Unsolvable 14.1 racks

justnum

Billiards Improvement Research Projects Associate
Silver Member
Advanced computing makes 14.1 a computationally interesting problem.

The history of 14.1 shows players making decisions in robotic ways. However the best computer hardware and software has not been professionally applied to the game.

The risk margins per shot make the problem challenging to simplify.

Instead of modeling the entire game, lets focus on the final five with ball in hand. Imagine the opponent missed and its your chance. What program leads to ideal conditions?

If there are five balls on the table with a clear break ball for the top side of the rack. What conditions must exist for the remaining 4 balls and cue ball in hand?

A classic math problem is buffoons needle which suggests all random distributions converge despite the random placement in a finite rectangular plane. The convergence is for distance between needles.

In straight pool all racks can be different but some racks can be lead to a breakshot. Of those breakshots some will lead to a second consecutive runout with a possible breakshot.

Is there a general description of all racks that can lead to a high run?

Top pros can demonstrate its possible, I challenge myself and others to develop a mathematical solution. I am on year 8 of my investigations.
 

measureman

AzB Silver Member
Silver Member
Its a general interest article. Any feedback is welcome.

If you want to show off your math knowledge I comprehend at a high level.
If you were hiring an accountant which one would you hire?
Accountant #1 2+2 is 4
Accountant #2 2+2 is 5
 

justnum

Billiards Improvement Research Projects Associate
Silver Member
If the question is too challenging think in terms of 1 ball and 1 breakball. Then slowly add balls and alter conditions.
 

sparkle84

AzB Silver Member
Silver Member
Advanced computing makes 14.1 a computationally interesting problem.

The history of 14.1 shows players making decisions in robotic ways. However the best computer hardware and software has not been professionally applied to the game.

The risk margins per shot make the problem challenging to simplify.

Instead of modeling the entire game, lets focus on the final five with ball in hand. Imagine the opponent missed and its your chance. What program leads to ideal conditions?

If there are five balls on the table with a clear break ball for the top side of the rack. What conditions must exist for the remaining 4 balls and cue ball in hand?

A classic math problem is buffoons needle which suggests all random distributions converge despite the random placement in a finite rectangular plane. The convergence is for distance between needles.

In straight pool all racks can be different but some racks can be lead to a breakshot. Of those breakshots some will lead to a second consecutive runout with a possible breakshot.

Is there a general description of all racks that can lead to a high run?

Top pros can demonstrate its possible, I challenge myself and others to develop a mathematical solution. I am on year 8 of my investigations.

I used to cut you some slack because you are amusing at times but this one takes the cake.

I don't wish to insult you but this post puts you right up there with double o as to who's the biggest flake on AZB.

I really hate to admit it but I think you're winning.
 

Dan White

AzB Silver Member
Silver Member
Advanced computing makes 14.1 a computationally interesting problem.

The history of 14.1 shows players making decisions in robotic ways. However the best computer hardware and software has not been professionally applied to the game.

The risk margins per shot make the problem challenging to simplify.

Instead of modeling the entire game, lets focus on the final five with ball in hand. Imagine the opponent missed and its your chance. What program leads to ideal conditions?

If there are five balls on the table with a clear break ball for the top side of the rack. What conditions must exist for the remaining 4 balls and cue ball in hand?

A classic math problem is buffoons needle which suggests all random distributions converge despite the random placement in a finite rectangular plane. The convergence is for distance between needles.

In straight pool all racks can be different but some racks can be lead to a breakshot. Of those breakshots some will lead to a second consecutive runout with a possible breakshot.

Is there a general description of all racks that can lead to a high run?

Top pros can demonstrate its possible, I challenge myself and others to develop a mathematical solution. I am on year 8 of my investigations.
Sometimes you have interesting ideas but it's not clear if this is one of them. You might have to provide an example of what you are after.
 

justnum

Billiards Improvement Research Projects Associate
Silver Member
Sometimes you have interesting ideas but it's not clear if this is one of them. You might have to provide an example of what you are after.

Each breakball has an ideal region for cueball to make the break shot.

The trivial cases to map out for 1 breakball and 1 ball anywhere on the table creates all the trivial cases.

My problem is I think there are multiple solutions, however I assume there is only one runout.

14.1 patterns are: These are profiles of the last shots for the breakball.
Cue ball hits only object ball and gains position.
Cue ball hits object ball, then 1 rail.
Cue ball hits object ball, then 2 rails.

There are some obvious patterns, the problem in my analysis is to integrate the beginning of the run and find the point of intersection to transition into the an obvious runout.

