Each ball has nine dimensions in a sense (location, spin and velocity) so a full rack of balls would have 144 dimensions. Or state variables, if you prefer.A more pertinent question would be, how many dimensions are there on a pool table?
Was Einstein Right About 6 Million Shots on a Pool Table?
- Thread starter CJ Wiley
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There would be an infinite amount of shots on a table even just moving one ball around.
If you have 100" of potential movement, and started with a movement tat used the full length, couldn't you always move it half as much as the time before?
If you have 100" of potential movement, and started with a movement tat used the full length, couldn't you always move it half as much as the time before?
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I'll preface this with the fact that I'm firmly in the infinity group here. Still, the matter can be made finite. I will use some approximations to keep it manageable.
For example:
The longest possible shot on a pool table is about 10 feet, the length of the table diagonal on a 9 foot table. That's about 3,000 millimeters. Hence, the length of a shot can vary from 1 to 3,000 millimeters, giving us 3,000 possible shot lengths.
Similarly, the cut angle on a shot can vary from 0 degrees and 0 seconds to 90 degress and 0 minutes. That's 5,400 possible cut angles, as there are 60 minutes in a degreee.
Numer of shots = possible lengths x possible cut angles = 3,000 x 5,400 = 16,200,000
That's one way of calculating it, and if you subscribe to this method, then you'll reckon that there are 16.2 million possible shots.
For example:
The longest possible shot on a pool table is about 10 feet, the length of the table diagonal on a 9 foot table. That's about 3,000 millimeters. Hence, the length of a shot can vary from 1 to 3,000 millimeters, giving us 3,000 possible shot lengths.
Similarly, the cut angle on a shot can vary from 0 degrees and 0 seconds to 90 degress and 0 minutes. That's 5,400 possible cut angles, as there are 60 minutes in a degreee.
Numer of shots = possible lengths x possible cut angles = 3,000 x 5,400 = 16,200,000
That's one way of calculating it, and if you subscribe to this method, then you'll reckon that there are 16.2 million possible shots.
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Well I strongly disagree with Einstein! I'm up to 4,376,731 shots and I think I've exausted about every one except maybe a few hundred.
maybe we should call it "pool room legend".
So you're answer is "none of the above"? :wink:
I've heard it referenced many times in pool rooms, although I have no proof. I guess it hasn't reached the status of urban legend, maybe we should call it "pool room legend".
This thread wasn't designed to get an exact number, just wondering how players would go about this calculation.
So you're answer is "none of the above"? :wink:
I've heard it referenced many times in pool rooms, although I have no proof. I guess it hasn't reached the status of urban legend, maybe we should call it "pool room legend".
This thread wasn't designed to get an exact number, just wondering how players would go about this calculation.
There are an infinite number of shots possible on a pool table. Take the cue ball and one object ball some distance apart. Move the cue ball half the distance. Do it again and again. The two balls will never touch, therefore there are an infinite number of shots right there,never mind the fact that there are an infinite number of spots possible for the cue ball and object balls to be located.
so we have a wide range, all the way from "1" to infinity in this thread.
So pocket billiards is a game with an infinite amount of shots?
That's a wide range, so far, all the way from "1" to infinity. :thumbup: .....could it possibly be somewhere in between?
So pocket billiards is a game with an infinite amount of shots?
That's a wide range, so far, all the way from "1" to infinity. :thumbup: .....could it possibly be somewhere in between?
I would say as far as variables, not all that many. Just a lot of the same shots positioned differently on the table. A cut of a certain degree into one corner pocket is the same shot into another corner pocket as well as side pocket. Then you have mirror images of these same shots.Einstein said there were over 6 Million possible shots on a pool table, do you believe this is fact, or another example of urban legend?
How many shots do you believe are possible on a pool table and what formula did you use to come up with your estimation?
For a 9 foot table, for area it is possible for a ball to land. That means the 1.125 inches at each rail the ball connot sit at, there is 8' 9 3/4" x 4' 3 3/4" of possible places for a pool ball to sit. Roughly ~38 square feet of places for a ball to sit. Convert to inches and we have ~456 square inches. For simplicities sake, we'll assume a ball rests on 1/32" of area. No overlapping of areas, gives us ~14,594 possible spots for one ball. Add in a second ball, we have to subtract the area the first ball is occupying from the total area. A ball takes up ~3.98 square inches. That leaves us with ~452.02 square inches of placement for our second ball. Assuming again 1/32" for area placement of a ball, there are 14,464 possible placements of that second ball.
That leaves us with 211,058,688 different possible placements for two balls. Now beings that we're dealing with a rectangle that has four corners, a placement of balls will repeat twice. So there's only 105,529,344 different positions on the table in which two balls on table can be placed in which the placement is not repeated.
Now if we remove distance as a factor and only concentrate on angels. Not interested in doing half angles will simplify the math. There are 181 possible contact points from left to right on an object ball. There's 1-90 left and right, and 0 center spot. For the cue ball, we'll assume that each tip position can be offset by 1/32". Without talking of the curvature of the ball, only 1 3/4" of the cue ball's width can be struck. I'm sure someone can help figure out that arc length. Take and figure out the circle area that the arc length is on that sphere. Take that number which should be in inches, times 32, then times 181, to determine how many number of shots are possible. That's for a static position back end of the cue and no banks/kicks. Add in varying degrees of jacked up cue, banks, and kicks, and that shot number is outstanding. Far more than a measly 6 million.
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Guess you didn't read my whole post. I made it clear that I was in the "infinity camp."
I offered an example of how one might attempt to make the subject finite.
More or less as sjm did just above, except I hope players don't waste too much of their time with such problems.
You divide each variable, such as length, into a finite number of pieces. You can either do this to taste or base it on something inherent in the problem. For example, sjm above divided lengths into 1mm sections. That's much too coarse for my taste. If the cue ball lands on the object ball 1mm from where you intend, that will cause a 2 degree error in the path of the object ball. 2 degrees is huge. (Degrees are divided first into minutes, by the way, not into seconds).
So, a reasonable length unit might be taken as how accurately the cue ball needs to be placed on an object ball to make that ball in a distant pocket. Well, what fraction of the pocket do you want to allow? If you're banking a ball long off the spot back to your pocket at one pocket, does it make any difference to you if it goes in the middle or side of the pocket? That's the sort of question that must be answered before you can start using a finite division of the variables.
It is easy to construct other example shots where a tiny change in how the cue ball hits the first ball in a combination makes a large change in the result. I remember reading about someone studying the break shot and concluding that it was basically a chaotic situation, where you need to know almost perfectly all the parameters involved in order to predict how the shot will come out. This all leads to the selection of a very small length unit for a finite analysis.
As soon as something hits a cushion you have probably squared the number of shots.
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There are two ways to reflect a rectangle, so you need to divide by 4, but a factor of 4 is negligible in doing this calculation.
Many people in pool rooms are not overly accurate in what they say.
Actually, just cut the table in half, corner to corner. Or side to side. You cannot repeat the same ball placement within either of the halfs. So no, you do not divide by 4. What you're trying to do is say that a cut to the left is mirrored to the right too. But that's not the way the math works. Left != right no matter what universe you're in. The better way to visualize it is as seeing cuts to the left as a negative shot and and cuts to the right as a positive shot.
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I think you need to study the properties of reflections more.
I think you do. A cut to the left is a cut to the left, not the right. They are mirrored, but are distinctly different shots.
Not for a physicist. If Einstein had been doing the problem I think he would have ignored the handedness of the shot. There is nothing in the handedness that is interesting to a physicist. Or Ronnie O'Sullivan.
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