Dr. Dave's answers to frequently-asked questions (FAQs), mostly from the AZB discussion forum
more information, see Chapter 6 and Sections 7.06-7.08 in The
Illustrated Principles of Pool and Billiards,
Disc III of How to Aim Pool Shots (HAPS), Disc IV of the Video Encyclopedia of Pool Shots (VEPS) ,
and Disc IV of the Video Encyclopedia of Pool Practice (VEPP)
advantages of fast speed
Why do many top bankers use fast speed?
With faster speed, there is much less variation from table to table and from shot to shot. There are many variables that affect how a ball banks (cloth friction, cushion friction and coefficients of restitution, OB spin transfer, and table roll-off). At faster speed, these variables don't change the shot as much with slight changes in speed as they do with similar speed changes at slower speeds.
Also, at fast speed, the OB will pick up less roll into the rail (as compared to a slower bank, especially with the OB farther from the rail), and this (combined with the fast post-rebound speed) will minimize how much the OB curves forward after rebound (as compared to a slow-roll bank). As a result, the ball will bank in a more consistent direction. At slower speeds, the path and final target of the rebounding ball varies a lot with small changes in speed.
The disadvantage of faster speed is the reduced effective "size" of the pocket. For example, a slow-rolling ball is accepted by a corner pocket much more easily than a fast ball, especially if it doesn't have complete rolling topspin. However, the advantages listed above more than overcome this limitation. That's why most top bankers use fast speed on most bank shots (except where a two-way shot with pocket speed is a good play). Faster speed definitely makes banks higher percentage for people who have put in the practice time.
For banks into a corner pocket at shallow angles into the rail, using faster speed can also help make the angle into the rail even more shallow (since the ball banks short). This can help the corner pocket accept the ball more easily (especially if the ball has some topspin into the pocket), but this is a small effect compared to the others. And for banks into a side pocket, since the effective size of a side pocket is larger at steeper angles (more perpendicular to the rail) and faster speeds, banking short with fast speed helps enlarge the effective size of the pocket; but again, these effects are very small.
Faster speed can also help one avoid an obstacle ball or reduce the chance for a double kiss. For demonstrations, see double kiss detection and avoidance. And for more info, see kick and bank shot effects.
Also, there are reliable systems for aiming fast-speed bank shots.
bank shot drills
What are some good drills for practicing bank shots?
See bank shot drills.
contact-point mirror system for aiming shallow-angle, rolling kick shots
How do you aim to kick at balls close to a rail at a shallow angle into the rail?
For shallow angles into the rail, where the OB is fairly close to the rail, the contact-point-mirror-kick method works well. It is described in "VEPS GEMS - Part VII: Contact-Point Mirror Kick" (BD, July, 2010) and "VEPP – Part X: Shallow One-rail Kicks" (BD, January, 2013), and here are video demonstrations with a complete explanations:
from Disc IV of the Video Encyclopedia of Pool Practice (VEPP):
Corner 5 System for aiming two-, three-, and four-rail kicks off a long rail
How does the "Corner 5" System work?
It is illustrated and explained, with examples, in the following articles:
"VEPS GEMS - Part XI: Corner-5 System Intro" (BD, November, 2010).
"VEPS GEMS - Part XII: Corner-5 System Example and Benchmark" (BD, December, 2010).
"VEPS GEMS - Part XIII: Corner-5 System Adjustments" (BD, January, 2011).
Here's a complete demonstration and explanation of the Corner-5 system, with lots of examples of how it is applied:
Another interesting and entertaining demonstration of the system can be found in Disney's "Donald in Mathmagic Land" (starting at the 16:40 point).
from Patrick Johnson:
[Here's] a simplified way to estimate 3-rail kicks to given targets on the fourth rail. This simplified 3-rail kick system is vaguely similar to the Spot-On-The-Wall system and the Corner-Five system, but instead of off-table visual references (Spot-On-The-Wall) or math (Corner Five), it uses simple diamond-to-diamond alignments.
Three rail kicks that start out parallel to each other (their first legs are parallel) end up hitting the fourth rail very close together - they "converge" on a fourth rail target. It's easy to see parallel lines on the pool table using the diamonds. If we start with a line stretched between one diamond on the near long rail and another diamond on the far long rail, we can simply move each end of the line one diamond to the right to find a parallel line. Move each end another diamond in the same direction (left or right) and there's another parallel line, etc. The angle of these parallel lines between the diamonds is determined by how many diamonds along the rail one diamond is from the other - call this their "separation". For instance, diamonds on opposite long rails with "4 diamonds of separation" make parallel lines at 45 degrees (see third diagram below), while diamonds with "3 diamonds of separation" make parallel lines at 51 degrees (see fourth diagram below).