Recognizing when I can gain access to the ideal region or begin my runout to the breakball has been my biggest challenge competitively.

When do I need to work on the run out, versus go for the runout and break its there.
 

Renegade_56

AzB Silver Member
Silver Member
Each breakball has an ideal region for cueball to make the break shot.

The trivial cases to map out for 1 breakball and 1 ball anywhere on the table creates all the trivial cases.

My problem is I think there are multiple solutions, however I assume there is only one runout.

14.1 patterns are: These are profiles of the last shots for the breakball.
Cue ball hits only object ball and gains position.
Cue ball hits object ball, then 1 rail.
Cue ball hits object ball, then 2 rails.

There are some obvious patterns, the problem in my analysis is to integrate the beginning of the run and find the point of intersection to transition into the an obvious runout.

Recognizing when I can gain access to the ideal region or begin my runout to the breakball has been my biggest challenge competitively.

When do I need to work on the run out, versus go for the runout and break its there.
you don't realize I'm certain, but there are literally billions of possible scenarios
 

justnum

Billiards Improvement Research Projects Associate
Silver Member
you don't realize I'm certain, but there are literally billions of possible scenarios

Of the billions there are maybe thousands that have similar features.

Those thousands are what makes the search interesting.

Then there could be overlapping or nonoverlapping groups of thousands with different features.

I am also a computer scientist interested in having a computer generate racks that can be solved and racks that can be unsolved.

I usually leave my opponent a rack that can be unsolved, however maybe a 100+ ball runner can solve it.
 

Renegade_56

AzB Silver Member
Silver Member
Of the billions there are maybe thousands that have similar features.

Those thousands are what makes the search interesting.

Then there could be overlapping or nonoverlapping groups of thousands with different features.

I am also a computer scientist interested in having a computer generate racks that can be solved and racks that can be unsolved.

I usually leave my opponent a rack that can be unsolved, however maybe a 100+ ball runner can solve it.
riiiggghhhttt!!!!!!!!!!!
 

justnum

Billiards Improvement Research Projects Associate
Silver Member
14.1 Exploration Exercise:

Place a breakball on the table.
Place an object ball near any pocket.

With ball in hand decide how many ways to make shape using no rails or one rail or two rails.

Then profile possibilities into no way to get shape, shape is less than ideal and shape is close to ideal.

This exercise is to recognize patterns to end a run or patterns to avoid to keep a run alive.
 

Dan White

AzB Silver Member
Silver Member
Of the billions there are maybe thousands that have similar features.

Those thousands are what makes the search interesting.

Then there could be overlapping or nonoverlapping groups of thousands with different features.

I am also a computer scientist interested in having a computer generate racks that can be solved and racks that can be unsolved.

I usually leave my opponent a rack that can be unsolved, however maybe a 100+ ball runner can solve it.
If your goal is to improve pattern play then the information on strategy is out there. You just have to spend time learning and trying. If, on the other hand, your goal is simply to see if a computer can calculate the best runout patterns then I'm sure something could be done. Maybe the Virtual Pool people have done it. Call Elon and see if AI has done it yet.

I think every rack can be "solved," even full racks of 15 balls at the beginning of the game. Some runouts are more likely than others.
 

justnum

Billiards Improvement Research Projects Associate
Silver Member
If your goal is to improve pattern play then the information on strategy is out there. You just have to spend time learning and trying. If, on the other hand, your goal is simply to see if a computer can calculate the best runout patterns then I'm sure something could be done. Maybe the Virtual Pool people have done it. Call Elon and see if AI has done it yet.

I think every rack can be "solved," even full racks of 15 balls at the beginning of the game. Some runouts are more likely than others.

I agree some runouts are more likely.
 

justnum

Billiards Improvement Research Projects Associate
Silver Member
I am trying to reimagine 14.1 as if it was written as general interest class towards independent learners.

Practicing mechanics and studying film is a good starting point.

However the technical aspects of 14.1 position play and cue control need development.

If I put together enough exercises, I think it would serve interested 14.1 players.

The exercises set clear achievements for 14.1 with a purpose in competition.
 

Dan White

AzB Silver Member
Silver Member
I am trying to reimagine 14.1 as if it was written as general interest class towards independent learners.

Practicing mechanics and studying film is a good starting point.

However the technical aspects of 14.1 position play and cue control need development.

If I put together enough exercises, I think it would serve interested 14.1 players.

The exercises set clear achievements for 14.1 with a purpose in competition.
There have been many books and internet articles etc. written about position play so I'm not sure what you mean. If you develop something useful that hasn't been done then great.
 
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