Using Math To Improve Your Pool Playing

 

I learned to play pool when my family stopped at a KOA camping ground in New Mexico.  I was a teenager, 17 or so, and it was a great way to meet boys but I wasn't real good at it.  Now when my students ask about when they'll use geometry, I tell them that you use it when you play pool because so much of it involves angles. 

From a mathematical point of view, playing pool involves a dynamic system. Mathematically, a dynamic system is a system in which a function describes the time part of a point in geometric space.

So lets look at the basics.  A straight shot is one that goes straight into the pocket and is considered one of the easiest to do. Then there is the angle shot where the player bounces the ball off the side using the law of reflection which states that the ball bounces off the side at the same angle it hits it. So if the ball hits the side at a 35 degree angle, it will bounce off at 35 degrees so knowing this you can predict where the ball will go based on the angle it approaches the rail.

Lets start with the break.  Mathematically, if you are using an 8 ball set up, you want to hit it straight on but if its a 9 ball set up, you should have your ball approach it at an angle so you are able to bump one ball into a pocket without scratching. In addition, it allows you to choose whether you want solids or stripes and it can put your opposition at a serious disadvantage. 

In addition, it is important to keep track of how much energy you use when you hit a ball with your cue.  If you hit the ball too hard, it may bounce off another ball or end up in a pocket so you are out.  If you don't use enough power, your ball won't go very far.  Furthermore, the angle you strike the ball determines where it goes. Now if you keep your cue more towards the middle of the table, it makes it easier to shoot the ball more accurately without using too much energy.

Now back to the law of reflection.  This can be used when you have the cue ball and the ball you want to hit and they are the same distance from the rail.  When you shoot the cue ball, you need to aim about half way between the two balls so the angle the cue ball hits is the same as when it bounces off.  Basically you are relying on congruent triangles.  If the balls are not the same distance from the rails, you have to rely on similar triangles to hit the object ball because the share the same angle but they travel different distances.  

A good player who understands the math also knows that that how they hit the object ball with the cue ball can determine which way both balls travel.  If the cue ball hits the object ball at the wrong angle, it could send the object ball the wrong direction while causing the cue ball to scratch.  So many different things to keep track of but its all mathematically based.  One person recommends that the easiest way to win is to play against someone who doesn't know the math involved in playing pool.  Let me know what you think I'd love to hear.  Have a great day.