17) +1.29    (160 / 17) +1.22
Historical Hnefatafl 11x11 (Welsh Tawlbwrdd-w) +1.23    (96 / 19) +1.20    (90 / 17) +1.28    (57 / 13) +1.35    (54 / 12) +1.25
Sea battle tafl 13x13 (Nielsen) +1.11    (95 / 21) +1.14    (92 / 19) +1.19    (57 / 13) 1.24    (56 / 12) +1.18
Historical Hnefatafl 7x7 (Scottish Ard Ri)
Ard Ri-39 throneless 7x7
+1.26    (158 / 20) +1.23    (156 / 20) +1.14    (105 / 15) +1.12    (104 / 15) +1.18
Chess (roughly 52% - 56% white wins)
(balance +1.08 to +1.27)
+1.17
David Brown Hnefatafl 11x11 +1.25    (63 / 12) +1.24    (56 / 8) 1.00    (22 / 6) 1.00    (20 / 5) +1.17
Brandubh 7x7 (Walker) +1.15    (284 / 30) +1.14    (268 / 24) +1.18    (133 / 15) +1.17    (130 / 14) +1.15
Historical Hnefatafl 9x9 (Saami Tablut-w) +1.12    (246 / 29) +1.07    (240 / 26) +1.04    (202 / 20) 1.00    (198 / 18) +1.04
Tyr 11x11 -1.03    (276 / 23) -1.03    (276 / 23) +1.07    (124 / 15) +1.07    (124 / 15) 1.00
Sea battle-204577-w 11x11
(Nielsen setup)
+1.07    (31 / 11) 1.00    (30 / 11) +1.12*    (17 / 8) 1.00*    (16 / 8) 1.00
Sea battle-2526 9x9
(Nielsen setup)
+1.01    (269 / 32) 1.00    (266 / 32) -1.07    (147 / 21) -1.09    (146 / 21) -1.03
Sea battle tafl 11x11
Sea battle T cross 11x11 (Dardell setup)
-1.03    (260 / 49) -1.05    (250 / 44) -1.08    (133 / 27) -1.06    (130 / 25) -1.05
Sea battle tafl 15x15
(Damian Walker setup)
+1.04    (114 / 30) -1.04    (106 / 27) +1.03    (71 / 20) -1.06    (66 / 19) -1.05
Old Hnefatafl 11x11 -1.09    (1010 / 93) -1.01    (826 / 81) -1.22    (442 / 45) -1.17    (380 / 39) -1.06
Sea battle tafl 13x13
(modif. Parlett setup)
+1.01    (387 / 45) -1.06    (352 / 41) -1.08    (232 / 28) -1.09    (216 / 26) -1.07
Daldos 3x14 -1.23    (250 / 14) -1.22    (244 / 13) +1.03    (118 / 9) +1.03    (118 / 9) -1.13
Tawlbwrdd Lewis cross 11x11 -1.09    (265 / 25) -1.10    (264 / 25) -1.14    (199 / 21) -1.15    (198 / 21) -1.12
Tyr 15x15 -1.07    (149 / 16) -1.08    (148 / 15) -1.19    (70 / 13) -1.19    (70 / 13) -1.12
Simple Tafl 11x11
Tawlbwrdd throneless Lewis cross 11x11
-1.09    (858 / 134) -1.12    (754 / 91) -1.14    (472 / 39) -1.14    (462 / 36) -1.13
Daldos 3x12 -1.08    (250 / 22) -1.07    (244 / 18) -1.15    (116 / 14) -1.15    (114 / 11) -1.09
Historical Hnefatafl 11x11 (Welsh Tawlbwrdd)
Tawlbwrdd Bell 11x11
-1.15    (1633 / 102) -1.16    (1540 / 86) -1.21    (1141 / 51) -1.22    (1090 / 48) -1.19
Historical Hnefatafl 9x9 (Saami Tablut) -1.18    (3147 / 144) -1.16    (2984 / 134) -1.26    (2148 / 67) -1.24    (2058 / 64) -1.19
Hex 11x11 -1.12    (127 / 15) -1.18    (124 / 14) -1.16    (80 / 12) -1.23    (78 / 12) -1.20
Simple Tafl T cross-w 9x9 -1.20    (44 / 8) -1.20    (44 / 8) -1.29    (32 / 7) -1.29    (32 / 7) -1.24
Historical Hnefatafl 13x13
(Parlett setup)
-1.18    (522 / 57) -1.24    (488 / 47) -1.25    (304 / 33) -1.33    (286 / 31) -1.27
Saami Sáhkku 3x15 (Kåfjord) -1.24    (217 / 18) -1.23    (210 / 14) -1.38    (114 / 12) -1.33    (112 / 11) -1.27
Simple Tafl 5x5
(Draganov setup)
-1.52    (111 / 14) -1.50    (110 / 13) -1.26    (61 / 11) -1.22    (60 / 10) -1.39
Historical Hnefatafl 13x13 (Nielsen) -1.42    (63 / 15) -1.40    (60 / 13) -1.48    (52 / 12) -1.38    (50 / 11) -1.39
Daldos 3x16 -1.55    (163 / 14) -1.58    (160 / 12) -1.35    (80 / 8) -1.35    (80 / 8) -1.50
Sea battle-204577 11x11
(Nielsen setup)
-1.52    (116 / 18) -1.52    (116 / 18) -1.81    (52 / 10) -1.81    (52 / 10) -1.60
Historical Hnefatafl 15x15
(Nielsen setup)
-1.42    (58 / 17) -1.60    (52 / 12) -1.79    (39 / 12) -1.77    (36 / 11) -1.67
Skalk Hnefatafl 9x9 (ExpoMedia) -1.66    (133 / 16) -1.85    (114 / 11) -1.73    (90 / 8) -1.73    (82 / 7) -1.80
Skalk Hnefatafl 9x9 (ExpoMedia-w) -1.85    (74 / 11) -1.85    (74 / 11) -3.00    (44 / 9) -3.00    (44 / 9) -2.19
Skalk Hnefatafl 11x11 -2.70    (122 / 19) -3.15    (110 / 16) -5.08    (76 / 12) -5.17    (74 / 11) -3.78
Ashton Tablut 9x9 -4.74    (89 / 12) -4.55    (86 / 10) -6.67*    (46 / 8) -6.33*    (44 / 7) -5.05

( David Brown Hnefatafl: Rules.
Skalk Hnefatafl: Identical to Tawlbwrdd, except that corners are added (king wins in corner).
Ashton Tablut: 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 max. rating 1500 in all games total.


Updated 24.10.2022
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