A neat probability paper Christopher Long shared with me

A longer than usual, and more fun than usual sequence started on Twitter yesterday with this tweet:

I was excited about it because we have some non-transitive “Grime” dice and the kids still play around with them. Here’s a little project we did when we got them:

Non-Transitive Grime Dice

Because of the original twitter post, Christopher Long ended up sharing this neat (and fairly accessible) probability paper:

Long wrote several more (maybe 10) tweets following this one which are all pretty great follow ups to the paper.

What especially caught my eye in the paper was section 5 on duration calculations. I’ve spent lot of time in the last couple of years thinking about how quantities like duration and internal rate of return change when you have both positive and negative cash flows. Originally my interest in these ideas came from noticing that many people in the financial area like to talk about internal rate of return (“IRR”) even when IRR seemed to be to be a pretty dubious way to analyze the particular financial product.

The interest in duration calculations followed a similar path when people were marketing some “short duration” products that didn’t seem to have short durations at all (to me).

The connection with fractional coins and dice seems fascinating. Although I haven’t really settled some of the ideas in my mind, I’m happy to have stumbled into this interesting connection to a problem that was already on my mind.

Pretty amazing power that Twitter has 🙂


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