what about table size? ;P
Was Einstein Right About 6 Million Shots on a Pool Table?
- Thread starter CJ Wiley
- Start date
If two balls are involved, the number of shots will probably scale with the fourth power of the size of the table.
When my body tells me there's a difference, guess what there's a difference. I cannot, as a right handed player reach from the right side of the table to the left as well as I can going from the left side of the table to the right. That's why the shots are different even though they are mirrored.
The dimension of speed seems to be ignored so far. The speed of the shot does change where the object ball goes, especially on banks.
Another dimension to worry about is the elevation of the cue stick which changes how far off the cloth the cue ball is when it contacts the object ball in combination with the speed of the shot.
Another dimension to worry about is the elevation of the cue stick which changes how far off the cloth the cue ball is when it contacts the object ball in combination with the speed of the shot.
No, I covered that too.
38 ft**2 = 38*12*12 in**2 = 5472 not 456.
The rest of the math checked out.
However you forgot to multiply by banks, kicks, caroms, and billiards (5) to get a reasonable intermediate answer.
We then need to divide by all axes of similarity--that is making a shot into the top left corner is no different than making a shot into the bottom right corner after you walk around to the other side of the table. There are at least 5 degrees of similarity on shots that do not involve a rail, and at least 35 degrees of similarity on shots that do involve 1-3 rails.
So we are still way more than Einstein's quote. Perhaps he found more axes of similarity?
How many layout variations exist after a break?
I have heard statements similar to the following situation:
Early in a match, Player A runs 7 balls in 8 ball and misses an easy shot. Player B runs out the table. The match ends up Hill/Hill and player A loses. A then states that if he wouldn't have missed that easy 8, he would have won.
I say that it is not that easy. If that 8 were made, the balls would have been racked differently on the next game than what they actually were due to the order that the balls are gathered for racking. Change the position of two balls, and you will get a different layout with identical breaks. All subsequent games would have been different.
Might be one for Mythbusters to test.
I have heard statements similar to the following situation:
Early in a match, Player A runs 7 balls in 8 ball and misses an easy shot. Player B runs out the table. The match ends up Hill/Hill and player A loses. A then states that if he wouldn't have missed that easy 8, he would have won.
I say that it is not that easy. If that 8 were made, the balls would have been racked differently on the next game than what they actually were due to the order that the balls are gathered for racking. Change the position of two balls, and you will get a different layout with identical breaks. All subsequent games would have been different.
Might be one for Mythbusters to test.
Whoops. But I did say that was for positions of balls, not shots.
Einstein made perhaps some of the most astute observations a person can make regarding motion and summed up his conclusions with a statement that in my opinion, is one of the most accurate statements ever made as far as comprehensively describing all events taking place within the realm of reality.
That observation is: "All motion is relative and all points of reference are arbitrary!"
Bearing that in mind, I would think he would've decided that there are an infinite number possible.
Perhaps he was basing his conclusions strictly upon mathematics (specifically geometry) and physics...while excluding the esoteric nuances of billiards.
That observation is: "All motion is relative and all points of reference are arbitrary!"
Bearing that in mind, I would think he would've decided that there are an infinite number possible.
Perhaps he was basing his conclusions strictly upon mathematics (specifically geometry) and physics...while excluding the esoteric nuances of billiards.
The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions.
Not mine.
Not mine.
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.????
Or, one could take Naji route, and state that there are 4,000 shots to be learned.????
You're what's different in those two cases, not the shots.
Show me one person that doesn't apply to. The shots are mirrored, so physics says there's no difference. But reality says there is because of our bodies.
And all these shots can be played on different cloths with different amount of hours played
on them.
A half ball cut is different on a Stevenson, a Mali 821 with directional nap, a 760 or 860,
a Tournament 2000, or a Granito Basalt.
Then think about humidity and temperature, where you grip the cue, how heavy the cue is,
how strong you are...........
It's starting to make calculating PI look more feasible than calculating varieties of pool shots.
Im not a math wizard but here's my go at this. If a 9 ft table was covered with all the balls it could hold, it would hold about 24x48 balls which equals 1,152. Each ball could present a shot at any other ball, but half of the shots would be replicated, so divide 1,152 by 2 you get 576. Since I tend to visualize the balls into sections of 1/8's, I would multiply 576x8=4,608. That should cover the possible combinations of shots available on a pool table for a normal shot, not banks or combos. This would be computed using the formula 4,608x4,607x4,606......and so on all the way down to 1. I personally don't have anything that can compute that, but I know 6 million would just be a drop in the bucket for that amount.