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

Measured tafl game balances.

Tafl variant Game balance
Overall Full matches Strong players Strong players full matches Average
Brandubh line 7x7 +1.70 (+1.35)    (73 / 15) +2.29 (+1.74)    (56 / 11) +1.74 (+1.35)    (63 / 11) +2.25 (+1.69)    (52 / 9) +2.27
Rachunek tafl 9x9 +1.95*    (28 / 8) +3.50*    (18 / 5) +1.27*    (17 / 4) +1.86*    (10 / 2) +1.95*
Tawlbwrdd Lewis diamond 11x11 +2.00 (+1.41)    (33 / 8) +1.91 (+1.34)    (32 / 7) +1.89*    (26 / 6) +1.89*    (26 / 6) +1.91
Tawlbwrdd throneless Lewis diamond 11x11 +1.53    (76 / 15) +1.78    (64 / 13) +1.45    (27 / 8) +1.67*    (24 / 8) +1.78
Foteviken tablut 9x9 +1.55    (65 / 18) +1.67    (52 / 10) +1.43    (28 / 8) +1.59*    (22 / 5) +1.67
Haphaz. 64%
Historical Hnefatafl 7x7 (Scottish Ard Ri)
Ard Ri throneless 7x7
+1.48 (+1.23)   (119 / 25) +1.48 (+1.21)   (104 / 21) +1.77 (+1.39)   (72 / 14) +1.82 (+1.41)   (62 / 12) +1.64
History Craft Hnefatafl 11x11 +1.61 (+1.25)    (64 / 15) +1.60 (+1.21)    (52 / 10) +1.40 (+1.00)    (36 / 7) +1.56 (+1.10)    (32 / 6) +1.58
Brandubh circle 7x7 +1.50 (+1.19)    (75 / 11) +1.47 (+1.16)    (74 / 10) +1.68 (+1.29)    (59 / 10) +1.64 (+1.26)    (58 / 9) +1.55
Sea battle T 9x9 +1.49 (+1.32)    (295 / 51) +1.55 (+1.36)    (232 / 25) +1.47 (+1.26)    (185 / 15) +1.55 (+1.33)    (166 / 13) +1.55
Haphaz. 52%
Sea battle tafl 9x9 (Imperial Contest) +1.87 (+1.49)   (79 / 19) +1.55 (70 / 13) +2.88*   (33 / 8) +2.53*    ( > +2.10)(30 / 8) +1.55
Copenhagen Hnefatafl 11x11 +1.55 (+1.50)    (4503 / 240) +1.50 (+1.45)   (3630 / 152) +1.45 (+1.38)   (1554 / 32) +1.48 (+1.40)   (1312 / 31) +1.49
Sea battle circle 9x9 +1.38    (38 / 8) +1.38    (38 / 8) +1.55   (28 / 7) +1.55    (28 / 7) +1.46
Haphaz. 67%
Fetlar Hnefatafl 11x11 +1.40 (+1.31)   (1013 / 161) +1.46 (+1.35)   (698 / 91) +1.32 (+1.17)   (270 / 24) +1.36 (+1.19)   (222 / 22) +1.41
Historical Hnefatafl 7x7 (Irish Brandubh)
Brandubh cross 7x7
+1.76 (+1.64)    (926 / 63) +1.27 (+1.17)    (656 / 48) +2.04 (+1.85)    (457 / 21) +1.41 (+1.26)    (326 / 20) +1.34
Old Hnefatafl 11x11 +1.20 (+1.12)    (1016 / 307) +1.33 (+1.22)    (524 / 126) +1.26 (+1.03)    (106 / 18) +1.33 (+1.02)    (56 / 15) +1.33
Historical Hnefatafl 13x13
Tablut 13x13 (David Parlett)
+1.24    (94 / 22) +1.19    (68 / 15) +1.15    (43 / 10) +1.46    (32 / 8) +1.32
Sea battle circle 11x11 (Nielsen) +1.33    (49 / 16) +1.21    (42 / 12) +1.47    (37 / 11) +1.27    (34 / 10) +1.24
Berserk Hnefatafl 11x11 +1.40 (+1.29)   (596 / 87) +1.28 (+1.16)   (470 / 46) +1.13   (250 / 20) +1.13   (212 / 14) +1.20
David Brown Hnefatafl 11x11 +1.21    (62 / 16) +1.17    (50 / 8) -1.40*    (12 / 5) -1.67*    (8 / 4) +1.17
Chess (roughly 52% - 56% white wins)
(balance +1.08 to +1.27)
+1.17
Sea battle tafl 15x15
Sea battle tafl 15x15 (Damian Walker)
+1.29    (39 / 13) +1.13    (34 / 11) +1.22*    (20 / 8) +1.00*    (16 / 7) +1.13
Sea battle tafl 13x13
Sea battle tafl 13x13 (David Parlett)
+1.35 (+1.18)   (206 / 30) +1.11   (166 / 22) +1.23 (+1.02)   (117 / 13) +1.15   (102 / 11) +1.13
Tawlbwrdd throneless 11x11
Tawlbwrdd throneless Lewis cross 11x11
+1.04    (143 / 30) +1.06    (128 / 22) +1.04    (48 / 12) +1.15    (44 / 10) +1.10
Sea battle tafl 11x11
Sea battle cross 11x11 (Dardell)
+1.22   (111 / 27) +1.13   (100 / 20) +1.18   (37 / 10) +1.25   (36 / 9) +1.19
Historical Hnefatafl 11x11 (Welsh Tawlbwrdd)
Tawlbwrdd Bell 11x11
-1.10    (518 / 53) -1.06    (454 / 47) -1.22    (224 / 21) -1.18    (198 / 21) -1.12
