A Very Viking Miracle

I was following along with a discussion of probabilities a while back and was reminded of this memorable episode from the life of King St. Olaf of Norway, as related in the (fascinating, but not always very reliable) Heimskringla, which was written by the great Snorri Sturluson (whose most famous work was the Prose Edda). There was once a meeting between St. Olaf of Norway and various Swedish kings. The most important of these kings, Olaf of Sweden, turned out to be a fairly reasonable person; Olaf of Norway and Olaf of Sweden understood each other well.

Thorstein Frode relates of this meeting, that there was an inhabited district in Hising which had sometimes belonged to Norway, and sometimes to Gautland. The kings came to the agreement between themselves that they would cast lots by the dice to determine who should have this property, and that he who threw the highest should have the district. The Swedish king threw two sixes, and said King Olaf need scarcely throw. He replied, while shaking the dice in his hand, "Although there be two sixes on the dice, it would be easy, sire, for God Almighty to let them turn up in my favour." Then he threw, and had sixes also. Now the Swedish king threw again, and had again two sixes. Olaf king of Norway then threw, and had six upon one dice, and the other split in two, so as to make seven eyes in all upon it; and the district was adjudged to the king of Norway. We have heard nothing else of any interest that took place at this meeting; and the kings separated the dearest of friends with each other.

There are infinitely many things to like about this story. (1) It is a contest between Olaf and Olaf, and Olaf and Olaf end up good friends. (2) It makes complete sense for two reasonable Viking kings, having decided something wasn't worth bloodshed, to solve the dispute the other Viking way, by gambling. (3) Norway wins, which is the only appropriate solution to a dispute between Norway and Sweden. (4) It shows that probabilities are actually statements about models, such as models of dice, and only statements about the real world to the extent that those models fit the real world; in the real world, unlike in the abstract model we use to talk about probabilities with dice, it is indeed possible to roll a thirteen with two six-sided dice, because real dice can split in two.