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

Measured tafl game haphazardness.

Tafl variant Game balance Counted games Game haphazardness
Total Hnefatafl 11x11 +1.28 145 12%
Sea battle-204577-w 11x11 -1.23 32 13%
Market Hnefatafl 9x9 +1.34 136 22%
Simple Tafl T cross-w 9x9 -1.09 103 23%
Historical Hnefatafl 9x9 (Saami Tablut-w) +1.07 251 25%
Historical Hnefatafl 11x11 (Welsh Tawlbwrdd-w) +1.07 113 34%
Simple Tafl-w 5x5 -1.45 109 37%
Fetlar Hnefatafl 11x11 +1.41 969 37%
Copenhagen Hnefatafl 11x11 +1.34 6945 38%
Sea battle-1571 9x9 +1.13 48 38%
Sea battle-2526 9x9 -1.05 179 40%
Saami Daabloe 11x9 +1.19 65 40%
Old Hnefatafl 11x11 -1.08 655 41%
Berserk Hnefatafl 11x11 +1.18 790 42%
Brandubh 7x7 (Walker) +1.17 232 45%
Irish Brandubh 2 7x7 +1.42 893 50%
Tyr 11x11 +1.08 265 52%
Saami Cuhkka 5x5 +1.32 34 53%
Frisian Dablo 11x9 +1.04 50 68%
Daldøs 3x16 +1.19 71 70%
Daldøs 3x14 +1.03 72 72%
Daldøs 3x12 +1.11 76 79%
Saami Sáhkku 3x15 (Kåfjord) -1.09 53 83%

The 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 counted games) * 2
Draws are counted as half wins.
Only games between players of adjusted ratings separated by at least 150, are counted.

Imagine a completely uncontrollable game, where the outcome is random 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 %.

A completely random game would seemingly have a game balance of 1. So some game variants can have seemingly good game balances, which are only caused by a random outcome.

Apparently, measured this way, the normal range of haphazardness is up to 50%.


Updated 9.3.2024
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