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Robotics Education Science

Deep Green - A Pool Playing Robot? 120

Posted by michael from the bank-shot dept.
o0zi writes "A Canadian scientist has created another game-playing machine, designed for a far simpler purpose than chess: playing pool. The world's first pool-playing robot consists of a slim box that glides along tracks above a pool table, and shoots using a camera-guided cue. Deep Green pots only half the shots it plans for - supposedly the same as a below average player - but this is expected to improve."
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Deep Green - A Pool Playing Robot? More

Deep Green - A Pool Playing Robot?

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  • My first thought was that it should be very easy to get a higher percentage of shots, but I guess that a lot of shots require 'english' to make, probably something that is not easily computed.

    Having recently tried snooker for the first time, I can appreciate the difficulty!

    • I played snooker at a fairly high level for a while (I could break over a 100 periodically) and regularly ran 40 to 70 point breaks.

      That said, I agree that the 'english', the spin placed on the ball will be a challenge. Especially if they wish to play on snooker tables as opposed to eight or nine ball tables. The correct cloth for a snooker table has a directional nap (kind of like the effect of velvet... if you brush it one way it raises up, the other way, it lays flat), while the cloth on an eight or n

      • You make a great point in regards to the nap of the cloth. Now would a robot like this take the speed of the cloth into consideration? How will it compensate for different tables as each table plays differently?

        Something tells me the game of snooker will be harder to program than say chess simply because there are a lot of unknown variables. Most of the time when I play snooker, I go by feel and instinct, which may or may not be correct.

        Most importantly, how does that robot chalk up the cue? hehe

        I love t

  • What's really needed is... (Score:5, Funny)

    by andy666 ( 666062 ) on Saturday August 07, 2004 @05:11AM (#9907662)
    a pool CLEANING robot.

    or at least something that can clean for me.

  • Far simpler? In ways... (Score:5, Insightful)

    by danamania ( 540950 ) on Saturday August 07, 2004 @05:13AM (#9907663)
    A Canadian scientist has created another game-playing machine, designed for a far simpler purpose than chess: playing pool.

    Far simpler perhaps, in ways. The strategy behind a pool game might be easier compared to chess, but there's nothing physical in chess that needs simulating. That's a whole new ball game (ha!) for a computer/robot over a chess simulation.

    This looks up there with the research into teaching robots to walk, scale stairs & run. Good solid research sure, but I wouldn't go putting it down by comparing it to a chess simulation.

    • Less Recognition (Score:5, Interesting)

      by mfh ( 56 ) on Saturday August 07, 2004 @05:24AM (#9907695) Homepage Journal
      Also there is less recognition for shots in pool because strategies are different compared to where you play. The base rules system is easier than chess, but you have near-infinite possibilities for aligning shots, taking shots and winning. If you're playing someone who can sink the table on a streak, the robot had better be able to do the same. Plus there's breaking... does the bot know how to break a rack and sink a couple each time? If not, it's not a very good pool bot, whereas it doesn't take much these days to create a chess bot that is *amazing* at chess by even pro standards. They have all the stats from previous games to go by. Stats won't help a robot with billiards, as there are no coordinates recorded to base new calulations on. Perhaps there *should* be? I think it would be fairly easy to record coords from each pro game from this day forward and the billiards industry should invent a table that does it. That would be awesome for so many reasons.

      • Re:Less Recognition (Score:5, Interesting)

        by danamania ( 540950 ) on Saturday August 07, 2004 @05:32AM (#9907707)
        Stats won't help a robot with billiards, as there are no coordinates recorded to base new calulations on. Perhaps there *should* be? I think it would be fairly easy to record coords from each pro game from this day forward and the billiards industry should invent a table that does it. That would be awesome for so many reasons.

        On top of the stats like this - not every pool table is identical. Chess is purely a logical game, where the table in pool may differ according to how old the table is, the humidity, the air pressure, temperature, how clean your balls are, the cue tip (chalking anyone?).

        You might have a robot that can be perfect at a game played on a known surface, but that'll only be the one table it's built for. That's where having the bot work as an adaptable machine would come into play.

        • ROTF (Score:2)

          by mfh ( 56 )
          > how clean your balls are

          Mine are pretty clean. How about yours?
    • I agree, in fact I'd say that making a pool playing robot is much more complex than making a chess program - all the engineering involved to actually getting it working.

