I have a small yard and I'm not optimizing for the fewest moves, I'm optimizing for both the longest continuous lines (because I think they look nicest) and the shortest distance to carry the clippings at the end.
I have a different definition of optimal to this game.
I'm right with you. My dad was a farmer and taught me: First deal with the irregular, annoying parts on the outside. Create rectangles with a long side and turning space on each shorter side. Then deal with each rectangle by going back and forth along the long edge. The turnarounds are also a great place for some wheelbarrows to collect the clippings closest to the Komposthaufen.
Hence why I went for the irregular strange part on the lower left first, and then the more regular part on the right. That's the weird rain collection, herb garden, thing we have at the back.
Or be like me and just mulch the clippings
(yes it looks uglier that way - and yes I think of mowing the lawn as a chore)
I always mow a different path each time because turns and wheels slowly build up damage to the lawn and so I want to spread that out over everything. Push mowers are light enough that this doesn't matter but a rider it does.
Conversely, I once had a very large yard for a suburban home, about a third of an acre. I sectioned my yard into about 5 sections, but I mowed pretty much the same way: whatever lines are longest without stopping.
The less time I spent in Alabama heat, the better.
Yeah, I think most people who have a yard wouldn't have played it for fewest moves... I don't know why but this whole piece reminds me of someone that never had to mow their yard, or AI that optimizes for something without carrying the full context or nuance of why we might not have gone with fewest moves optimization.