Using these easy-to-see diamond-to-diamond lines, we get sets of parallel lines to use as reference tracks for 3-rail kicks. Fortunately for us, each set of parallel lines converges near a pocket or diamond on the fourth rail, making both our first legs and our fourth rail targets easy to remember. The correlations are:
- a first leg line with 6 diamonds of separation will come close to the corner pocket on the fourth rail
- a first leg line with 5 diamonds of separation will come close to the 1st diamond on the fourth rail
- a first leg line with 4 diamonds of separation will come close to the 2nd diamond on the fourth rail
- a first leg line with 3 diamonds of separation will come close to the 3rd diamond on the fourth rail
Below are diagrams illustrating these basic reference tracks:
Use a "6-diamond separation" to hit the corner pocket on the 4th rail.
Use a "5-diamond separation" to hit the 1st diamond on the 4th rail.
Use a "4-diamond separation" to hit the 2nd diamond on the 4th rail.
Use a "3-diamond separation" to hit the 3rd diamond on the 4th rail.
I think this will be extremely easy to remember. Notice that for each of the cases you cited, the number of diamonds of separation plus the 4th-rail convergence diamond (counting from the pocket as zero) totals 6. That is, 6+0=6. 5+1=6. 4+2=6. 3+3=6. So we could call it the "Sixes System" for three-rail kicks.
What effect does cut angle have on bank-shot aiming?
The following video from Disc IV of the Video Encyclopedia of Pool Practice (VEPP) covers the important basics concerning how cut-induced-spin (CIS) affects bank shots:
Banks can also be affected by spin-induced-spin (SIS). For more info and examples, see the spin-transfer bank shots resource page.
diamond systems for aiming kick shots
How do diamond systems work?
All of the most common and useful banking and kicking systems (those listed below, and others) are described, illustrated, and demonstrated on Disc IV of the Video Encyclopedia of Pool Shots.
The simplest diamond systems are the equal-distance mirror system and the through-diamond rolling-ball system.
For shallow angles into the rail, where the OB is fairly close to the rail, the contact-point mirror system for shallow-angle, rolling kick shots works well.
The most famous"diamond system" is the Corner 5 System for aiming three-rail kicks off long rail.
Another famous diamond system is the Plus System for two-rail kicks off short rail.
Spot-on-the-wall kicking systems offer an alternative to formula-based systems.
Here's an article on Jimmy Reid's 3-rail systems.
Liberty Games has a nice online illustrated summary of diamond systems here: Introduction To The Pool Diamond System.
Here's a simple summary with examples, from Marcel Elfers, showing how to apply the Corner-5 System and Spot-on-the-Wall Systems to 3-rail kick shots. This document numbers the diamonds in 10's instead of the standard 1's to eliminate the need for fractions or decimals (e.g., 15 vs. 1 1/2 or 1.5).
complete "kicking academy" document describing and illustrating many diamond systems for kick shots.
double kiss detection and avoidance
How do you know if a bank shot will cause a double-kiss, and how can you avoid it?
The video demonstrates an easy method to use to detect and avoid cross-corner bank double kisses:
This video shows several techniques to avoid a double kiss with a cross-side bank shot.
This video shows how to detect a double kiss when banking a ball frozen or close to the rail.
Here's an excerpt from Disc IV of the Video Encyclopedia of Pool Practice (VEPP) showing how to use speed and transferred spin to avoid double kisses:
The classic one-pocket straight-back bank in NV H.2 - Bending, Twisting, and Stiffening Kick and Bank Shots is another good example of how to avoid a double kiss.
Here's a good article from Bob Jewett (BD, July '99) covering how to detect and avoid double kisses.
This video shows some examples of how to use a double-kiss bank to your advantage:
Here's another somewhat-unusual example of a double-kiss bank shot:
from freddy the beard:
Determining whether a bank shot lays in the "kiss" zone is often misunderstood, and usually winds up as an educated guess. In the following diagrams I have outlined exactly when a bank cannot normally be made using a rolling with or without english. In diagram #1, I deal with the shorter angle cross-corners. If the straight-in angle of the cueball and object ball is lined up and aiming into the pocket facing, the shot is a certain kiss. Left or right english, follow, center, or draw is not going to help you beat that kiss. With a slight angle adjustment, as per diagram #2, lined up to the middle of the back of the pocket, the bank can now be easily made with rolling or center ball, no english.