      But because of the simpler tactics (basic physics), building a world-beating pool robot would, I'm sure you'd agree, be easier than building a world-beating chess program like Deep Blue.

      So I'd say you CAN compare it in terms of difficulty to chess simulation - getting it working harder, getting it working well easier. I'm sure the submitte
    • You are kidding, right? Walking, running, and climbing stairs require much more than simply striking a cue ball with a cue, even if you include using english on the ball.
    • I don't know how well the two compare. The chess problem to me seems to mainly be exploiting what computers do well (doing vast numbers of computation with blinding speed and a perfect ability to "remember" all the possible permutations and outcomes). Chess is essentially a "math" game, there is no functional difference between the coded representation the computer manipulates to determine its moves and the physical board a player plays on. Hence, the computer's strengths give it a very real and critical
    • I've always felt that I wouldn't truly be impressed by computers beating human opponents at chess until they can play the whole game by themselves without a human there to make the moves for them.

      I'd love to see the computers making their own moves and with a camera so that they can 'see' the board.

  • 3 points... (Score:1, Interesting)

    by Anonymous Coward
    Wouldn't an overhead camera have worked a lot better and been simpler to make, not to mention not violating the rule about sitting on the table?
    • As long as the bot has one foot on the floor, it's still legal. :-)
    • Not necessarily. Making a good shot in pool requires more than just lining up a shot and hitting the cue ball into another ball. The cue ball often times needs to be hit with the proper left/right/top/bottom spin ("English") so that it rolls into a spot where there is another shot. The best place to hit the cue ball would be very difficult to calculate with an overhead view.

      If you watch professionals play, you'll notice their stance is such that their chins are almost touching their cue stick, and the stic

  • Chalk (Score:5, Funny)

    by pjt33 ( 739471 ) on Saturday August 07, 2004 @05:16AM (#9907677)
    At last: a pool opponent who doesn't spend the entire match distracting you by chalking their cue!

    • Re:Chalk (Score:3, Funny)

      by Pharmboy ( 216950 )
      At last: a pool opponent who doesn't spend the entire match distracting you by chalking their cue!

      But what if he constantly distracts you with small talk, and he sounds just like Stephen Hawking?

  • Vs Humans (Score:3, Funny)

    by ubera ( 107426 ) <oconnoat@@@tcd...ie> on Saturday August 07, 2004 @05:21AM (#9907689) Homepage
    I wonder if it will be able to beat Kasparov?
  • Ofcourse you have...
    Interesting question: could you ever be truly happy with a 'copy-cat' human-like robot (or dog, cat) as a partner/friend, that looks like, smells like, behaves like a real human?

    Personally, I will always prefer the real thing, flesh and blood, but a good copy could be fun company...

    • If it was so similar or even subtly different why would you consider it *less* than you. The whole point of replicants is that they are *slaves*. Slavery is alive and well despite centuries of fighting it.

      Personally, I'm all in favour of alienness in my life.
      It's why I live here in Greece. It isn't the UK or US. (we also have better food).

      If you're looking for a slave (presumably of the sexual variety) then since your'e a slash dotter you ought to be able to code one...
    • Interesting question: could you ever be truly happy with a 'copy-cat' human-like robot (or dog, cat) as a partner/friend, that looks like, smells like, behaves like a real human?

      Yeah, I think so. If it behaves the same, does it matter if it's artificial?

      Personally, I'd be pretty damn pleased even if all it ever said was 'chii!'

    • And if its sufficiently human to satisfy you, can it be happy with you? And does it have the choice?

  • Sucky robots (Score:5, Funny)

    by Zorilla ( 791636 ) on Saturday August 07, 2004 @05:27AM (#9907699)
    Now they only need to make a robot that sucks at golf. Of course, important aspects of the design will include a synthesized "FUCK! God DAMMIT! Stupid fucking sandtrap!" on 50% of shots made.
    • Now they only need to make a robot that sucks at golf.

      Ask an ye shall recieve. Lego golf robots. [www.hh.se]

      .
    • Now they only need to make a robot that sucks at golf. Of course, important aspects of the design will include a synthesized "FUCK! God DAMMIT! Stupid fucking sandtrap!" on 50% of shots made.

      Don't forget the helicopter-style club launcher that can hurl a 3 wood further than the ball you just shanked.

