Professor Veselin Jungic from Simon Fraser University, Burnby BC CANADA, gave a wonderful presentation, entitled, "No Strangers at this Party," at SIMIODE's EXPO 2025 recently and sent SIMIODE some examples of artwork from The Haida Indigenous People. The Haida are an Indigenous people of the Pacific Northwest Coast of North America, traditionally inhabiting Haida Gwaii (formerly the Queen Charlotte Islands) in British Columbia.
The caption on a card image of the dice received by SIMIODE reads, "In The Haida `Throwing Game' the die was held by the thin flange, with the thicker part up, and flipped over and over. If it fell upon either side the opponent took the die to toss; if it fell on the long, flat side or on the concave side it counted for the one who threw it a score of 1; if on the bottom a score of 2; if on the smallest side a score of 4. The game was usually played at camp, in the smoke-house, and the winner had the privilege of smearing the loser's face with soot." From page 59 of John Swanton, "Contributions to the Ethnology of the Haida," 1905. Freely available from the American Museum of Natural History.
Professor Jungic went on to share his recent experiences and probability notions.
"Lately I've been reading a lot about the traditional Indigenous games. As part of my learning, I commissioned several Haida dice from Billy Yovanovich.
"Last week I spent one morning throwing a Billy's die 500 times. Here are the outcomes with the corresponding probability:
· Throwing player gets 1 point: p=0.38
· Throwing player gets 2 points: p=0.22
· Throwing player gets 4 points: p=0.09
· Change of the thrower: p=0.31
"I've shared this with a colleague who is a prominent Canadian statistician and asked him if he would calculate the expected number of rounds under the assumption that each player starts with 20 counters.
"Counters, being sticks, pebbles, or anything, else were used to keep the score during the game: a player who wins, say, two points, takes two counters from the opponent. The game is over when one player has no counters. In my view, the score at any point during the game captures a pair of cardinal numbers. I am both tempted and hesitant to say that this is a zero-sum game: on one hand the fact that what one player wins the other player loses is a definition of a zero-sum game. On the other hand, this mathematical itch to use negative numbers as a way to describe a zero-sum game seems both unnecessary and some kind of divergence from the spirit of the game - if that matters for anything.
"In any case, my colleague used Markov chains to do the required calculations. He teaches the subject in one of the upper division courses at SFU. My colleague told me that he would love to replace some of the "artificial" examples that he uses in the course with this example. He was particularly intrigued by the shape of the die that causes multiple outcomes with different probabilities and the fact that the game includes the change of the roles of the players without the change of the score. He claimed that in a "standard" undergrad course on Markov chains, students do not learn about cases like this."
Artist: Billy Yovanovich, The Haida Nation
Material: Alder and abalone
Photo: Eugene Doudko, ECU Photography
Concept: Veselin Jungic
Copyright: Math Catcher Outreach Program
This Math Catcher Outreach program is a rich set of richly illustrated resources, including Indigenous People stories read with videos in English, Cree, Blackfoot, French, Spanish, and American Sign Language.
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Brian Winkel
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