Diagram #3 is another variation that must be considered. It involves crossing, or passing-over, the object ball from a much more severe angle. Rather than calculate off of a straight-in angle as per dia.#1 & 2, the kiss/no kiss reference point is determined by lining up the actual cut angle needed to make the bank. If an imaginary line from the center of the cueball, extending thru the cut area on the object ball, continues into the middle of the back of the pocket, the kiss is "on." If the line instead, is aiming at the short/bottom rail, you can go ahead and shoot the shot with impunity. Provided of course you are using a natural rolling ball, center ball, left english in this case, or draw. Right hand english when the bank is "on" could result in a kiss.
effects and factors to consider
What effects does one need to adjust for when aiming bank and kick shots?
First, "VEPS GEMS - Part V: Banks and Kicks" (BD, May, 2010) and the video below illustrate, describe, and demonstrate basic terminology for bank and kick shots:
The basic mirror (angle in equals angle out) systems provide a point of reference only. Your aim with a given shot depends on many effects. The effects that require aim adjustment include:
If one doesn't understand all of these effects, or have great intuition built up from years and years of experience (i.e., lots of mistakes and successes), the mirror systems are not very useful. Here's an excerpt from Disc IV of the Video Encyclopedia of Pool Practice (VEPP) that shows you how to develop a feel for some of the effects during practice:
Here are some example shots where speed and spin can be used to change the rebound angle and path with kick and bank shots:
For more information, see: "Bending, Twisting, and Stiffening Kicks and Banks" (BD, October, 2016).
For kick shots with small approach angles (i.e., almost straight into the rail), it sometimes helps to know how topspin and bottom-spin change off the rebound. For more information and examples, see:
Concerning HSV B.41, why doesn't speed shorten the rebound angle? Doesn't the ball compress the cushion sideways more at higher speed, and wouldn't that create sideways forces that would shorten the rebound angle?
There are many physical effects that control the immediate rebound angle and the amount of masse curving after rebound. I use the phrase "rail throwback" to refer to the effect you are describing. With more speed the cushion deforms more and can generate more sideways force to shorten the angle; however, the rebound angle is also affected by the efficiency (coefficient of restitution = COR) of the cushion, and this can vary with speed and angle also. Based on the results in HSV B.41, these two effects are balancing each other out. The rail throwback effect tries to shorten the rebound angle and the efficiency effect apparently tries to lengthen the rebound (because the cushion is returning less energy, maybe partly because of the ball shift down the rail). This is all conjecture, but it makes sense physically. There are also friction effects between the ball and cushion and ball and table during impact. These might also vary in complicated ways with speed.
from Patrick Johnson:
For kicks the important thing is what kind of "vertical spin" the CB has on it when it hits the rail:
- CB sliding when it hits the rail will rebound with no curve at the "mirror angle" (minus something for rail friction)
- CB with forward spin (including natural roll) when it hits the rail will curve longer than the mirror angle
- CB with backspin when it hits the rail will curve shorter than the mirror angle
How much longer or shorter the CB rebounds (with forward spin or backspin) depends on how much spin is on the CB* and how much friction there is between the CB and the cloth.
For banks the important thing is how much vertical spin is on the OB when it hits the rail. This can only be controlled by hitting harder or softer (harder = less or no forward spin; softer = more forward spin). This is also why hitting harder shortens bank angles.
*: How much spin is on the CB depends on: - how hard it's hit - how high it's hit - how far it is from the rail when it's hit - how much friction there is between CB/cloth
As this drawing shows, when the CB changes direction off the rail its spin does not change direction. That means that forward or reverse spin which was rotating parallel with the CB's path before hitting the rail is rotating across the CB's path after hitting the rail - this across-the-path rotation is what causes the CB to curve after hitting the rail.
Forward rotation (topspin) can be the result of the CB rolling naturally or of hitting high on the CB. Reverse rotation (backspin) can only be the result of hitting low on the CB.
bending a bank shot
Is it possible to bend a bank shot back (i.e., curve the OB's post-rebound path in the short direction)?
The short answer is: Not nearly as much as many people think. For the long answer, see the following video, follow-up explanations, and the $2000 Bank Bend Challenge.
