Is pool actually just mathematics?

Get a signed first edition of Love Triangle from Maths Gear: mathsgear.co.u...
All UK options: www.penguin.co...
All USA options: bit.ly/3wCTesR
Huge thanks to Rollie and Jenn. Check out their videos on the diamond system.
• The Easiest 2-Rail Kic...
• 2-Rail Kicks Using Par...
Rollie's Climate Town videos: / @climatetown
Rollie is an average pool player: • Your Average Pool Player
Jenn's pool videos: / jenn9mmbarretta
We filmed at Jenn's fantastic venue: Skyline Billiards and Bar. You should go there! www.skylinebil...
And that Grant guy makes some pretty good math videos: / @3blue1brown
Huge thanks to my Patreon supporters. Whenever I bounce off them they give me plenty of spin. / standupmaths
CORRECTIONS
None yet, let me know if you spot anything!
Filming by Alex Genn-Bash
Editing by Gus Melton
Written and performed by Matt Parker
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson
Playing darts in the background out of focus: Bec Hill
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinran...
UK book: mathsgear.co.u...

[@0cellusDS]

As a physicist, if my shot doesn't miss the pocket by 10 pocket lengths, it is pretty accurate and should thus count as a perfect hit.

[@WestOfEarth]

As an astrophysicist, if the shot keeps the ball in the pub, it's good.

[@dm9910]

one of the funniest things about physics is that depending on the field, the inaccuracy panic threshold of "either our study or the entire theory needs to go in the bin" could be anywhere from the tenth significant figure to several orders of magnitude

[@charliethunkman]

As a cardiologist, If the shot misses by 10 pocket lengths the cue ball is in cardiac arrest and needs immediate response.

[@Dystisis]

@@WestOfEarth the ball remains within orbit of the sun, i see this as a win

[@Imperial_Squid]

As a statistician, so long as half the balls miss to the left and half miss to the right, you're golden 👌

[@joaopedromullerlima654]

"There's more air in the room than I'd assumed" that actually broke me

[@TheFantasticMrFish]

It's a really good line

[@aryasaktiflister_aw]

the scene of a pair of mathematicians breaking out the notes and measuring tape in the middle of a pool game is something straight out of a comedic skit

[@mikescorpio13]

well watching modern player is as boring as this,when they turn around the table 4 times each shot and the lay the tip of their cue too many times on the cloth just to aim their shot that they will miss 75% of the time.Idiotics mathematics and tricks about spot on walls is what made this sport a snoozefest during the 90s. Too much pseudo-mathematicians equipped with ridiculous 1000$ cues but not many natural physicist who can do all the same stuff even better with regular house cues.

[@JC_923]

​@@mikescorpio13We get it. You don't like smart people who make you feel small

[@mikescorpio13]

@@JC_923 hahaha i love smart people like me,i hate pretenders

[@JustASunflowerSeeD]

well this is "stand-up maths"

[@Daniel-h8c1u]

These guys are mathematicians, yes. But they make a lot of videos like this BECAUSE it's funny! If you don't have the intellect to understand that, please don't vote.....

[@Sharivari]

12:04 is incorrect. Running side is the opposite. It opens the angle, and therefore will arrive at the same point on the third rail, but coming from a different line of the second rail. Jennifer explained it correct at 13:17

[@jewby08]

Yep. This was the comment I was looking for.

[@emberklavins9567]

Thank you! just came down here to say this!

[@LimitedWard]

I don't play pool, but intuitively I thought his animation seemed wrong.

[@SocietyIsCollapsing]

I knew someone else would have replied with this info.

[@calebmaddox8979]

"There's more air in the room than I assumed." 😆🤣😆

[@Simon_Laserna]

the pre-game banter was A-tier!

[@lasagnahog7695]

Matt's understated but incredible comedy chops really show in this one.

[@vegiimite]

Best line ever

[@benbooth2783]

In more ways than one lol

[@samvknip3297]

I am 100% going to use this joke mid conversation

[@MSPcraps]

I love the way this validates the system. The "phantom table" actually shows that we're aiming roughly into the phantom version of the pocket. Awesome.

[@decked2199]

2 mathematicians enter a bar with a measuring tape...

[@dj_laundry_list]

"Let's use inches!" Says one of them...

[@russellbeaubien7430]

@@dj_laundry_list The other stabbed him with a bar stool

[@Kyle-nm1kh]

I can't believe they measured in inches then scaled in millimeters

[@kindlin]

@@russellbeaubien7430 And decimal inches while we're at it.

[@weakw1ll]

This is more fun than i thought

[@IamtheWV17]

The second they said "about --- inches" They were doomed

[@sarmadgulzar]

"The math doesn't make a difference if you don't know how to hit the cue ball." Genius.

[@MichaelKingsfordGray]

Facile.

[@Kyle-nm1kh]

He said at one point 80% skill 20% math. That's probably pretty accurate. Math is there but it's a shadow in comparison to the physics.

[@McSlobo]

Yeah, but it's a stochastic process, so you can still use statistics...

