gsf wrote:There is a difference between looking for patterns like row/col/box based naked/hidden tuples

or rectangular area based xwing/swordfish versus serpentine forcing chains.

They differ by degree. One could make a list of steps to make to search for a naked pair that would always find one that exists and always prove that one does not exist if it fails. One could do the same for any and all other patterns, including xy-type forcing chains. One who is "looking for serpentine forcing chains" may not be looking for them in an efficient manner, though I have to admit that I am usually only able to locate xy-type chains, not comprehensive chains (those that require conjugates mixed in).

...seem to grab forcing chains, sometimes very long, from thin air.

I've had the same feeling when someone says the next step is a hidden quad -- a pattern much harder for me to spot than the most serpentine of (xy-type at least) forcing chains. I *always* have that feeling when an Almost Locked Set is given -- how *do* they find those?

Solving by hand, such long chains would be a big time investment,

especially since there's no guarantee that a particular chain will result

in any placements or eliminations.

May or may not be true. Depends on the skill and toolbag of the solver as well as the specifics of the puzzle.

How much of a time investment is there to search all possible naked/hidden tuples or Swordfish? No guarantee there either.

The length of an xy-chain is not always the deciding factor for how difficult it is to find.

Before Sudoku became popular, before BUG was discovered, before labeled egdes and repetitive paths and nice loops, my favorite puzzles ended with a dozen or 20 bivalue cells and as few as one polyvalue cells. Then I'd trace a path from cell to cell with my finger, mumbling "if this is 3, then this is 5, then one of these three are 6, then this 8, etc" until I found a contradiction or saw that all values from a single cell lead to the same result. I could care less how many cells I used -- I didn't count and it didn't make it easier or harder.

BUT -- back then, puzzles were rarely if ever published that required this level of logic. Most or all these puzzle could have been solved by something much simpler, probably no more than an x-wing, maybe only a triple. They just didn't *make* puzzles really hard back then. (Pappocom might say that I cheated myself out of finding the "correct" solution.) But the point is clear -- each time I found a forcing chain to solve the puzzle, it was easier to find than the "simpler" tactic that I had overlooked!