At first, I was very disappointed that I didn't see any bend in the OB path with any of the shots on any of the equipment or conditions I tested. It is possible to bend a bank since the cushion nose can impart masse spin (about an axis perpendicular to the rail) and topspin (about an axis parallel to the rail), both of which can curve the OB's post-rebound path; but bending a bank a significant amount is not as easy as some people might think. One reason a large bend cannot occur is that much of the small amount of topspin or masse spin imparted to the ball during cushion nose compression has an effect or "takes" (and dissipates) only when the OB first interacts with the bed of the table when the cushion nose pushes the ball down into table. This effect can help "twist" or "shorten" the bank, but only the curving spin that remains after the bounce out of the "rail groove" can contribute to bending or curving the OB's path to the pocket. The downward push into the table (into the rail groove) is what causes the OB to bounce into the air with fast-speed banks. While the OB is in the air, it can head only in a straight line (relative to the table). But when it lands, any remaining curving spin can start to "take" and bend the post-rebound path. On slicker cloth, less spin will be lost during the first bounce out of the rail groove, and any remaining curving spin will take longer to bend the ball's path, making the curve more clearly visible. Once the curving spin totally dissipates, the OB heads in a straight line to the pocket.
Now, speed and reverse spin can most certainly "twist" or "shorten" a bank a significant amount, allowing one to easy avoid obstacle balls or double kisses, as demonstrated in the following videos:
NV H.2 - Bending, Twisting, and Stiffening Kick and Bank Shots
NV H.3 - Pool Myth Buster - Bending Bank Shots
NV C.14 - Bank shot cut-angle-effects drills, from VEPP IV
It is possible to bend a bank a small amount, and this could allow one to pocket a bank that could not be made otherwise, but the amount of bend possible on typical shots on typical equipment is much smaller than many people think is possible. That's one purpose for the $2000 Bank Bend Challenge ... to show people how difficult it is to bend a bank, and do so accurately and consistently. Here's a good example (from pool101 on AZB) clearly and convincingly showing that a bank can be bent with a good hit and suitable conditions:
Now, it is easy to bend a bank shot forward in the long direction when the OB rolls into the rail with topspin (due to slower speed and/or greater distance to the rail). This effect is the same as with the rolling and bending kick shots demonstrated in NV H.2 - Bending, Twisting, and Stiffening Kick and Bank Shots. In fact, the main reason why fast speed is used by top bank-pool players is to limit forward bend, which varies too much with shot angle, speed, and conditions. For more info, see advantages of fast-speed banks.
The problem with anecdotal statements about what people claim they have seen in person concerning bank bending is that our eyes and brain aren't fast enough to accurately visualize the path of the OB with fast-speed banks. There are too many visual clues that can create optical illusions and mislead us:
- the ball can compress and slide down the cushion a significant amount during rebound.
- the ball typically bounces into the air (sometimes high, with multiple subsequent bounces) after rebound
- the ball typically has a combination of sidespin and topspin after rebound that might visually look like masse or bank-bending spin.
- the ball "turns" when it heads into the pocket if it hits the pocket point or facing first.
- we are used to seeing slower-speed banks curve long (due to incoming topspin), so a fast-speed bank might seem to curve short in comparison.
Again, when all of this happens very quickly, or if poor-quality video is being used, our eyes (and brains) can easily be fooled into thinking something is happening that is not. Freddy's "bank benders" included and analyzed in NV H.3 - Pool Myth Buster - Bending Bank Shots are good examples of this. That's another reason for the $2000 Bank Bend Challenge. It totally eliminates the potential for optical illusions or deception, and it provides a direct measure of the amount of bend possible. It also rewards the person who can achieve more bend than anyone else. This will also help us figure out how much bend is possible with the best possible hit of a well-chosen shot on typical equipment.
equal-distance mirror system for aiming bank and kick shots
How does the basic mirror system work?
"VEPS GEMS - Part V: Banks and Kicks" (BD, May, 2010) and the video below illustrate, describe and demonstrate basic terminology for bank and kick shots, and explains the basic equal-rail-distance mirror system:
The mirror system is a visual application of the classic 2-to-1 system. The following video from Disc III of How to Aim Pool Shots (HAPS) shows how the classic "mirror system" works:
For more information, see HAPS - Part VII: Kick Shots (Billiards Digest, May, 2015). Sometimes, people mirror and aim with the tip under the cushion. This works well for medium-speed shots at medium kicking distances under typical conditions, but it doesn't work well for all types of kicks. Whether you mirror and aim relative to the rail groove (in from of the cushion), along the line of diamonds (behind the cushion), or under the cushion depends on shot speed and distance. It also depends on conditions. See the video above for more info and demonstrations.
