Women's dice game

Menominee women's dice game as seen in the Milwaukee Public Museum.

Six of the dice were thin circular disks; one was carved in the form of a turtle, and one represented a horse's head. They were formerly made of buffalo rib, but horse ribs were common in later times. One surface of each die was colored blue or sometimes red, and the other was left white. The bowl was held with both hands and the dice were shaken to the far side of the bowl. Then the bowl was given one flip and set on the floor and the score was counted, as follows:

• All of similar color except 2: 1 point
• All of similar color except 1: 3 points
• All of similar color except turtle: 5 points
• All of similar color except horse: 10 points
• All of similar color: 8 points
• All of similar color except turtle and horse: 10 points

The scoring varied according to each tribe, and each woman kept her own score using beans in front of her. Each woman shook until she missed twice and then passed the bowl in clockwise rotation. The first to score ten points won the game, and her prize-a piece of yard goods-was given to one of the men spectators, who in turn was obliged to reciprocate with a gift of equal value in the future.

OK, obviously the lady can score more than 10 points in a turn, though that won't happen often. If the chips (not really dice) were fair, the probability of red or white would be 0.5, but it might vary a bit. If they were fair, how much would a woman score in a turn--on the average? I made a stupid typo in my program, and I wanted to use the exercise to learn some python plotting I wasn't familiar with, so this took longer than it should have, but for your interest:

And if you want to know how things change if the chips aren't fair (systematically), that's here:

The award scheme is clever. The woman probably didn't need any "yard goods" herself--that was the sort of thing women made anyway. But she got to make a forced exchange with a man for something the men provided.