An interesting cognitive phenomenon: if you ask chess experts and novices to memorize and recall an arbitrary chessboard, the experts are significantly better than the novices _only if_ the board is a legal board that can be arrived at during play. If it is not a legal board, there's no particular difference between novices and experts. Original ref: Chase & Simon 1973, Perception in Chess.
This is usually taken to mean that the brains (or whatever) of experts see structure that can be used for compression that novices don't, but that compression has assumed invariants you cannot break.
This isn't just for chess -- it's practically any knowledge task that you can build expertise in.
E.g. take programming. Suppose I sat down an experienced programmer and a novice and gave them the same small (~10-20 line) function to reproduce from memory. If the function is a "reasonably written function" I'm willing to bet that the experienced programmer could reproduce the function with just one or two "peeks" -- once you have enough experience, you can better recognize patterns / chunk your knowledge. A novice doesn't have this ability, so it would likely take them many more peeks.
On the other hand, if the function is some random gibberish with little structure, you could imagine that it's probably equally difficult for both the experienced programmer and the novice to reproduce the function from memory.
For chess, one reason why masters can better recall positions is because they know what typical positions look like (e.g. a position typical of the "London" opening). Then, they only need to store a "diff" of the given position and a typical position. ("It's a typical London setup for White, except White also played a3 and b4.") A novice doesn't have this knowledge, so they have to store the whole position.
Not a "legal" board, but a typical board. Both this and the original de Groot study picked positions from real games played by strong players. Experts don't do retrograde analysis on the positions, but they do recognise typical patterns that often occur in real play.
It's not really about whether it's legal, but whether it looks normal. Very bizarre positions can easily be legal, but they're hard to remember for everyone.
I’ve heard this corroborated by exhibition players who play ten or fifteen opponents at once. They do better with moderately skilled opponents than random people.
I don't know what you mean with "exhibition" precisely; I'd expect that to be true for blindfold chess (where you have to keep all the games in memory the whole time), but not for normal simultaneous as the strong player hardly has to think to find moves good enough to beat random players.
This is usually taken to mean that the brains (or whatever) of experts see structure that can be used for compression that novices don't, but that compression has assumed invariants you cannot break.