Was Einstein Right About 6 Million Shots on a Pool Table?

[CJ Wiley]

we didn't say all the "shots" had to be pocketed shots

Why not multiply all the possible places you can hit the cue ball (spins), by all the different elevations times all the possible angles, times all the different speeds? I don't think the pockets even matter in this particular instance....we didn't say all the "shots" had to be pocketed shots......they're just shots of different speed, spin, angle and distance, we'll take it for granted that the balls must stay level with the table.

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.

 

[SmoothStroke]

One, the one I have in front of me at the time.
Let me know when they figure out how many shots for 3 cushion.

 

[Ron Swanson]

One can easily say there are millions of shots on a pool table, or there is only one shot. That one shot being the one you are faced with when it is your turn at the table.

Or, one could take Naji route, and state that there are 4,000 shots to be learned.????

Yeah, way to ruin naji's christmas guys! Aside from talking lots of impenetrable shit on the internet, what's he done to us?

 

[Ron Swanson]

There are countless dimensions because our perception is part of the game.
I know what it feels like to start a session and see nothing but troubles...
....the table, the game, and my opponent is an enemy....
I have finished some of those encounters where the game and the table
are my friends....and sometimes the old vice-versa happens.

Most players are whacko....it's just a matter of how much.
When you finally hit 'dead stroke', I call it a sanity window.

Lol.

I have never been troubled by this insanity window you talk of. Now i know it exists, I'll look out for it.

 

[nick serdula]

What he said.

I figure there are a gazillion to the third power shots on a pool table.

How many angels can fit on the head of a pin?

A mathematical point is infinitely small and in theory the center of the cue ball and object ball can sit on any of those points. Until a tolerance is defined as to what will be considered a different shot then there are an infinite number of shots.

If a tolerance is defined then what constitutes a different shot has to be defined also. Until then we are just talking about those angels on the head of a pin. On the other hand, in honor of Hal Houle I can also say there is only one shot on a pool table!

Hu

Like my little brother used to say, Yup.
Nick

 

[Kim Bye]

I`m no math genious, but 6 million combinations seems like a low estimate.
A billiard ball is 57mm. The table is 9'x4.5'
Those numbers gives you some idea of how many ball placements there are on a table. Then you have to factor in that you are doing shot combinations, wich requires two balls and to make it easy, say that every mm you change the ball you have a new combination.
Must be way more that 6 million combinations!

 

[acesinc1999]

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.

I am a snooker player by nature, only occasionally pick up a pool cue, and I lurk in the main forum due to inactivity in Snooker. This thread may well explain a few things to me. My answer to the question is a very simple "five" (or more accurately five TYPES of shot) based on a write up I have done on the topic.

In my snooker club, I am amazed by how tediously methodical is nearly every player of the game. All profess to emulate their professional idol, but very few professionals require more than a few seconds before setting up for the following shot. I have found amateur snooker players to be mind numbingly slow in making decisions on a snooker table and amateur pool players who also play snooker on the side to be "gnaw your own leg off to escape" slow in making decisions on a snooker table.

I think Einstein, through C. J., has finally explained this for me....these players are obviously thoroughly going through each and every one of the six million possible scenarios before deciding which shot to play. To me a "shot" is not determined by relative positions of balls and pockets; instead the "shot" is defined by the intended outcome, and there are not too many of those: you can pot the ball or not pot the ball, play safe or not, two way shot, move other balls on the shot or avoid them, and.....well, that's about it. It doesn't matter if the angle changes by a degree or the distance changes by an inch, it's the same shot.

I don't know if it can be applied to pool at all (that will be for others to decide), but if anyone is interested, the "Five Types" write up can be found here: http://www.acesmachinery.com/league/5_types.pdf

 

[naji]

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?

only 4000 (four thousand) everything beyond that is the less or more separation between balls. 4000 possibilities covers a 6x6 squares separation on table, add to that all possible shots with english, no english, stun, no stun, ...etc.

 

[pt109]

only 4000 (four thousand) everything beyond that is the less or more separation between balls. 4000 possibilities covers a 6x6 squares separation on table, add to that all possible shots with english, no english, stun, no stun, ...etc.

I guess you need weight from a man who knows 4,001 shots.

 

[yankee817299]

I see that you are having fun again CJ.

 

[Bob Jewett]

only 4000 (four thousand) everything beyond that is the less or more separation between balls. 4000 possibilities covers a 6x6 squares separation on table, add to that all possible shots with english, no english, stun, no stun, ...etc.

You seem to have left out some details. Where does the 6 come from?

 

[seven_7days]

Einstein: "There are 6 Million possible shots on a pool table."

<<--after watching Efren's Z kick.

Einstein: "6 Million and ONE!...There are 6 Million and one possible shots on a pool table."

 

[bdorman]

There are only two shots on a pool table: the ones I make and the ones I miss.

The later outweighs the former.

 

[Neil]

Yeah, way to ruin naji's christmas guys! Aside from talking lots of impenetrable shit on the internet, what's he done to us?

Why should that ruin his Christmas? He has stated numerous times that he believes there are 4000 shots to be learned, not millions. Why not also state that we have ruined Einsteins Christmas, since he said there are only millions of shots? (I think the number he used was 6 million) Why do you have to read things into posts that aren't there??

 

[ps611846]

The number is 7. Razor thin cuts included.

 

[Texdance]

The number of shots has nothing to do with position of the two balls. It has everything to do with the angle between the cue ball and the object ball, measured as the angle between two vectors - starting point of CB to contact with OB, and from contact with OB to pocket (or a cushion intermediate to a pocketing)..