[@asdads3948]

As a maths guy who likes to play billard from time to time, that was my first thought. You can have the perfect idea, but playinga perfectly straight shot is hard af, and the slightest spin will make any plans about bouncing off the walls useless :D

[@sarmadgulzar]

@@asdads3948 absolutely. In ideal conditions with no air, drag, friction or spin, simple geometry might work but in reality, the math involved is very complex.

[@yannickpit6886]

I love that it's implied that rollie doesn't have a specific editing style, random eagle and explosion effects just kinda show up in whatever video he's in

[@adammcveigh]

Alternative title - "Mathematicians discover how engineers feel when handed drawing plans from architects

[@GaryBickford]

My brother's entire career in beam steering systems was converting physicists' abstract theoretical designs through the black art of making it actually work.😊 This required a kind of intuitive, empathic understanding of real-world electrons, photons, and materials. The pool table is probably a pretty good analogy.

[@FatGringo]

Counter - "Engineers discover how Builders laugh when handed plans from an Architect"

[@GaryBickford]

@FatGringo Boy, is that the truth. My dad was a builder. Outside of a few, he had little respect for architects. At that time, architects were not required to take any structural engineering classes. And most didn't. A few schools, such as Cal Poly in San Luis Obispo California, did require structural engineering, and graduation requirements included actually building a small building. One example - a home my dad was building had a cantilever deck. But the architect forgot that a cantilever requires so.ething to hold down the other end. Well on the way to building the house, they had to stop construction, wait for new plans, tear out significant work, and rebuild.

[@justamanofculture12]

Engineers realize the nightmare of architects 😂

[@lemon4087]

​@@GaryBickfordcantilever

[@LARAUJO_0]

"To answer that, we need to talk about parallel universes" ~ Pannenkoek2012, 2016

[@strixt]

Man of culture

[@anto8722]

Now this is a great reference

[@Muhahahahaz]

Only if they’re going for Minimum calculator button presses… 🤔

[@krovelMx]

Now that I think about it, speedrunning and math interests overlap a lot. Such a great reference you got there friend!

[@anto8722]

@@Muhahahahaz we should worry about half presses tho

[@sharkinahat]

I think you need a bit more janky Python code for this one.

[@vlc-cosplayer]

By the time the Python code has given him the position and angle, the place is closing up 💀

[@pierreabbat6157]

@@vlc-cosplayer Do it in Julia, you'll get the result sooner.

[@DaTimmeh]

Oooo I got you covered! Wrote an incredibly mediocre billiards physics program in college. It's a bit more accurate than their math, but not by much lol.

[@silvncr]

@@DaTimmeh i'd love to take a look

[@mildu545]

what about some terrible, terrible python code?

[@EvilTim1911]

I love this, Jenn has such deep knowledge of the game, it's very interesting to hear these things explained by a pro

[@NaHBrO733]

"Is there friction?", "I assume not" LMAO🤣

[@yna418]

so real bro😂

[@themostselfishman]

I loved your last two books and it is a real treat to see you and Grant together. I would 100% watch a show of you both trying to model or solve real world problems, maybe with a physicist in tow to be confused.

[@elmamaco7303]

That would be amazing 😂

[@iamalsopropaganda]

Pool Players: “They’ll never get it because they’re measuring based on the walls and not the diamonds.” Mathematicians: “Jokes on you, we’re pretending that we’re playing in a hall of mirrors!”

[@DeltaEntropy]

Jokes on you, we just constructed a ghost universe

[@kindlin]

As one of those novel individuals that's good at both pool and math, I've long known the diamonds just made no sense at all, and to me, are nearly useless. I do use them as I can, but only as a vague guide or reference to compare to other points of reference, they don't help in determining how to actually shoot the shot. Even as stated in the video, the add-to-80 rule is only a rough guide, so it really does just all come down to practice and feel.

[@engywuck85]

⁠@@kindlinthe real question now is: can we come up with a better system for guiding marks than those diamonds?

[@Squant]

@@engywuck85 I think the better question is: do we need to? Snooker tables don't have diamonds. If anything, we should be making things harder for the players.

[@DM-kv9kj]

Jokes on the mathematicians in this case, because they still can't play well at all and no amount of inventing theoretical universes and nonsense will change that. Pool is pure feel and tactile skill.

[@maxeuker2949]

Can't get enough of Rollie on this channel. Keep the partnership up, two of the best people on youtube!

[@positivity3311]

remember, these are mathematicians, not physicists.

[@Anvilshock]

Correction. They're mathmematicians. See 1:23 and look closely.

[@handledav]

correct

[@Varksterable]

​@@Anvilshock🙄 Shush, Hock of Anvils.

[@Flyingcar100]

They should have gotten a physicist for the team

[@keithmartisius781]

So should they assume perfectly spherical balls still 😂

[@ThatBenKraft]

Grant’s animations are just always out of this world.

[@theaxer3751]

"100.4 inches" Wow, you upset both metric AND imperial users in one phrase. That's next level!

[@jonathanrichards593]

Yeah, was that really a tape measure with markings in tenths of an inch? Or was Grant approximating to 100⅜" in his head?

[@AalapShah12297]

I was wondering why Matt didn't ask whether it is 100 4/8 or actually 100.4, instead of talking about metric vs imperial.

