Rolling the bones

As I drifted off to sleep, the 2009 Metric song "Gimme Sympathy" was playing in my head.

As I entered the hypnopompic state, most of the song had fallen away, leaving the pre-chorus:

We're so close

To something better left unknown

We're so close

To something better left unknown

I can feel it in my bones

That last line -- with bones understood in the slang sense of "dice" -- led into a brief dream scene. I was sitting at a large round table in some kind of casino, rolling a handful of dice. Just as you can "feel" the tip of your pen on the paper or the tires of your motorcycle on the road, I could feel the dice hitting the tabletop, rolling, and coming to rest, and I could feel on which face each had landed without looking.

These were ordinary six-sided dice -- Asian-style, with the aces and caters in red -- but the game we were playing with them was called Seven Eleven because the four had a value of 7, and the six had a value of 11, while the remaining four faces were counted at face value. The value of a given throw was not the sum of the numbers rolled but their product. Thus, for example, if you rolled a two, a four, and a six, that was worth 154.

After I woke up, I realized this was a perfect system for solving a problem I have blogged about before, that of "The linear ranking of dice rolls." If each die face (except the ace) has a prime value, and we take the product rather than the sum, than each possible roll yields a unique integer, and these can be ranked straightforwardly from greatest to least. I may experiment a bit with the Seven Eleven system and see if I prefer it to the Air Hexactys.