Maths professor shares simple puzzle to win your next game of pool at the pub

For those who are determined to smash it at their next game of pool at their favourite local bar, some simple maths and puzzles can help.

With the country slowly getting back to normal, bars have opened and people can finally sit inside and have a pint with their mates and shoot some pool.

As fun as the game is, especially when you're a bit buzzed, there is a decent amount of strategy to the game. Surprisingly there’s a lot of maths involved too.

Understanding some basic mathematics and simple shapes and puzzles could be the key to being the best pool player in your friends' group.

As reported by Popular Mechanics, Victor Donnay, a mathematics professor at Pennsylvania’s Bryn Mawr College, says the maths behind pool involves a “dynamical system.” This is basically a study focused on systems controlled by a specific, consistent set of laws over time.

It usually involves differential equations, and no matter how pro you are at pool, there’s always one fundamental mathematical aspect of a game of pool you need to focus on – and that’s simply the shape of the table.

Victor said: “Square or rectangular is one of the simplest shapes. That’s the one people use for real billiards, there’s a lot of regularity of what’s going to happen…so that’s a very simple and easy-to-understand dynamical system.”

A rectangular table pool shot will play out like this:

It will bounce off the table’s edge with an angle equal to the angle it arrived at, and traverse a square shape, keeping parallel lines all the way.

A circular table pool shot will play out like this:

This one’s a little more complex, says Donnay, as it involves traversing a star pattern instead of a square one. The ball's trajectory is predictable from a mathematical perspective.

Things get tricky when you flatten out the edges of that circle into a shape that math’s brainboxes call a “stadium” (which in geometry is a rectangle with two semicircles on opposite ends.)

Mathematicians have found that concave curves, like the edges of a stadium or the circumference of a ball, can cause a bit of chaos when playing your game of pool. To avoid this, the real trick of the trade is to keep an eye on the angle you strike your cue ball with.

So, what about the skilled pool players out there, do they think of mathematics when they’re playing?

We spoke to Max Shepherd who was a pool college captain and represented Lancaster university at BUCS.

He said: “I know plenty of good pool players, I’d say over half the university pool team majored in a maths/science-based degree. It’s all about angles, so I guess they do go hand in hand.

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“Pool is very much down to skill and strategy, although there is some luck to it like with any game or sport. As Gary Player the famous golfer once said ‘the more I practice the luckier I get’ – this applies to pool also.”

When it comes to succeeding at pool, Max has some sound advice for those who want to up their game: “You want to intentionally leave yourself a nice angle between your white ball and object ball, if the two are lined up straight towards the pocket.

"You are limited on where you can get the white ball to go. If you have an angle, however, you can manipulate the cue ball to go more places. Too much angle though and you lose control of the white a bit and the pot becomes harder.

“Leave the cue ball in the middle of the table, this way you need the cue ball to do less ‘work’ for you, and won’t need to play your shots as hard or make it spin round the table."

To really succeed in a game of pool, Max advises: “Identify the problem balls you have early (for example a ball on a cushion), are you going to develop it (try and get it to the middle of the table) or play onto it (for example play it down the cushion or double it).”

It would seem that avid pool players are very aware of the mathematical link to pool with a lot of them coming from a mathematical background. Whether it’s a coincidence or not, the link is very much present.

Max added: “I don’t think you need to be good at maths to be good at pool though, it’s an art as much as a science."

So there is hope for some of us then.

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