The following paragraph is the push-shot rule from the current 8-ball world rules:
Definitions: Most shots commonly known as “Push Shots” in the game of “Snooker” are allowed in the game of Eight-Ball Pool. Generally, any shot played with speed will not be deemed to be a Push Shot regardless of the fact that the cue tip may have come into contact with the Cue Ball more than once.
Exceptions that are Standard Fouls:-
When, during the playing of a shot, the tip of the cue strikes the Cue Ball twice and the referee is able to actually see each contact.
When, during the playing of a shot, a player plays the cue so slowly through the Cue Ball that the cue tip remains in contact with the Cue Ball so as to be visibly pushing it along.
This has to rate as the most ambiguous and stupid rule in the game. In effect, the referee and the player know very well when a push shot has been played. The referee can see from the reaction of the cue ball that it has been hit twice or pushed, but he is unable to call the foul providing the player has hit it quickly enough that he cannot clearly see the dual or pushed contact.
As a player in a league and superleague team, this is one ruling that I will completely ignore. If I push a ball, I know I’ve done it and I will call a foul against myself. In the past I have known my opponents to call fouls against themselves for push shots and they have my respect. Those who declare they can get away with it by playing the shot quickly are IMO cheating.