Tawlbwrdd Lewis cross 11x11 -1.05    (78 / 15) -1.11    (76 / 15) -1.15    (58 / 11) -1.15    (58 / 11) -1.13
Haphaz. 62%
Historical Hnefatafl 9x9 (Saami Tablut) -1.02    (847 / 74) -1.05    (750 / 53) -1.19    (254 / 22) -1.19    (230 / 22) -1.12
Historical Hnefatafl 15x15
Tablut 15x15 (Damian Walker)
-1.15    (56 / 17) -1.19    (46 / 12) -1.14*   (15 / 8) -1.50*    (10 / 6) -1.19
Magpie cross 7x7 -1.05    (76 / 15) -1.20    (66 / 13) -1.13    (32 / 9) -1.36    (26 / 8) -1.28
Haphaz. 55%
Sea battle diamond 11x11 -1.29    (55 / 12) -1.27    (50 / 11) -1.75*    (22 / 7) -1.57*    (18 / 7) -1.27
Magpie line 7x7 -1.38 (-1.07)    (62 / 10) -1.40 (-1.08)    (60 / 9) -1.40 (-1.00)    (36 / 8) -1.43 (-1.02)    (34 / 7) -1.41
Brandubh throneless line 7x7 -1.36    (33 / 7) -1.46    (32 / 7) -2.17*    (19 / 5) -2.60*    (18 / 5) -1.46
Tablut 13x13 (Nielsen) -1.39    (43 / 12) -1.53    (38 / 10) -2.00*    (21 / 9) -2.00*    (18 / 7) -1.53
Magpie circle 7x7 -1.43 (-1.12)    (68 / 13) -1.36 (-1.06)    (66 / 12) -3.33*    ( < -2.00 ) (26 / 8) -3.00*    ( < -1.80 ) (24 / 7) < -1.56
Tawlbwrdd throneless T cross 11x11 -1.71    (92 / 16) -1.71    (84 / 12) -14.00*    (15 / 6) -13.00*    (14 / 5) -1.71
Skalk Hnefatafl 9x9 (ExpoMedia) -1.43 (-1.22)    (158 / 40) -1.64 (-1.36)    (116 / 14) -1.70 (-1.37)    (89 / 9) -1.81 (-1.44)    (76 / 8) -1.72
Tawlbwrdd throneless T diamond 11x11 -1.73 (-1.36)    (67 / 14) -1.73 (-1.32)    (56 / 10) -8.00*    (9 / 6) -inf*    (6 / 4) -1.73
Tawlbwrdd T diamond 11x11 -1.08    (130 / 23) -1.40 (-1.15)    (102 / 19) -2.60 (-1.84)    (36 / 7) -2.75*    ( < -2.20 ) (30 / 7) < -1.75
Tawlbwrdd T cross 11x11 -1.76    (58 / 15) -1.84    (54 / 12) -2.00*    (24 / 9) -2.14*    (22 / 8) -1.84
Tawlbwrdd throneless Bell 11x11 -1.37 (-1.10)    (83 / 12) -1.50 (-1.20)    (80 / 10) -2.25 (-1.62)    (39 / 7) -2.45 (-1.75)    (38 / 7) -1.92
Ard Ri-1 7x7 -2.20 (-1.54)    (32 / 6) -2.20 (-1.54)    (32 / 6) -2.14*    (22 / 5) -2.14*    (22 / 5) -2.20
Skalk Lewis diamond 11x11 -3.40*    (22 / 6) -3.40*    (22 / 6) -11.00*    (12 / 4) -11.00*    (12 / 4) -3.40*
Skalk Hnefatafl 11x11 -1.73    (172 / 55) -2.54    (122 / 24) -5.35    (73 / 12) -8.14*    ( < -5.60) (64 / 11) < -3.77
Ashton Tablut 9x9 -5.07 (-3.89)    (88 / 13) -4.79 (-3.68)    (84 / 10) -6.50*    (45 / 7) -6.33*    (44 / 7) -4.79

( Sea battle tafl 9x9 (Imperial Contest): Identical to Sea battle T 9x9, except that the cargo ship cannot move more than four squares per move.
Rachunek tafl: Identical to Sea Battle tafl, except that a throne is added. Rules.
Old Hnefatafl: Identical to Fetlar Hnefatafl 11x11, except that the king can be captured on the board edge.
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    (one standard deviation subtracted)    ( number of games / number of players )
*    Number unreliable, too few games.

Games selection 1, "Overall".
All games in the games archive, excluding timeouted games and extremely short, abrupted games.

Games selection 2, "Full matches".
Subset of games selection 1, only including 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, only including players rated above 1600.

Games selection 4, "Strong players full matches".
Subset of games selection 3, only including 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 as the geometric mean of columns 2 and 4 (full matches). Only balances based on at least 20 games, of which the least winning side won at least 10 games, are included in the average.


Updated 12.9.2017
Copyright © 1998-2017 Aage Nielsen, All Rights Reserved;