[@andrasszabo1570]

It's 96 inches = 8 feet anyway. But they measured the bed of the table, not the playing area.

[@AalapShah12297]

@@andrasszabo1570 That's not the point of this comment. Rulers with inches always show markings with increments of 1/8th or 1/16th inches. 100.4 is not a standard way of measuring something in inches.

[@dimitralex1892]

ohh wow, didnt know you guys use fractions instead of decimal places. Isnt it uncomfortable? not making fun, just really interested. an inch is "not as accurate" as centimetres (because inch>cm) and then instead of decimal places you opt for fractions? isnt this far more complicated and also somewhat inaccurate? or do you simply try to use full inches and leave out fractions?

[@macnolds4145]

If you want a mathematician/scientist/engineer who also knows how to correctly apply math to pool, you get Dr. Dave (a guy who Rollie has already made a great video with, btw).

[@cobaltcloud64]

3:18 i love how Grant expected that exact reaction from Matt to the use of inches that he had is face ready for the comeback

[@cobaltcloud64]

and with how he just nods when the reaction actually comes, you can basically hear him thinking "mmh yes all according to plan"

[@capitalcitygiant]

My guy preloaded his face 😂

[@HanabiraKage]

Grant's clearly watched Matt's video on imperial units.

[@juandesalgado]

"You're such an imperialist", said the man using imperial units.

[@havardmj]

@@HanabiraKage He's a mathematician. He knows how impractical imperial units are.

[@artificercreator]

This is the Math vs Physics pool battle i didn't know always wanted to see. Thanks.

[@Varksterable]

So many spherical, weightless cows in a vacuum.

[@lvn5609]

Just a minor rounding error

[@gordonwiley2006]

I was going to say that they should probably assume a spherical pool table.

[@Sandeepan]

I was waiting for someone to bring up the spherical cows

[@Varksterable]

@Sandeepan They have to be frictionless too. And with a maximal coefficient of restitution. Cows. Such wonderful physical ideals.

[@gary.h.turner]

​@@VarksterableAnd on a frictionless field!

[@StyxAnnihilator]

The main issue is to transfer the math into physics, that is position and direction and force of the cue. Normally you do some angled test shots on a table to see the friction and bounce, along check edges for differences.

[@_Matchu]

obviously math can account for every possible thing... friction, humidity, air drag, etc etc... it's just a matter of building all these factors into the simulation I would LOVE a part two where you over-engineer a simulation program running on a laptop and try to beat them using THAT !!!!!!!!!!

[@diskgrinder]

Well a laptop is probably too small to fit the balls on

[@Sgrunterundt]

They might need someone like Mark Rober in on that

[@HellHeater]

stuff made here breathing intensely

[@Kleyguerth]

That reminds me of the Stuff Made Here channel. He built an automatic pool stick that accounts to all that, you just aim and let it do the magic. Just mathing it out is not enough, as the software telling you to hit a 23.5 degrees at 34.33N giving it a spin of 14.2RPM clockwise will hardly translate into you actually hitting the ball with those parameters... You need a robot.

[@ratinthecat]

@@Kleyguerth You need a robot? There are only three parameters involved in executing the shot. Angle, position of the cue striking the ball, and force applied. The last one is a bit tricky, but with practice you could use perceived effort and muscle memory.

[@ucantSQ]

2:09 Rollie sounds harsh here, but I almost immediately thought of the Parker Square. I already love this episode.

[@A.F.Whitepigeon]

"The table is 100 inches long, so when you divide into 80 segments, each segment is 1 inch." New unit unlocked: the Parker Inch.

[@aceman0000099]

Time stamp or it didn't happen

[@pjarnfelt]

@16:18, but he said "so that's the number of inches" a bit vaguely about it 100 is the number of inches (which it is) or if the 80 system is the number of inches.

[@AalapShah12297]

And then Grant says 'hmm' but his expression changes 2 seconds later as he realizes the mistake. 🤣

[@robgoodsight6216]

🤣🤣🤣🤣🤣🤣🤣🤣🤣

[@thaumar64]

1 parker inch=1.25 inches

[@johnfau06]

At 12:24 you got the direction of spin wrong. You animated "check" side not "running" side. Running would be in a direction that would open that initial angle. It's called running because it actually imparts more energy to the ball and carries it further.

[@lasagnahog7695]

What a great way to show the difference between theory and application. Jenn was super patient and cool about everything, she's a great communicator. Rollie was there too!

[@sebastianjost]

Clearly the model wasn't accurate enough. If your model is bad, even a perfect calculation won't get you to the goal. A good model delivering only an approximate solution is often more desirable because you at least get what you calculated

[@Anvilshock]

Glorious. "Jenn was cool and good at teaching. Also, there was Rollie."

[@matt45540]

Rollie is there for the lols, drinking his coffee in a bar

[@emperortgp2424]

the guy was so annoying

[@thenonsequitur]

@@emperortgp2424 He made one decent joke ("the table is way larger than 10cm"). For the rest of the video he was just kind of there.