  • OLD News by decades! (what about Silent Running!) (Score:1, Interesting)

    by Anonymous Coward
    OLD News by decades! (what about Silent Running!)

    In the movie it features and shows the first billiards playing robot. Mind you it was no doubt laboriously programmed to take its shots using CADCAM coordinates rather than optical feedback.

    But it was first... in early 1970's.

    Of course 3D chess by Lucas in Star Wars years later out classed the entertainment on the ship Valely Forge in Silent Running.

    I can't believe I am the first to point this out here, and I'm not even a true uber geek of techie culture.
  • I know that some engineers at my Uni (Adelaide University) made the same kind of thing a few years back. I don't know too many details (or a webpage), but it was about as good as this one appears to be.

  • true simulation (Score:2, Funny)

    by ctime ( 755868 )
    Where's the 'aimjuice' aka beer intakes on this baby? Not to mention, does it smoke and enjoy country music as well? What about karaoke!?

    ALL IM ASKING IS THAT IT PARTICIPATE WITH THE REST OF US HUMANS.

    Mod me down as robot-insensitive.

  • Horizon snooker robot (Score:5, Informative)

    by rjforster ( 2130 ) on Saturday August 07, 2004 @05:45AM (#9907740) Journal
    Any British /.ers remember a Horizon[1] episode where they built a snooker playing robot. Must have been 10/15 years ago now. Played on a reduced size table with fewer balls (10 rather than 15 reds IIRC). The gantry for the robo-cue included steel pillars at the corners of the table, thus making it really hard for the human competitor.

    [1] Horizon is a science program on BBC2.
    • Like the other replier, I think it was longer than 15 years. More like 20 years I would say.

      And I'm sure I saw it on Tomorrows World not Horizon. Maybe the presenters were the same and I'm not remembering correctly.

      I do remember a huge flow-diagram that was used to help program the code; a huge roll of paper that covered a whole wall. I've written webpages with more logic than that... :)

    • The world's first snooker playing robot was the subject of a QED programme shown on 16th March 1988 on BBC TV in which the 1988 world snooker champion, Steve Davis, played and won a match against the robot. I helped to develop the image-processing software for the robot's vision system. The research project ran from 1986-1988 and was funded by BBC TV. There is further information about the project here. [slashdot.org]
    • Yeah, I remember that.

      Snooker's a much harder game than pool, since the table is larger, the pockets smaller, and there's more balls on the table to start with. The robot on Horizon could actually play a real game, following the rules or snooker, and making intelligent shots with positioning.

      From the article it sounds like this pool playing robot is pretty crummy right now. They hilight its strength as being able to pot the white in any pocket, but make it clear that it has trouble potting any coloured
  • to use genetic algorithms to improve the robocue efficiency?

    Maybe toss in a little fuzzy logic for good measure.
    • GA's tend to produce programs which out slimy hack the ultimate slimy hacker. They exploit areas we don't even know are slimy hacks. But this makes them horribly fragile - the same program *won't* do well if the input params change.

      I like GA's. But they are no substitute for the painful process of writing real programs painfully.

      One day when we have "computers" (read 10K+ nodes
      parallel processing with terabyte memory) we will
      idly fiddle with these things to hose people in deathmatches...

      I wish I had to e

    • Re:Might it be possible... (Score:1, Funny)

      by Anonymous Coward
      You forgot to suggest neural nets. Add in bayesian networks, simulated annealing, an expert system, Lisp, Prolog, and mind.forth, and you'll be able to convince any AI groupie that the thing is intelligent. Even if it misses the cue ball 90 % of the time.

  • linux (Score:2, Funny)

    by Anonymous Coward
    But does it run linux?

  • Simpler eh? (Score:5, Informative)

    by Rosco P. Coltrane ( 209368 ) on Saturday August 07, 2004 @06:13AM (#9907803)
    designed for a far simpler purpose than chess: playing pool.

    This comment shows the poster has no idea what playing pool is about.

    It's more than just line up / aim at the center of the ball / shoot more or less hard : you have to pot the ball, yes, but you also have to replace your white ball so that the next shot is easier. Often you have to think 2, 3, 4 shots ahead. Often you plan your entire game before playing the first shot.

