O.P , Do you would like to (a) improve chess by doing tactics or (b) do you enjoy playing tactics (puzzles)?
I will answer on first question. This is what I do in tactics in chess.
There are three steps in decision making of a move
1. Whether there is tactics/no tactics( Time management/ where should I spend my time)
2. What is my candidate move( predictive move)
3. Need to recheck my candidate move is right or wrong (tactics)
Most tactics training will categorize drills like, decoy, discover check. In the real game , no one is going to hint you "hey there is decoy in 2 moves" . So how can I know whether there is a tactics or not.
There will be shortcuts in memorized pictures in our brain that leads to that decision.
In this example, I will not consider tactics for checkmate with those pieces in mate in 2, cos my brain has shortcut that " I can block opponent king's one row escape when only my knight and bishops have different colors" . This is waste of time in calculating tactics.
But in this diagram , I will consider attempting checkmate opponent king with my rook cos, my knight and pawn have same color"
There are also multiple patterns or shortcuts in my brain where there is a possiblilty of tactics or not.
For example, think about knight fork only when your knight and two opponents pieces are in same color.
Step 1. Those pattern recognitiions will tell you where there is likely tactics or not. If there is no tactics, dont waste time, improve your pieces to better location, files etc.. In fact if you have well placed pieces logically and positionally, you can prevent 90% of tactics. For example, in this position after. 1. e4 ..e5.2.Nf3..f6 .Black misplaced weak move 2...... f6 , so there is 3. Nxe5 tactics possiblilty. If black play 2. Nc6 instead , no need to consider tactics.
Step 2. I think there is tactics, where should I hit. That need experiences, about weak pawns, hanging pieces , checkmates etc
Step 3. Did i check all lines.
In conclusion, better players dont waste time in doing unlikely tactics moves. Instead they spend time in step 1 by putting pieces in well corordinated places. Step 2, They have better accuracy in prediction of likely tactics, checkmate or promotion etc. Step 3. Tactical calculations according to your available time limit.
That is the reason, where amateur playing 2 hours /game cant win a GM playing 2 mins per game.
Nice explanations!
So, basically, the best puzzles book would include diagram of the position, which is 1-2 moves before the actual tactics happens? For example, if there is a fork at White's move 27, then the diagram show the position at move 25 or 26?