[@Clyntax]

I think the "diamonds" already respect the cushions. So the first and last diamonds have an offset. You can see at 22:07 that the imaginary last diamond of the bottom edge would be exactly on the cushion line of the right edge.

[@n0tthemessiah]

"These guys have been failing up for their whole lives, I don't want that to happen at this table'' -- Man who affixes all mics with blue tape

[@EmyrDerfel]

That blue tape is brutalism.

[@qirex3093]

16:22 I can feel a ‘pool table to find pi’ coming on

[@kameronpeterson3601]

@12:00 you completely misunderstood what Jenn was telling you. In the animation the spin you gave the ball is reverse spin, it's working against the natural way the ball wants to spin off the rail. Jenn tells you to give running spin (in this case left spin). Recall that in your first attempt the ball went to the right of the 8 ball (from the POV of the balls movement). This is because you hit too far to the left on the second rail. Using reverse spin makes the cue ball rebound at a greater angle than incident which makes it move even further left before it hits the rail, missing by an even larger margin. Instead, you should have used running/left spin so that it rebounds at a lesser angle, rebounding to the second rail further to the right, and putting you more on track to the 8 ball.

[@whitelion204]

Yeah I also noticed the wrong spin haha

[@fasullamail]

Exactly. It was almost the opposite.

[@spaskis1976]

A mathematician without physics skills it seems. Awful representation of a science video.

[@michaelkim4743]

Immediately searched for this comment after seeing the diagram and vigorously shaking my head at the incorrect animation. The running side causes the cue ball to open up off the first cushion. It will hit a closer spot on the second cushion but since it has running side it will open again and head towards the intended target.

[@idontwantahandlethough]

@@spaskis1976 calm down

[@ericmoss6110]

Who would win? Mathematicians, Stuff Made Here, or actual pool players?

[@adityaagarwal2341]

stuff made here will use a cannon instead of a cue...

[@Alehud42]

As soon as Grant started measuring in inches I immediately switched allegiances to the pros, a travesty of practical calculation.

[@notquitehim]

Lmao same here, also the Pros use a zero based index system for counting diamonds, pretty sure Matt felt out mathematiciaed there for a second

[@rmsgrey]

Yeah, you should clearly measure in table-lengths.

[@Asiago9]

As an American, you really should use centimeters for any physics calculations

[@gertboltenmaizonave2421]

​@@Asiago9There's only one country in the whole of America who doesn't.

[@jetison333]

​@@rmsgrey good idea! We could even do centitable lengths! ;)

[@T1J]

i love watching people who are really good at what they do

[@poolians]

Hi Matt, the animation at 12:08 is wrong. Jen uses running spin, which in this case is left spin - the left spin widens the angle after hitting the first rail, making the ball hit the second rail higher. This compensates for the induced spin, and the cue ball will reach the ideal target point.

[@landsgevaer]

Clockwise seen from the top, I presumed. Makes sense. I was thinking that the ball should ideally contact the cushion rotating as it would if it was "rolling" along it, i.e. no slip condition with the cushion. Then it need not transfer angular momentum into momentum or v.v.

[@AalapShah12297]

Yeah, the phone footage at 22:03 shows Jenn applying clockwise spin, as opposed to the anti-clockwise spin in the animation.

[@masterdurick5667]

I appreciate this kind of video to show the differences there really are between math and pool, and very little math is needed to play pool well. Though there are mistakes and ambiguities in the explanation from both sides, it also shows how complicated things are

[@nikitafilippetti7504]

"there's more air in the room then I assumed" Matt Parker, 2024

[@Anvilshock]

than*

[@leonardo.1024]

possibly *error, not air, too.

[@1e1001]

nope it's "air"

[@nikitafilippetti7504]

Sorry guys, not my native language

[@Anvilshock]

@@nikitafilippetti7504 may or may not be my native language either, so …

[@seanbarton9175]

12:09 actually, they give it the opposite spin in this case! Running spin is spin in the direction that the ball is hitting the rail, and check spin is opposite the direction the ball is hitting the rail (which is what the animation shows in this case) Essentially any time a ball hits the rail with spin, it’s going to change the angle that the ball comes off the rail. Running spin will make the angle slightly larger than a perfect reflection, and check spin would make the angle slightly smaller than a perfect reflection In the animation shown, the friction between the ball with check spin and the cushion would actually change that first angle to be slightly smaller, meaning it would land even further down that second rail and miss the ball by even more! What Jen suggests in this case is actually to use running spin, so the angle off the first rail will be larger and therefore hit higher up on the second rail. There’s a little more physics that goes into how spin wears off over time, but generally running spin will last longer than check spin because not as much energy is transferred for each bounce. So in this case there would still be some spin when the cue ball hits the second rail, increasing the angle again and taking the cue ball on line to hit the 8 ball :)

[@geoffstrickler]

As an excellent mathematician and pretty good pool player, my money is on the pool players. Every time. As a mathematician, I love the collaboration between Matt and Grant. As a pool player, I love having the pool players here to teach them a lesson.