    In order to control the white ball, there's a certain about of spin to give it on the vertical plan and horizontal plan (english) so that the ball is deflected differently on the cushion(s), depending on the angle they arrive. Giving english to a ball also deflect its path (it won't roll straight), so that has to be accounted for in the aiming (you aim a little off). And then all tables don't react the same, some have newer, less "grabby" cloths than others... Then there's the roughness of the cue tie and the chalk, and the suppleness of the cue's wood that affects greatly how much english is put on the ball. Then of course there are all the "special" shots, like massés, that require a lot of practive to control... etc...

    Playing pool is a LOT more complex than chess, and that's not just because it involves real physics. The problem has many many variables, and it takes many years of practice to master. I've been playing for 20 years, at least 2 hours per day, and I still couldn't beat a professional. It's a very demanding game.
    • I agree with the parent.Sometimes a shot is played not to pot a ball but TO DENY IT TO YOUR OPPONENT.That why those soft touches to park the cue ball right where the other chap can't do a thing.

      Pool/Snooker are all about strategy.Any one, who watched the semifinals of this year's snooker championship when Ronnie O'Sullivan came back to win brilliantly,knows what I am talking about.

    • I've been playing for 20 years, at least 2 hours per day

      Man, where do you find the time to still read slashdot?

    • Re:Simpler eh? (Score:4, Insightful)

      by Kjella ( 173770 ) on Saturday August 07, 2004 @08:49AM (#9908173) Homepage
      I assume that "simpler" in this context means to find a winning set of (reasonably possible) shots. That is not really that hard, it is the skills to make the shots that is incredibly difficult.

      I suspect that the computer would do extremely well on a "perfect" board - single uniform friction coefficient, perfectly level, perfectly straight edges, perfectly chalked cue every time, perfectly accurate aiming mechanism and so on.

      The biggest challenge is to deal with the imperfections of the real world. If the computer could have a simple look-up table of input velocity, direction and magnitude of the english -> output velocity, direction and magnitude of the english (for edges and ball-ball contact) + some simple calculations of (potentially curved) lines, I think I could program up a quite good one fast.

      It'd do great in simulations, but still suck in the real world.

      Kjella
      • This not as simple as it seems. Realistic simulation of multibody dynamics with contact is still subject to research. There is no such thing as a single uniform friction coefficient, in reality, you have (probably nonlinear) elastic bodies with varying contact surface. Parts of this surface stick together, in other parts the bodies are slipping against each other. I doubt that it is possible to reproduce a complicated shot from a professional player in a numerical simulation.
        • Realistic simulation of multibody dynamics with contact is still subject to research[...]

          It seems like a lot of that could be delt with simply by letting the robot make a bunch of shots under various conditions and build its own charactarization of the motion of the balls. For the reasons stated I agree that coming up with accurate calculations would probably be difficult, but people don't play that way, and I doubt a successful robot will either.

          A successful pool-playing robot will learn to play the sa
          • You make some good points. However, what is more interesting always depends on your background. For people interested in computational mechanics, billiards is very interesting because a well-done billiards simulation, augmented with nice graphics, can be used to impress people who would not give a damn about the most impressive algorithms for solving systems of nonholonomous differential equations or such.

            Basically, I just wanted to point out that the physics involved are a lot more complicated than most

    • Re:Simpler eh? (Score:1, Interesting)

      by Anonymous Coward
      You've been playing for roughly 14,600 hours and you can't beat a pro? You should really find a different hobby, since you suck at pool.

      I play about an hour or two a week, each time on a different table in a different location. I usually intentionally biff my first shot to get the feel of the table. Perky nipples or dead cushions can seriously ruin your game. And while a custom cue can improve your game, I always pick a random house cue as long as it's 19oz or heavier. Nothing makes me smile more than moro

      • Re:Simpler eh? (Score:2, Funny)

        by Anonymous Coward
        You're only better than 75% of all pool players? Christ, you suck at pool.

        I play once a year, always in a different state. I usually intentionally miscue three or four times a game to allow the poor schlub I'm playing a little hope. I only use warped house cues with no tip and try to find a table with wrinkled felt and plenty of bare patches. I laugh at the professionals who whine that they only lost to me because of the beer puddle on the table. Pool is about playing the conditions.

        I've never played in a

    • Re:Simpler eh? (Score:3, Interesting)

      by The_reformant ( 777653 )
      I would have to disagree with you here. Even without mastering spin and such like given a high enough degree of accuracy it is likely that a very good execution plan could be calculated.

