Nine Men's Morris: Cultural Meanings and Social Contracts
The cultural meaning and social contract of nine men's morris, or “mills”, are interwoven with each other, and deeply rooted in its origins as a game of the people. Its simple board can be scratched into dirt or cleared in a field, and can be played with simple pieces. Quick, accessible, and portable, it was a game for workers and laborers.
This egalitarian nature of the game can also be seen in its end condition: the game is finished when one player is reduced to 2 pieces. Other popular abstract board games don't end until one side is completely wiped out. (Checkers, chess, e.g.) But in mills, the losing side always has two of their own pieces remaining, and is afforded a modicum of dignity in loss.
Furthermore, mills can be played as a gambling game. Consider playing with coins as pieces. One side heads, and other tails. It is possible for the losing side to “lose optimally” by taking a large number of their opponents pieces, while also retaining their own final two pieces on the board. It is possible for a player to lose, but still keep the majority of their coins, instead of losing it all and being wiped out. Even if one loses horribly, they at the very least get to keep their final two coins. This further shows the egalitarian nature of the game, and demonstrates how winning can be more cooperative, as opposed to one side utterly dominating the other. This is the social contract of the game: there will be a winner and a loser, but we will not destroy one another.
The shape of the board game itself has in the past taken on extra cultural meaning. It has been found carved into walls and ceilings, places where you obviously couldn't play the game. It served as a decoration, talisman, or ward.
I believe that its cultural meaning in this case was elevated by the previously mentioned social contract, and that the board can be viewed as a talisman of luck, or as a means of protection against misfortune. As an assurance that even should the worst happen, one would at least keep their last two pieces and not lose everything.
Reference: Nine Men's Morris: cultural meanings, social contracts and game mechanisms Dr Barnaby Dicker, Loco Ludus podcast