[@RymdTeknisten]

I it's more interesting that they were both engaging with each other. Jenn teaching them about the tricks they use but still open and curious about how Matt and Grant were thinking and trying it their way

[@robertcole1272]

This is a video from three creators I already watch, about two topics I enjoy. Why didn’t youtube recommend this to me? This is fantastic.

[@trys9262]

Annimation at 12:08 is incorrect. The cue should be applying left (running) spin on the ball so that the bounce off of the first cushion has a smaller angle of reflection, which then means the impact on the second cushion is closer to the left side of the screen and then the ball, again, has a smaller angle of reflection than incidence and goes towards the pocket. (backed up by viewing the ball at 22:20 and Jenns explantion of "opening the angle" i.e opening the angle between the incident and reflected line)

[@moonshine7753]

Huh. This is very interesting because I think it should work both ways. I was confused at 22:20 because I expected what the animation shows, but your explanation makes sense. On the other hand, if you spin the ball the other way (like in the animation) the ball should stop spinning when it bounces for the first time and wouldn't open the angle on the second bounce, which I think should also work.

[@trys9262]

@@moonshine7753 if you were to apply the displayed spin, you would actually need to aim further down the screen as it would steepen the angle of reflection, however the spin of the ball would still be reversed after the impact due to friction on the cushion meaning the angle would still open up on the second bounce. But yes, still playable

[@2563dicko]

It will only work with left hand spin, right hand spin will affect the angle of the first bounce making it come longer down the table for the second bounce and it will likely still have spin from the first bounce, the original comment is correct and the only way to make the correction apart from aiming differently.

[@jama211]

yes, well said.

[@ScottiStudios]

Yeh it was wrong. He showed the animation and Jen explained it, the two didn't match up 😅 The first bounce would have come off at a different angle, which was the compensation, not the spin/lack of spin on the second bounce.

[@Derek_Read]

Love mine for driving and removing deck screws for decks and fencing. Switched a few years ago when I got a DeWalt set with drill and impact drill. ymmv if not using Robertson deck screws, but I love it. Screws are usually reusable in my situation as well.

[@steampunk_willy]

Reminds me of the time in high school where I proclaimed, "I CAN SEE GEOMETRY," and proceeded to totally whiff my pool shot. My friend was dying with laughter 😂

[@JH-ji6cj]

Contrast 11:30 with 22:20 to see that the rotational spin needed to be imparted on the ball is actually OPPOSITE the running english (spin) used in the diagram. The diagram shows right imparted spin to the first rail, yet it SHOULD show left rotational spin into the first rail. The exercise as performed by Jen is better shown here.

[@devttyUSB0]

"My brain REFUSES to look at the inches"

[@guiorgy]

My brain refuses to accept the existence of- uhh... What were we talking about?

[@BartdeBoisblanc]

Weeping Angels are in the chat.

[@scottshedden5094]

Don't tell anyone 🤫 ...but modern US inches are defined using the metric system.

[@robo3007]

There is one thing that both Brits and Americans agree on measuring in inches

[@lucaillgen1248]

​@@BartdeBoisblanc More like the Silenc- what was I talking about?

[@BingoDan936]

Muscle Memory - Can you make the cue stick remain parallel to the line of aim. The line of aim - a point on the cue ball and a point on the object ball. Object ball point is determined by the direction goal, like a pocket. To make an object ball in a right hand pocket, draw a line from the pocket through the object ball, should exit the left half. Using the right half of the cue ball, make the two equal points meet. This line between the cue ball and object ball, your cue stick must be parallel to this.

[@sirmyself]

Matt: "is there friction?" Me: "You leave physics out of my maths, mister!"

[@0Caracalla]

Friction from the cloth is such a huge variable in billiards, like it makes an enormous difference in table playability lol

[@sirmyself]

@@0Caracalla stop justifying a mathematician thinking about physics!!! 😛

[@TheEvilCheesecake]

friction is maths but you want to be proud of your ignorance it seems.

[@victorlc.vabeiryusa7458]

Heh how about leaving out maths from physics 😂 physics without math is philosophy..

[@ThePrufessa]

@@TheEvilCheesecake friction is PHYSICS!!!

[@byronwatkins2565]

Actually, the friction at the first rail causes the first angle to be steep (closer to 90 deg.) AND the spin causes the second angle to be shallow.

[@Cowmilker98]

Matt! You got the explanation at 12:05 wrong! They don't add 'check side' (as you've animated - side spin to narrow the angle of reflection) to counteract the imparted spin. They add 'running side' (the opposite), so the angle off the first cushion is widened, causing an earlier second-cushion bounce (i.e., further to the left as we look at your diagram) such that, during this second bounce, the angle of reflection widening due to the running side actually brings the cue ball back on to a line that leads to the target!

[@liam3284]

That "spot on the wall" is also the math behind navigation using leads. If you want to follow a straight line, pick a near and far point with the angle you want between them, and position yourself until they line up.

[@DrTacoPHD665]

I remember watching Rollie's pool videos years ago, then finding his climate town channel and other colab with Matt. Very sweet to see him playing pool again

[@Ensrick]

This takes me back to classical mechanics problems in physics. I knew straight off the bat, this is going to be complicated because it's not so simple to measure the force applied to the ball, and that's an important variable, as it determines the spin of the ball, and thereby the angular momentum, which you have to control when you hit it.

