I don't know anywhere where it says that, but maybe I'm overlooking something.
Polymorph certainly seems to feel that level and CR are interchangeable though.
I really thought I read it somewhere in the DMG, but now that you mentioned polymorph, there is a real chance my mind is playing tricks on me. Unfortunately I won't be able to clarify myself right now, as my books are 15000 km away.
Sure, absolutely. "Medium" fights are a slaughter, like beating up on a kindergartner. The monsters are typically outnumbered and outgunned. The only justification for so-called "Medium" fights to occur is if the monsters think they're dealing with a bunch of standard humans, not actually realizing that it's a whole band of high-level humans. Even there, the realistic reaction is for the monsters to bail out of the fight as soon as they realize what they're dealing with, e.g. after a Fireball gets thrown and another human fells two orcs with two swipes of his axe.
One of the biggest reasons I hate "Medium" fights is that after low levels, it's really hard to make them make sense from an in-world perspective. On the other hand, it's pretty easy to explain why fourteen Umber Hulks and their Neogi masters (including an 8th level wizard) don't knuckle under to a mere four humans--that makes it a good encounter from a story perspective, but it's also quadruple-Deadly or higher. Ditto for a squad of eight giants, or a drow war-party. So I just embrace quadruple-Deadly+.
Sounds like fun to me.
Possibly. Or possibly the solo monster was run poorly. I like spellcasting dragons, but even the base dragon can be a lot more scary if you use it to its full potential as a hunter. (See: discussion on Strahd, earlier in this thread.)
Yes, I was following that closely, and I acknowledge Strahd is a formidable opponent that will probably crush all but the most patient and resourceful 10th level parties. Anyhow, Strahd is CR 15. It seems to me this also suggests solo monsters should be chosen from a CR range higher than the adventuring group.
That makes the dragon take a lot longer than three rounds though, and it assumes some narrative importance; some people don't seem to like that. They want a straightforward fight with a big brute; these people are the ones who tend to be most disappointed with solo creatures, especially if their players have a high nova potential from paladin smiting or similar. (Sometimes these DMs get disappointed in how quickly their demons/dragons died to a PC nova, without contemplating the cost of that nova to the PCs.)
I find it interesting here in the forums that several people mention fights being very short. It is definitely not my experience. On that fight against the old white dragon in the last chapter of HotDQ, the party I was DMing for had to play a very narrow cat and mouse fight, them being the mice crawling through narrow tunnels and trying to squish some advantage in order to engage, while being chased by the dragon. The fact that the dragon had blindsight made it all very scary to them, as the dragon could usually anticipate their position and preempt his offence. The fight not only took several rounds, it actually was interrupted twice, with each side retreating to try to recover and set a different strategy. In the end, they didn't even kill the beast, but left him with so low HPs that he absolutely had to drop the fight. The heroes themselves were not in their best shapes, with HPs in the single digits for almost everyone, they suffered no casualties, but it was almost a TPK at the same time.