the Hand/Fingers/Cue/Tip relationship will always be VERY important.
Did
3) My opponent missed and left me...
4) I made 2 balls on the break and...
cross your mind?
That's keen "spidey sense".

....and indeed there's many times you HAVE to be able to make a length of the table draw. Many of which (like the two you mentioned) don't have anything to do with situations you can "control".
I remember when I was 7 - 9 years old and I could not draw my ball. I watched the older players, and even though I could beat them I was so impressed with how they made the cue ball spin back after contact. No one would show me how to do it, because,
they said "it will hurt your game".
I'm not sure the real reason, but it proved to not be the last time I was lied to in a pool room. :wink: There was one guy that especially irritated me by brushing me off and not showing me the "secret draw method".
This was the guy that "drew" his cue ball especially well in my home pool room that was overly "confident" and refused to play me. One Saturday afternoon he accepted my challenge and we played 5 games of which I won 4 of them.
He stormed out of the pool room, and I stayed behind to practive, because
in the course of playing him I had uncovered his "secret". I tried it and immediately drew my cue ball for the first time. What a thrill, and come to find out it didn't hurt my game. On the contrary it became my best shot.
I have helped players learn the power draw method many times over the years and I've broken it down into a very simple method.
1) Make sure your grip is solid and able to control the top part of your pool cue. You will use the top part of the tip to create the "draw" so you want to be confident in your hand/fingers that you control the top in particular. Also, MAKE SURE your bridge is firm and contolled as well. I firm bridge is essential to controlling distance and the only time a closed bridge is better than an open one. imho
2) Measure up below the center of the cue ball with the TOP of your cue and make sure you feel the contact point your seeing on the cue ball with your hand. Connect the top of your tip with that feeling in your hand.
3) Now, take your pool cue back a few inches and return it as quickly as possible To Where is Started. No matter what type of stroke you use the key component is the ability to take the cue back (on the backstroke) a few inches and return it to where it started (where you were measuring up to the cue ball).
The main objective in the game of pool is forming and unifying your hand/tip relationship. Your hand touches the pool cue, your tip touches the cue ball, and the cue ball touches the object ball, so if you want the "touch" to play the game well it's best to understand these basics.
No matter what level you reach the Hand/Fingers/Cue/Tip relationship will always be VERY important. When a beginner learns this right away it opens up the door to learn advanced techniques much quicker and easier. 'The Game is the Teacher'