[@Ilix42]

When I was a kid, I used to watch this Disney VHS all the time called “Donald in Mathemagic land” (or something very similar), and there was a whole segment about using math for making shots in pool.

[@stco2426]

The mirror 'table' is also used as shorthand when playing squash - to play into an adjacent court thereby using a couple of the court's walls. It can be quicker to imagine 'mirror' courts when playing off a couple of the walls, than try to work out the ball's bounces in the actual and single and real court. Fun vid.

[@-AT-WALKER]

Paused to comment, JENNIFER BARRETTA on your channel?!?!?! Played pool against a friend (an aeronautical engineer) half a lifetime ago, I was already okay at pool but the maths data dump he put on me regarding angles changed my pool game. This video excites me and I've not watched it yet, pool, Jennifer Barretta and another maths data dump... triple combo of the finest kind in the early hours no less. Life is good.

[@arjadre]

Is anyone else suspicious that the voice-over starting at 24:00 is actually Grant impersonating Matt?

[@pallepirat]

It was simply a fantastic video. Significantly better than ever before. When I’ve been in my studies, the very best and most inspiring sessions have been when we’ve had guidance, and several of us have stood by a board discussing and collaborating to solve questions or explore a topic. Where there has still been an adult to steer the conversation or provide help. Somehow, you capture exactly that feeling in your video - a sense of being in that room. Congratulations. Really impressive.

[@RichardsWorld]

A few things. Your representation of running English is backwards. And speed makes a big difference because the cushions compress. The harder you hit the ball, the more it sinks into the cushion. The harder you hit the ball, the shorter the rebound angle. Also, their are imaginary diamonds in the center of the pockets used for banking systems. Temperature and humidity, how clean ir dirty the balls are, how old the cloth is, etc, etc makes a difference. Changing the brand of pool tables makes quite a difference also. And something you can fix with math is your execution of the shot. You need good fundamentals to perform your shot accurately. All the best math in the world won't help someone that can't shoot straight at the target.

[@mustafachhawniwala297]

OK WHEN DID GRANT GET MUSCLES 3blue1built

[@forever_stay6793]

This comment actually made me laugh out loud! also his arm veins!?!?

[@amicloud_yt]

3buff1built

[@ace.of.space.]

😂

[@idontwantahandlethough]

dude looks great!

[@joachimong8404]

Really enjoyed this. I'm into ten pin bowling and there are very similar rule of thumbs derived from geometry which we use. Similarly, "feel" and sensing the playing environment is more important because it is impossible to account for every single variable.

[@TamaraTkacova]

as a math student who's obsessed with pool, this crossover makes me so happy :')

[@AndrewT]

Same. They should have included Dr. Dave for a mixed perspective.

[@kindlin]

It's too bad math hardly helps for actual pool shots, it would be nice if it did. It's also a pet peeve of mine that your average bar denizen will happily tell you otherwise.

[@AndrewT]

Yeah a lot of people think I'm good at pool because I studied math. Couldn't be further from the truth 😂

[@zivi_aevalia]

This is a super interesting idea. Hope you do more with other sport/game/activity

[@oasntet]

23:30 Oh. I just realized that if you have to bounce off two walls, it's basically a retro-reflector (in 2d) and so that singular point should work for anywhere along that side of the table...

[@smenci]

In the vacuum maybe, in a pool table, where balls roll and there are frictions, not even close. For example, the shot angle that they are showing, would be completely different if the cue ball was on the same line, but closer to the rail. If you shoot from a short distance from the rail, the cue ball has not started rolling yet, and it's still flying (not touching the table), so the reaction with the rail is completely different. Math or geometry don't explain that, physics kind of does, years of practice absolutely do.

[@rezwanmahmud6773]

this took me 24 years in the past, when in basic mechanics I used pages to calculate whether I'd successfully cross the road without getting hit by the car, while in real life it was just 'instantaneous'. that's when I realized it was all useless and showing off with such knowledge was RIDICULOUS.

[@forever_stay6793]

5:43 genuinely had no idea that air conditioning makes a difference in how pool is played

[@TehFrenchy29]

Felt is very water-absorbent and almost sponge-like in its ability to draw in fluids from its surroundings; if the humidity is high enough (like say in a very wet tropical climate) the density and surface friction of the felt will be different because of the greater water content in the felt itself. This will also have an effect on the compression and rebound of the felt and cushion along the table rail and so alter the way the ball bounces off the rail and how much spin it gains / loses in the bounce. Every pool table has its own feel that an experienced player can pick up on, any two tables in the same environment my be very marginally different, but the same table in two very different environments will also behave differently. Similar to the "run" in golf, how much friction that species of grass has against the ball and how slick the surface is from dew or rain, and so forth, or to the surface quality of an ice sheet in hockey affecting how far and fast the puck travels from the same input.

[@DonkeyYote]

@@TehFrenchy29 I get that thinking about all these factors matter in pool and in golf, and I know the ice surface matters in hockey but I am not so sure that thinking about this happens as much in hockey. Both pool players and golfers have several seconds to think about these factors, hockey shots are taken in milliseconds. Also, I am not an expert on either pool or golf, but I am pretty sure that body checking is not allowed in these games.

