Updated 2021-12-17: A closed-form solution has been submitted
The Royal Game of Ur, also known as the Game of Twenty Squares, is one of the oldest known board games, with attestations from 3000 to 250 BC. It was an enduringly popular game, played across multiple civilizations and across the Middle East.
This is the 60th anniversary of the proof of Little’s Law, a widely useful rule for queuing systems that links throughput, response (cycle) time, and number of requests (work items). Unfortunately, although software engineers often operate queues or pipelines (modern computer systems are rife with queues, implicit and explicit), they aren’t exposed to the mathematical foundations and often fail to build intuition around how queues act operationally.