      I think the real issue here is firstly getting the vision system coupled with the actual physical movement in an accurate enough manner.

      In some ways this game is much smaller than chess, although you may say that there are infinite variations and whatnot you forget that we already understand the physics of the pool tab

      • Re:Simpler eh? (Score:2, Informative)

        by Miniluv ( 165290 )

        Even without mastering spin and such like given a high enough degree of accuracy it is likely that a very good execution plan could be calculated.

        Unless spin and the like are mastered a great many execution plans are removed from the realm of possibility. There are fundamentally two things that separate pro level players from amateurs: Planning and cue ball control. Planning is a lot easier to learn than cue ball control, since you simply have to know whats possible. Executing that plan requires a very, v

        • Well i fail to see how you think a robot wouldnt be able to judge a safety shot! Firstly a robot is perfectly aware of exactly the angle required to make a shot either its own or an opponents and further could effortlessly caulculate the margin of error. Some simple adjustment to a standard mini-max algorithm would make this possible.
          • Safety shots tend to require significantly more creativity than simply potting a ball. This is even more true in a game like snooker where there are up to 15 valid targets for the escape shot.

            Is it possible? Sure, the AI already exists to play moderately decent safeties in games like Virtual Pool 3. The issue is that those games still lack the creativity necessary to play truly imaginitive safeties that human players use as a matter of course. Getting a machine to think creatively is much harder than wirin

  • *YAWN* (Score:5, Funny)

    by Chineseyes ( 691744 ) on Saturday August 07, 2004 @06:28AM (#9907835)
    Deep Blue now Deep Green *YAWN* someone wake me up when we see Deep Pink the nympho robot.

  • C2H5OH (Score:2)

    by SW6 ( 140530 )
    Deep Green pots only half the shots it plans for - supposedly the same as a below average player - but this is expected to improve.

    My pool playing is likewise below average, except when I've had a few pints and I start clearing tables. No, I don't understand it either. Do you think the robot would play better if somebody tipped a pint of beer over it?

    • Re:C2H5OH (Score:5, Funny)

      by Jeremy Erwin ( 2054 ) on Saturday August 07, 2004 @06:51AM (#9907884) Journal

      RIMMER: How many of those are you going to drink?
      LISTER: I told you not to talk. Game on.
      RIMMER: You're going to drink an entire six-pack of wicked-strength
      lager?
      LISTER: I'm not gonna get plastered, Rimmer, just ... just nicely drunk.
      RIMMER: Define "nicely drunk." Is "nicely drunk" horizontal or perpendicular?
      LISTER: Rimmer, I can handle it.
      KRYTEN: I'm not sure I can.
      LISTER: We're in the wrong position. It's an easier shot if we go over here. (He moves into the "better" position and lines up the shot.)
      RIMMER: But that's right in the orbital path of the planet! If you miss, we're going to get a planet in the face.
      LISTER: I'm not gonna mish.
      RIMMER: "Mish?"
      LISTER: What?
      RIMMER: You said "mish." "I'm not gonna mish," you said. You've only had two cans and you're steaming!
      LISTER: Rimmer, will you relax? I know what I'm doing! I am not pished!


      --From "Whitehole", Red Dwarf, Series 4
    • Even the pool playing robot in Silent Running missed its shot, and that was on board a pretty advanced spaceship.

      I wonder if any other pool playing robots have faired better?
    • So according to this even someone who pots half their shots is below average? Geesh. I must be way further below average than I thought then, cuz I only get about a quarter of them...

      I wonder what that says about the people I beat?

    • Re:C2H5OH (Score:1, Funny)

      by Anonymous Coward
      My pool playing is likewise below average, except when I've had a few pints and I start clearing tables. No, I don't understand it either.

      You don't really play better after a few pints, you're just so drunk you think you're playing better. In reality, everybody at the pub's been laughing at you for the past half hour after you came out of the bathroom with your fly open and toilet paper coming out of your pants.
    • I've seen this happen with a number of people. I'm guessing that having the alcohol in your system makes you relax, which improves your stroke and follow-through. A lot of people hold the cue much too tightly and try to control their stroke way too much, resulting in a stilted, unnatural motion - remove these impediments and it's quite possible that your shooting will get better.
  • "Let's play the adding game. Which can add faster, a calculator or a woman or a man?. The calculator can, right?...[My} point is that if you light a match near a calculator it's not going to scurry away. If there's a fire in my living room where me and my calculator are sitting, I can escape the fire, but my calculator can't!"