[@benjaminlynch9958]

@@DonkeyYotepretty sure both golf and pool would have MUCH higher broadcast ratings if body checking were allowed!

[@TehFrenchy29]

@@DonkeyYote This kind of thing definitely doesn't get considered nearly as much in hockey by the players while they're playing the game, but it is definitely something they do give a small amount of thought to. But the ice in a hockey game is also wholly resurfaced multiple times per game, in a climate-controlled arena, so it will pretty much always be within the same set of parameters and the extremes aren't that far apart. In pool just what time of year you're playing at that table can alter how the table plays, in a game where even very minimal differences can enormously alter how the balls behave on the felt.

[@forever_stay6793]

@@TehFrenchy29 Thank you for the explanation!

[@vic1ous511]

10:16 the ball does not bounce at the aimed spot, it goes narrower There's a bit of an offset (the ball is not a dot, it has a radius) so they effectively miss the designated spot and it bounces off narrower at first but then even wider

[@ralfbauerfeind8236]

First thought: Can professional pool players do math better by playing pool than math professionals? 😂

[@lasagnahog7695]

We need a chess-boxing like event with maths and pool to really figure it out.

[@kruksog]

I'm sure some high level pool players possess better geometric and trigonometric intuitions in certain situations. Heck, maybe some calculus intuition too. Having such an inbuilt model of this kind of game would be interesting. Like chess players and certain kinds of pattern recognition.

[@DomenG33K]

@@kruksog I think they mostly just hit a million balls and get a sense for it...

[@EebstertheGreat]

I don't think anyone thinks pool is just geometry (any more than basketball), but some people believe it's just geometry and execution (ie hitting the ball straight in the computed direction). And it kind of is, but the way pool players compute the direction is different than you would expect, and the strength and spin matter a lot on every shot that hits two banks. Not everyone knows that.

[@travcollier]

​@@DomenG33KThat's how the overwhelming majority of calculations are done... Train those handy neural networks to produce good enough approximate solutions ;)

[@TheSuzberry]

Hand-eye coordination is part of the equation. And the tolerances are in micrometers.

[@TheSuzberry]

Now, I’m back to watching snooker.

[@AnonymousFreakYT]

23:38 - Matt invents raytracing.

[@roadofsnookerfinals6572]

Nice to see Rollie Williams back in are screens been a while since whe haven't seen him.

[@yaboyJJJJJ]

As much as I love Rollie, he really didn't need to be here for this video haha, he just stands in the back silently the whole video

[@rk9island]

He is very much playing the "mutual friend" role here, being the link that connects the chain from Matt to Jen

[@OhJustSomeRandomGuy]

Did you miss the scale burn?

[@thenonsequitur]

@@OhJustSomeRandomGuy Have to admit the scale burn was pretty good. Otherwise he was just kind of there.

[@rj6thstreet]

And whenever he did say something it was pointless and not funny.

[@paulc8821]

Great cover of this song Zoe, perfect singing, great acoustic playing and love the enthusiasm of the drummer

[@cozyfoxtrot5095]

Whaaat

[@soxfansince97]

I liked the visual comparison between the add-to-80 method and the radial fan at the end. I wonder if the amount of english that a pro pool player would intuitively know to use would reduce the error between the add-to-80 lines and the purely mathematical ones.

[@rmsgrey]

The angle you come into the cushion at will change how much spin the cushion imparts, which changes what the correction from the mathematical approximation needs to be.

[@bobstaats8127]

A "point" that maybe was missed during the discussion, is that as a cue ball rebounds off multiple cushions there can be a slight " arcing" in the cue ball path. Adding either " running" or " helping" english ( differing opinions on what each is and which situations to use...a whole other discussion there) allows these " arcs" of sort to follow the angled rebounding paths around the table more consistently...thus allowing the more straight path "systems" to work.

[@mikki429]

I am fairly good at putting the cue ball where I want it to go, but not so good at calculating where that should be. I have a friend who is the opposite. We made a killer team the few times we played.

[@goswinvonbrederlow6602]

The ball is near the 30/50 lines. By aiming at the wall, i.e. a far point along the 30/50 lines, the line through the ball is nearly parallel. I don't think it has anything to do with mirror tables in that case. It just needs to be decently far away so as to not throw of the line through the ball too much.

[@christianlawrence2714]

Using Let's Play: Bar Billiards as my other data point, see you in 10 years.

[@Flyingcar100]

Wow I remember that video

[@TheEvilCheesecake]

extrapolation hasn't let me down so far.

[@vigilantcosmicpenguin8721]

Matt Parker: regular billiards player.

[@grouchyfluff]

glad to see rollie still playing pool. Missed the updates on the road to the US open!

