For a given number of positions/holes and a given number of colors, which initial guess eliminates the most possibilities for the solution at a minimum?
For 4 positions, it's AABB. What is it for 5, or 6 positions?
Edit I made another minor decision making improvement, and I've let it run many thousands of times now. It's been somewhere between 4.469 and 4.470. Scrolling up, I still see brief periods where the average is +/- 0.004, so I suppose it could eventually settle at 4.478, but I find it unlikely that it would ever go that high, so I consider my goal of beating Knuth reached, but only for 4 holes, for which I already know the best initial guess.
I'm removing the background stuff and leaving the question that hasn't been answered precisely.