# Unsolvable 14.1 racks

#### justnum

##### Billiards Improvement Research Projects Associate
Silver Member
Let me save you another 8 years of toiling:
There is no universal solution on how to run racks. Different players will have different specialities when it comes to shots. Some may prefer outside english, some play mostly plain ball, some play all shots. General principles, which are time tested, are as follows:

1. Shots should, whenever possible be shot in a way to minimize the risk of skids, but at the same time not so hard as to make pocketing more difficult.
2. Movement of the cueball should be minimized.
3. Movement of the cueball should take place in a manner which decreases risk of accidental contact with other balls, and scratching.
4. Reach should be considered for all positions.
5. In general, key balls should be positioned near a pocket or near a rail, but usually not frozen to a rail. Key balls in the middle of the table should be avoided, unless you have a key ball to the key ball which is close to a rail or pocket and leads directly to the key ball in the middle of the table.
6. The cueball should be kept near center table for most shots, in order to maximize opportunities.
7. The cueball should be kept above the rack for most shots, in order to maximize opportunities and to enlarge the position zones.
8. The cue balll should be kept away from the rail at all times.

For breakshots, I think the Mosconi style has been the one method that seems more condusive to high runs. High angle, high ball into center or slightly above center pack. Object ball close, but not too close to the pack, so as to enlarge the pocket.

Here is the programming problem.

All reds can be made, which red should be first?
The classification problem begins:
A break ball and pocket have to be assigned early on.
Assign the red "arbitrarily." The corner pocket and the red nearest it, to define the break conditions and ideal position for cueball.
That invokes a condition the cueball must be on the left side of the break ball in the grid and above it, with an angle.
The only shot that has contact with the cue ball in the break section is the left side pocket shot.
Right pocket side shot has to be made, minimum power, draw or stun.

What happens when the computer has multiple shots that can leave the cue ball in that region. I would need a return theorem for traversing the table using available shots.

I appreciate you explaining the general strategy. The problem I am dealing with is for logic of individual cases.

If you added another red to the table, where would you place it to confuse the above logic?

#### Straightpool_99

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.
Well I don't know if anyone has done it, but I know only this for sure: Virtual Pool has not done it in any released game! The computer player in Virtual pool uses it's own logic on how to run racks, which seems to be:

1. Being close to the object ball is always preferable to being further away, no matter how awkward of an angle or extremely close you are
2. Any position route that leads to the above is preferable to any other.

If you watch the best computer players in Virtual Pool, it's comical. It's all multi rail, short-side shape. They never miss a combination or extremely awkward close angle, and since you can't really double hit the ball in normal circumstances you get shots that the best players in the world would have extreme difficulty with. For instance power shots with the cueball almost touching the object balls. There are also extremely risky slow cut shots being used a lot of the time, which would never fly in real play on real world tables.
I pity the fool who tries to learn pattern play from this games computer players. It's a fun game to play, and I salute the people who made it, but it doesn't translate to any sort of real play, unfortunately. It also shows the pitfalls of mechanically applying rigid rules without any consideration to human anatomy or psychology or even real world physics. The end result may be impressive, but completely useless for any learning of pattern play, for practical application, unless you use it as a guide on what NOT to do.

I do not mean to belittle the game in any way. It's an extremely impressive game which has held up for many, many years, and will continue to do so. It even has some applications in demonstrating shots and many of these can be applied to real world situations. HOWEVER this is only true as long as you realise the limitations of the game and especially the somewhat clunky AI.

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#### Bob Jewett

##### AZB Osmium Member
Staff member
Gold Member
Silver Member
Well I don't know if anyone has done it, but I know only this for sure: Virtual Pool has not done it in any released game! The computer player in Virtual pool uses it's own logic on how to run racks, which seems to be:
...
The version of virtual 14.1 player in VP I remember playing could simply make any cut shot and did not worry so much about where the next ball might be. I might have played two matches against it -- amusing but useless. I wonder if the one pocket player was any better. As I remember, there were several levels of virtual player but I only looked at the strongest.

Many years ago there was a carom simulator that could figure the percentages for a 3-cushion shot. You put in how accurate your aim and tip position and speed were and it would tell you your chance to make the shot. I think it could also figure out the best combination of shot parameters to make the shot most likely. I recall the author said that some of its conclusions seemed unreasonable, but he hadn't figured out whether it was the algorithm, simulation, or operator error that might be at fault.

The developer of Virtual Pool has retired but maybe the company will find an AI hotshot to work on it. It seems like it would be fairly easy to do three-ball patterns in a way that reduced both shot difficulty and position difficulty. I suppose a value needs to be attached to things like breakouts and key balls.

#### justnum

##### Billiards Improvement Research Projects Associate
Silver Member
Here is an initial concept for solving this diagram.

The application of this exercise is to develop a fast approximation for no rail and 1 rail shots at the red ball.

The user designates which ball is pocketed and into which pocket.
The computer begins to provide path assessments.
1) Deadball position is used to calculate center of red ball to center of pocket. (angle and direction)
1) L2 vectors generated are filtered, the far right black ball does not provide the displacement in the desired horizontal direction.
2) R1 (1 rail) vectors are generated using simple rectangles, this is to determine adjustments for deadball position. (true/fase logic)
3) R1 vectors are ordered in terms of least adjustments, the clear winner is trivial. Secondary options can be stored for analysis

The computer should have 2 no rail shots and a 1 rail kick as its options.

This solution package is to be part of a general pool solver. Ideally the table will be broken down into x,y coordinates and the computer can show interesting intersections.

The next program will do calculations for after the collision.

Solving the next AI sub module will be in a few months.

My long term goal is to make a screensaver (non-repeating) that can have a higher 14.1 run than any human player.

#### ChrisinNC

##### AzB Silver Member
Silver Member
Let me save you another 8 years of toiling:
There is no universal solution on how to run racks. Different players will have different specialities when it comes to shots. Some may prefer outside english, some play mostly plain ball, some play all shots. General principles, which are time tested, are as follows:

1. Shots should, whenever possible be shot in a way to minimize the risk of skids, but at the same time not so hard as to make pocketing more difficult.
2. Movement of the cueball should be minimized.
3. Movement of the cueball should take place in a manner which decreases risk of accidental contact with other balls, and scratching.
4. Reach should be considered for all positions.
5. In general, key balls should be positioned near a pocket or near a rail, but usually not frozen to a rail. Key balls in the middle of the table should be avoided, unless you have a key ball to the key ball which is close to a rail or pocket and leads directly to the key ball in the middle of the table.
6. The cueball should be kept near center table for most shots, in order to maximize opportunities.
7. The cueball should be kept above the rack for most shots, in order to maximize opportunities and to enlarge the position zones.
8. The cue balll should be kept away from the rail at all times.

For breakshots, I think the Mosconi style has been the one method that seems more condusive to high runs. High angle, high ball into center or slightly above center pack. Object ball close, but not too close to the pack, so as to enlarge the pocket.
Super informative post! I am among a very small list of players who prefers using inside spin for positioning off 1,2 or 3 cushions, when I have that option available to me.