GM Kotov wrote a famous book about calculation in chess, Think Like a Grandmaster. He discusses the calculation of variations using an extended metaphor, the tree of variations.
The basic idea is that players should calculate a tree of variations. Players should only examine each branch of the tree once. Why once? To keep from dithering over multiple lines and then feeling time pressure, when they can be tempted to play a completely new candidate move and not even verify if it is sound.
A tree of variations implies that there are a small number of candidate variations to examine. Kotov recognized this is not always the case. Sometimes a player has to make a decision without the benefit of careful calculating every candidate variation sufficiently.
The game below is instructive for us improving players. GM Walter Browne felt he had a winning position. He likely calculated a handful of variations out several moves. Out several moves, there was still uncertainty. What GMs and IMs have that we do not is much greater experience and – as a result – a better-refined intuition about the outcome from a sacrifice and the initiative that follows. They make better evaluations. After black played 12. … 0-0, GM Browne reasoned this was the critical moment to begin a kingside attack. He sacrifices a rook in exchange for a swift and crushing initiative. He made his evaluation on the basis of partial calculation.
There’s another instructive lesson here for us improvers. GM Browne missed that 20. Rf1 was premature one move. It was his good fortune that his opponent missed it, too, since 20. … Qa5 would have given black some counterplay after 21. … Qe1+. Black further blundered by making the move Qa5 one move too late. Had he played 21. … Rg7 instead, white would have won the exchange and had a much better position but black could have continued to play on.