    --Moxy Fruvous (good, funny band), commenting on Kasparov vs. Deep Blue
    • "Let's play the adding game. Which can add faster, a calculator or a woman or a man?"

      That depends on who gets to start first ;).

      Seriously though if the questions come from a human it may be faster if the human comes up with the answers immediately rather than output them slowly (and possibly erroneously) to a machine and then get the answers.

      So a human with a wearable computer+cam that automatically totals numbers "in a blink of an eye" could be faster than a calculator. e.g. look at top left of area con
      • But the human would still be augmented with machinery. The point that the guy was trying to make in the quote was that it should be no big suprise that a machine programmed to just play chess or whatever can do it better than we can.

        In my opinion, the real marvel would be if the computer came up with new strategies based upon its opponents' moves. Otherwise, the machine is simply an extension of human thought.
    • Majors props for the Moxy Fruvous reference....:) If there's a transcript of that whole exchange it would be pertinent here....:)

      -Tom

  • An average player will miss 3 out of 4 shots. But most average players don't play that much.
  • A small correction of the summary; I do believe he's an engineer, not a scientist. In fact, you'll see the URL is hosted off the electrical and computer engineering faculty site.

  • Reminds me of a (bad) joke (Score:4, Funny)

    by Nic-o-demus ( 169477 ) <jwecker@NoSpAM.entride.com> on Saturday August 07, 2004 @10:41AM (#9908611) Journal
    Q: What's green, and if it falls out of a tree and lands on you it could kill you?

    A: A pool table.
  • This has been done before to some degree with a robot called Iron Willie [allsportsbid.com] by a company called Predator whom used the robot to create low deflection cues and empirically measure how "accurate" cue designs were. Predator Cues [predatorcues.com] are to pool what high dollar putters are to golf. These cues utilize a pie wedge design in the shaft combined with a stiff taper and lightweight, short ferrule to decrease deflection and maximize energy transfer to the cueball. Many people report a 10-20 percent improvement when they s

  • Thank god its the weekend..... (Score:4, Interesting)

    by idfrsr ( 560314 ) on Saturday August 07, 2004 @11:54AM (#9908942)

    Goodness... our poor server may survive....

    I must admit that is pleasing to have our project on slashdot. It's been a fun project and is getting me a M.Sc out of it :P. Having a pool table in your lab is a lot of fun on friday afternoons.

    For those /.'s interested the robot should be playing a game entirely on its own in the spring. We are still very much in the early stages of development, but we have made lots of progress over the last 16 months from when the gantry was delivered.

  • Another piece of prior art (Score:1, Informative)

    by Anonymous Coward
    They didn't do much search for prior art, did they? Here's another billiards robot [autonlab.org], put together more than ten years ago by a guy who's currently a professor at CMU [cmu.edu]. (Look at the last page of the paper for a very grainy photo of the robot.)

    The cool thing about this robot is that it learns from experience: it watches to see where the ball goes, learns a model of how that depends on its stroke parameters, and tries to compute a better way to sink it next time. As pointed out by another poster, it doesn't

  • OK, not that anyone will care... But the name "Deep Green" is already taken. Deep Green [planetnewton.com] is a Chess app for the Newton, and up until somewhat recently, was the best PDA Chess app around.

    So there. :)

  • I, Pool Shark (Score:5, Funny)

    by Gigantic1 ( 630697 ) on Saturday August 07, 2004 @04:08PM (#9910075)
    Supposedly the Robot makes only about half it's shots: Don't believe it folks. The robot is missing those shots on purpose - "laying down" - until the money gets right, and then it will start to hustle.

    Hey...I watched the "The Color of Money" starrring Ton Cruise and Paul Neuman - I know all about Pool Hustlng.

  • OK, I'll start the game:
    Marco!

  • I think I should challenge the OrionRobots [orionrobots.co.uk] people to build one. We could have a pool tournament in the local Mr Q's in East Finchley.

    This will be an interesting challenge. I can already see many different designs, ones on legs, ones on wheels - or even ones on rails around the table - though I mighty disallow the rails...

    The nice thing about a pool table is that you have bright coloured balls ona distinctive green (or blue in some cases) background. This makes it a little easier for working things out. A

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