A few years ago I did a post called Counting Pieces where I noted that in his book The Inner Game of Chess-How to Calculate and Win Andy Soltis discussed the problems of keeping track of material in a complicated position, especially in situations that result in a material imbalance.
While playing through one of the games in the chapter on "Counting Out" where Soltis discusses the problems involved in counting pieces, especially those involving material imbalances, he didn't bother to analyze this game after move 21 because the remaining moves were not relevant to his theme. Also because the book was published back in 1994, I was curious to check the validity of his conclusions with Stockfish and Komodo. Whether he was exactly right isn't all that important because his general advice on dealing with such positions is excellent.
While it may be difficult for us amateurs to evaluate the effectiveness of the pieces on the board, counting them is no problem. The problem is that when calculating a sequence of moves where there are multiple captures, especially if the material in not even, it can be easy to lose count of who has what left!
For example, in the game Capablanca vs. Alekhine, Nottingham 1936, even the great calculator Alekhine lost track of the pieces left on the board when he was calculating his 24th move, f4. He thought he was winning two exchanges, but he actually gave up three pieces for two Rs.
There are two basic ways of determining what pieces are left when mentally calculating a long variation:
1) Review the sequence in your head and keep track of the pieces captured by each side along the way.
2) Visualize the final position and count the pieces remaining. Either way, it's not always easy!
This game is not only interesting in itself, but it illustrates that counting the pieces can be difficult. It was made even more so in this game because after a flurry of tactics beginning with 16.Nd5 Onoprienko won Liberzon's Queen and when we win the other guy's Queen, that always seems like a good thing, but the resulting position was very difficult to evaluate even using Stockfish.