For one example of a compound combination, Euwe used the famous Lilienthal - Capablanca game where Lilienthal played a brilliant Q sacrifice. Another example of a compound combination was the following Capablanca – Kan encounter.
In his book The Art of Attack in Chess, Vukovic also discussed compound combinations only he used the term “creation of preconditions” to describe maneuvers necessary to build up to the final blow. These conditions come about in a variety of ways: slowly improving one's position, some happen by surprise and others are the result of risks taken by one of the players.
Vukovic advised that of all the preconditions for an attack on the King one should first create those that entail the least degree of commitment. i.e. those that also strengthen one's own position. By that he meant positional play that includes finding good posts for one's own pieces, a strong center, a space advantage and K-safety. After these conditions are met one can then induce weaknesses around the opponent's King. One caveat that CJS Purdy hammered on was that tactics can happen at any move due to peculiarities in the position, even those where one has all the positional advantages. Therefore, the position must combed for tactics at EVERY move. Another handy piece of advice from Purdy was that if no sound tactic is available and you aren't sure what to do, look for your worst placed piece and find a way to improve its position. This last piece of advice is in line with Soltis' statement that “planning” often involves a maneuver of only 2-3 moves.
Now would also be a good time to ask the question, “How much should you calculate?” Sometimes you simply must, but other times it just isn't worth it. Some claim that you must try to find the best move every turn otherwise you will end up playing second or third best moves for which there will eventually be a price to be paid. On the other hand, some think the search for the best move is worthwhile only a few times during a game. Even if there is only one “best” move sometimes the time and effort required to find it isn't worth it because the variations are so numerous that calculating everything is out of the question.
Of course, there are times when you must calculate. Andrew Soltis gives a simple rule: You must calculate when you suspect there is a move that forces a concrete result as opposed to the times there is a solid but relatively small difference between moves. For example, in this game at black's 20th turn Stockfish's top three choice are 20...Bg4 (-0.37), 20...Kg8 (-0.45) and 20...Kh7 (-0.47). For a human that's not much of a difference and any one of them would have been a reasonable choice.
In this game we see Capablanca building up a series of preconditions for an attack on Kan's King without making any moves which committed him to it. However, with move 19.h4 Capa undertook a premature attack when Kan's King wasn't ready to be stormed. At the time, Capa's Q was not in its best position and Kan could have used that small point to gain time for defense. Fortunately for Capablanca, his position was strong enough that he managed to get away with it. Capa received the Brilliancy Prize for his victory in this game.
All brilliancies require some cooperation from the loser and that is the case in this game. Some annotators give the impression that this game was a one sided crush of what Alex Yermolinsky called a “tomato can", but that is not the case. Kan put up tough resistance and it wasn't until he got into time pressure that his game was finally lost.