I theorize there are only 45 basic different shots in pool, the rest are just mirror images, or different distances of those same shots, or affects of OB throw caused by dirt or spin on the CB. Longer distance shots make execution of the base 45 shots more difficult, but do not change the shots themselves.

The things that add to the base 45 is spin and dirt. By calculating how many degrees off-angle spin or dirt can and will throw an OB, one can estimate how many variations there are to each of the 45 basic shots.

Call it 1.0, 1.25, 1.5, 1.75, and 2 tips of English available. Throw out high or low since they do not change the OB direction. Throw out either Left or Right since one is just a mirror of the other. That leaves 5 different English affects to the OB.

As for dirt, the amount the OB gets thrown is not infinite, since in no case are there infinite angles to a pocket - because in every case a range of angles will get the OB into the hole. Let's assume 1 degree of difference per shot, so given the longest shot needs to be within 1 degree of accuracy to be pocketed, the dirt on a ball falls into the 'either/or' category, as in off/on or yes/no. Either the balls are dirty and affect play enough to miss a shot, or they are not. The number to represent that is 2.

45 basic shot angles, 5 basic spin conditions, 2 basic conditions of dirty/clean, gives just 675 shots in pool. Don't forget your shaft may deflect and not put CB at the right contact point on the OB, but that does not make a difference in the number of shots to master.

675 shots. Master them, and you rule the pool world.

I thought everyone knew this.

 

[pt109]

In my snooker club, I am amazed by how tediously methodical is nearly every player of the game. All profess to emulate their professional idol, but very few professionals require more than a few seconds before setting up for the following shot. I have found amateur snooker players to be mind numbingly slow in making decisions on a snooker table and amateur pool players who also play snooker on the side to be "gnaw your own leg off to escape" slow in making decisions on a snooker table.

I think Einstein, through C. J., has finally explained this for me....these players are obviously thoroughly going through each and every one of the six million possible scenarios before deciding which shot to play.

I'm gonna use this to explain slow players from now on.

 

[ps611846]

The number of shots has nothing to do with position of the two balls. It has everything to do with the angle between the cue ball and the object ball, measured as the angle between two vectors - starting point of CB to contact with OB, and from contact with OB to pocket (or a cushion intermediate to a pocketing)..

I theorize there are only 45 basic different shots in pool, the rest are just mirror images, or different distances of those same shots, or affects of OB throw caused by dirt or spin on the CB. Longer distance shots make execution of the base 45 shots more difficult, but do not change the shots themselves.

The things that add to the base 45 is spin and dirt. By calculating how many degrees off-angle spin or dirt can and will throw an OB, one can estimate how many variations there are to each of the 45 basic shots.

Call it 1.0, 1.25, 1.5, 1.75, and 2 tips of English available. Throw out high or low since they do not change the OB direction. Throw out either Left or Right since one is just a mirror of the other. That leaves 5 different English affects to the OB.

As for dirt, the amount the OB gets thrown is not infinite, since in no case are there infinite angles to a pocket - because in every case a range of angles will get the OB into the hole. Let's assume 1 degree of difference per shot, so given the longest shot needs to be within 1 degree of accuracy to be pocketed, the dirt on a ball falls into the 'either/or' category, as in off/on or yes/no. Either the balls are dirty and affect play enough to miss a shot, or they are not. The number to represent that is 2.

45 basic shot angles, 5 basic spin conditions, 2 basic conditions of dirty/clean, gives just 675 shots in pool. Don't forget your shaft may deflect and not put CB at the right contact point on the OB, but that does not make a difference in the number of shots to master.

675 shots. Master them, and you rule the pool world.

I thought everyone knew this.

I use only 7 and they cover every possible angle....... Thank God I don't have to learn 668 more.........

 

[CJ Wiley]

with a "loose grip" the number shoots up to 60,000,000.

It started out as fun, then I decided to prove to myself whether Einstein was right or wrong. It took me all night, and finally proved that Einstein was indeed correct. Amazingly there are exactly 6 million possible shots when you factor the following:

1) All Distances between the Cue Ball and Object Ball (squared) X Every Possible shot speed (squared) X Every Conceivable "Tip Target" (where the cue contacts the cue ball) (squared) X Every Possible cue elevation (rounded {and squared} to the tenth degree)

No matter how I arrange the results from these calculations they always equal 6,000,000 - and what's really strange is it's the exact same number in Billiards. Also, I had to use a firm, controlled grip - with a "loose grip" with a "long follow through" shoots the number up to 60,000,000 - interesting, very, very interesting.

How could Einstein have possibly known? Was he secretly a world class pool player? Did his pool playing abilities factor into his Theory of Relativity?

I see that you are having fun again CJ.

 

[SmoothStroke]

It started out as fun, then I decided to prove to myself whether Einstein was right or wrong. It took me all night, and finally proved that Einstein was indeed correct. Amazingly there are exactly 6 million possible shots when you factor the following:

1) All Distances between the Cue Ball and Object Ball (squared) X Every Possible shot speed (squared) X Every Conceivable "Tip Target" (where the cue contacts the cue ball) (squared) X Every Possible cue elevation (rounded {and squared} to the tenth degree)

No matter how I arrange the results from these calculations they always equal 6,000,000 - and what's really strange is it's the exact same number in Billiards. Also, I had to use a firm, controlled grip - with a "loose grip" with a "long follow through" shoots the number up to 60,000,000 - interesting, very, very interesting.

How could Einstein have possibly known? Was he secretly a world class pool player? Did his pool playing abilities factor into his Theory of Relativity?

Geez, as of now I only have to learn 5,999,999 more shots, unless the number changes.
With a loose grip I see I have more work to do. Thanks for putting in the effort.