Updated: Feb 7, 2019
This comes up all too often, and unfortunately there is no way for the human eye to discern a double hit. First lets discuss the definition of it, strategies to identify and avoid making a double hit, and finally how to avoid issues and controversy during a match.
What is a double hit?
A double hit occurs when the tip makes contact with the CB, leaves the CB, then touches it again. In slow motion you can see that this occurs extremely often, and when the balls are close it's nearly impossible to see it happen without a high speed camera.
It looked good to me!
The problem general exists when the CB and object ball are within 1 inch, or the width of a piece of chalk. If you shoot that straight on, it is nearly impossible to stop the forward momentum of the cue before it reaches the object ball. One way to tell is by the behavior of the CB after contact. If it follows the object ball down the table, then there's a good it was hit twice. A rule that many leagues and tournaments follow is if you are in a possible double hit situation, the cue must approach the object ball at a particular angle. Some say 30 degrees, some 45 degrees. This does not guaranty a double hit will not occur but is a good rule to keep everyone playing with the same understanding.
The balls are frozen. Now what?
If the CB is frozen to the object ball, then a double hit will not occur, it will be a push instead, but this is where you will get the most difference in opinion. The APA rule book states in this case you must shoot away from the object ball, and if required to make contact, hit it coming back off the rail. For years I've been told it's legal to hit it any way I want because it's not a double hit. In fact I can push it through the whole stroke as long as the cue doesn't separate from the CB. I wish this rule would be examined fully and be followed consistently in all formats, but for now its still a gray area for many.
What's the solution?
So... if your rules don't specifically address the situation, and there is ever a doubt as to whether a shot will be considered a double hit or foul, it is important that all parties discuss what's expected before the shot, and agree on what you plan to do, and what the criteria will be for a legal hit. It's more important to be up front and honest, and understand there is no right answer (until we have high speed camera replays?), no matter how much someone thinks they understand the physics of pool, which way the cue should go after contact, or... blah, blah, this is one place that we all just need to agree on the solution before the shot is taken. If someone says phooey and it's not a double hit, or they can just tell because they're so experienced, then they just don't understand the physics of cue to ball interaction.
One interesting solution I've seen is to address the cue ball by placing the tip under the edge of it and flipping straight up on the cue tip. If the overlap with the ball is less than the distance to the object ball you are guaranteed not to double hit. Anyway, lots to debate here and I'd love to hear comments...