[@LonkinPork]

can't believe this is how I learn Rollie has a channel about pool

[@farrel66]

Rollie used to recreate famous pool shots on the Kamui channel, that was the start of his KZbin career

[@jayjayb89]

0:36 that voice crack 😂😂😂

[@diskgrinder]

If you were doing this on a snooker table you’d have to factor in the Higgins Boss particle

[@apmcx]

I don't get this, but I imagine it's an incredibly clever joke

[@snafu2350]

@@apmcx Alex Higgins was a world champion snooker player back in the day

[@Kyle-nm1kh]

Now I want to name a boson the Boss Boson

[@kindlin]

@@snafu2350 Ah, I didn't even notice he spelt Higgs and Boson as Higgins and Boss, I think I literally just read the letters I expected to see and was confused about the joke without ever actually having noticed the joke.

[@gary.h.turner]

​@@apmcxIt's a play on the "Higgs boson" particle and Alex Higgins, the "boss" of snooker.

[@4PeteSake9]

With 3B1B involved, a question I would have loved to see attempted to answer would be: 'Given any 'spot' or pocket to aim for, and any starting position, is there a general formula or way we can work out how much spin and power we will need to apply to the cue ball to get it into the pocket?'

[@Chris-vw2tl]

“Donald in Mathmagic Land” is when I first learned about math and billiards.

[@gabotron94]

Yes! I loved watching it in school!

[@eliasmochan]

Me too, but I never understood what was the "key position". Sadly, after this video I still don't understand that concept too clearly (I have a PhD in mathematics now)

[@erikberg7891]

Thank you for mentioning this memory from Elementary School… maybe during a rainy-day recess in the mid-1970s?

[@DaveHartley]

As a Math teacher, I still show this at least once a year 😁

[@charlesgantz5865]

Darn, I was going to mention that too. kzbin.info/www/bejne/r6bRpX5ra9x_baM

[@jvebarnes]

First principles determine the nature of the thing you're calculating. Which means a close examination of the mechanics of the table would be necessary before doing any calculations.

[@Rubrickety]

I wouldn’t have been shocked if the punchline was that Grant is a pro-level pool player. Because Grant.

[@MrBrukmann]

If it took a book plug to bring this together, I'm all for it! However, there is so much more potential left in this group, literally and figuratively. Release the b-roll!

[@donsample1002]

There’s an old Disney cartoon, _Donald Duck in Mathmagic Land,_ that has a segment explaining how to use the diamonds on a pool table.

[@azurita1974]

bingo!! I knew someone was going to make this comment. I saw it when I was a child and this video also brought it to my mind.

[@Laurabeck329]

Is that the one where he met Plato and learnt how harmonic scale works?

[@donsample1002]

@@Laurabeck329 Pythagoras, not Plato.

[@jpa_fasty3997]

This was a really good video for showing the limitations of models. Great work

[@Thee_Sinner]

Should have invited Steve Mould; he has experience with balls picking up spin as they bounce.

[@marctelfer6159]

"The ball's gonna pick up some spin Steve Mould: "Hold my Perspex box"

[@shaunzink7542]

That would be a sweet collaboration with the bank shot into the side being too shallow which would cause a double kiss so you shoot it wide of the intended pocket, it comes almost straight across the table to just past the far pocket and then appears to reverse direction and travels into the original side pocket that you hit wide of. Man that sounds like gibberish when typed out, but it's basically the pool version of his why does the rubber ball bounce out the same side of the box instead of through it. Pool balls have much less friction than a rubber bouncy ball, obviously, but the rubber rails and the spin they impart do allow for basically the same non intuitive physics reaction.

[@shadowofthecandle]

Anyone remember the show No Ordinary Family? The son's superpower was math and he did a pool game scene and nailed every shot.

[@davidmoore1253]

If you haven't already seen it, you should watch "Automatic pool stick vs. strangers" by Stuff Made Here

[@forever_stay6793]

I thought of that video when watching this too! Would've been nice to have the path projected on the table like in his video

[@puboh]

Hi Matt as a graduate student who loves math and pool it's so cool to see this video!!! One thing I want to point out is that at 12:07, the diagram shows you are putting right spin, however in reality people put left spin (running spin) to overcome the angle-widening effect on the second rail.

[@Screwball6986]

Aiming through the diamonds compensates for the cushion, is what I have always been told.

[@AwesomeSheep48]

It probably just happens to be (or was designed to be) accurate enough for people who are starting, and then you learn to compensate anyway.

[@Kyle-nm1kh]

The diamond is a different distance from the table depending on the angle. The shortest distance being 90 degrees to the wall, and the greatest distance being along the wall. This variable change is what makes the difference when aiming because you are adjusting your aim according to the angle.

[@pogyboipinoy]

What you guys did is called the mirror table or extending the line and it's a great basis for learning how to kick a ball

[@haph2087]

Ahh, mathematically simple function approximations to save time calculating, neat.

[@sohamdas]

My hypothesis for considering the diamond and not the rail is to account for the spin compensation that might arise because of the interaction of the velvet bed and the ball. As a result, if you are aiming for the diamond you will hit the rail a wee-bit shorter and a more 'tighter' angle/closed angle(compared with hitting the reflection of diamond on the railing). Once it hits the rails, the larger counter-spin from the rail will get compensated, leaving only with the spin induced by the velvet bed, which will be compensated by the "tighter angle of incidence"