I don't think Play Magnus is close to indistinguishable, it's a modified version of Stockfish on the backend, having the same rating doesn't mean you have the same style
Yup. It's absolutely possible to determine whether you play versus a strength reduced/weak engine or a human. Humans make human plans and play according to human best practices, which you can find in chess literature. Engines, however, do not make long term plans and often play very inhuman (perfectly precise, unobvious tactical) moves, that often suprises even on grandmaster level.
I'm not sure if saying engines don't make long term plans is accurate, since we can set them to plan an arbitrary number of moves ahead. I think you mean that they don't have a theory of mind, and thus don't modulate their play based on their opponents.
AlphaZero / LeelaChess - neural net / genetic learning based ones; although they're not really commercially available, technically anyone can download the code to LeelaChess and train it if given enough CPU power. They learn chess by repeatedly playing chess against itself and in such a way simulate the organic development that has occurred in human play as well.
That's the next generation of chess engines - AlphaZero trounced Stockfish in a match of 100 games with 28 wins and 72 draws and not a single loss. And if you decrease the power a little bit (take an earlier generation), it makes significantly more human-like moves than Stockfish.
HIARCS or Lucas Chess are engines that have been made explicitly to play like a human. You won't be able to distinguish them, with some human play in conjunction, from a very strong human player.
Thanks, those do look like they are attempting to play like humans, but neither says how that claim was tested. How would you test the their ability to imitate humans?
That doesn't help you prove they're indisputable from humans, even if you admitted to using them to cheat. You said some engines are indisputable from humans, can you give me some evidence of this?
So you can set some engines not to pick perfect moves but to pick moves consistent with a particular rating or style...