The basic mirror (angle in equals angle out) systems provide a point of reference only. You must compensate your aim for a given shot based on the many effects and factors to consider.
For shallow angle kicks, where the object ball is close to the rail, the following mirror system works quite well:
Here's another useful video, from Disc III of the Billiard University (BU) Instructional DVD series:
For more information, see: "Billiard University (BU) - Part IX: Kicks," (April, 2014).
from Patrick Johnson (in AZB post):
You might already know this trick for aiming "equal angle" banks/kicks:
- Stand away from the table in the position where a mirror image of your target pocket would be.
- Sight from there back through the rail to the ball you want to bank/kick.
- Note the position on the rail that you're line of sight passes through - that's the equal angle rail target for your bank/kick.
But even if you have the room to do it, how do you know exactly where to stand? You can use the pockets and diamonds on your table to visually "triangulate" the exact position of any mirror-image pocket.
Just stand where two triangulation lines cross - in the spot where you're able to see straight along both lines - and you'll be at the mirror-image pocket location.
The pic below shows how to triangulate pocket positions for long rail banks/kicks - the trick works the same way for short rail banks/kicks too, but I'll leave that for you to work out.
from Patrick Johnson AZB post:
Here are the reference angles for banking/kicking to the bottom left corner pocket - they connect each 1/2 diamond on the far rail with the whole diamond twice as far along on the near rail:
Of course, I don't visualize all these reference angles for every shot to that corner. For instance, the 2 ball is very near one reference angle, so I'll just compare it to that one:
The 1 ball is midway between two reference angles, so I'll compare it to both of them:
Here's the same technique applied to kicking at a ball that's not on the near rail. Just move the near "rail" (where you measure the whole diamonds) up to be parallel with the target - it doesn't matter if the cue ball is above or below the adjusted "rail".
Here's another way of measuring kick shots, a little different from the "reference angles" method I posted earlier, but using the same 2-to-1 principle. It should be self explanatory...
Like the "reference angles" this measures the "equal angle" kick, so of course you need to adjust for cloth stickiness & ball speed/spin.
from Patrick Johnson AZB post:
The most common adjustment you'll make when using equal-angle reference tracks is to aim a little short to compensate for a rolling ball's natural tendency to curve long as it rebounds from the rail. Fortunately, it's also pretty easy - just aim at the diamond on the rail rather than the cushion nose (may differ slightly on different tables).
Here's a pic illustrating those adjustments:
fast-speed bank aiming system
How do adjust your aim for a fast-speed bank?
The bank shot aiming system described in the following articles works well for fast-speed banks: "Fast Speed Banks" (BD, July, 2013) and "HAPS - Part VIII: Bank Shots" (BD, June, 2015). It also works well for banks of any speed if the OB is close to the banking cushion (where it doesn't have time or distance to develop forward roll). Here's a diagram from the article illustrating how it works:
And here's a video demonstration from Disc III of How to Aim Pool Shots (HAPS):
The aim always originates 1/3 of a diamond above the standard 2-to-1 mirror system (measured across from the diamonds in the rail groove). It can be referred to as the "(2x + 1/3) to x" or "1/3-more-than-twice system. See the article and the video above for examples of how it is applied. The system is also described and demonstrated in "VEPS GEMS - Part V: Banks and Kicks" (BD, May, 2010). Here's the diagram from the article that illustrates how the adjustment works. The exact amount of adjustment needed will vary with conditions and the angle of the bank, but 1/3 of a diamond is a good general benchmark reference. The diagram also shows another useful reference for fast-speed banks: the 3-to-1 through-diamond reference. On most tables, shooting through 1 from 3 with very fast speed pockets the ball.
An alternative to the "(2x + 1/3) to x" system described above is a through-diamond system described in the following video: Eckert's bank shot reference lines. It can be described concisely as the "2x-to-3/4x through-diamond system" as opposed to the "(2x+1/3)-to-x rail-groove system." Both this system and the system above are described and illustrated in detail in: "Fast Speed Banks"(BD, July, 2013). They actually agree fairly well in the resulting aim, except for very-large-angle banks. Another way to interpret the Eckert system, is the "8/3x to x" or "x to 3/8x" system (by dividing the "2x to 3/4x" numbers by 2). This implies that the aim point on the banking rail (3/8x) is between 25% (1/4) and 50% (1/2) of the distance from the target pocket as the distance on the adjacent rail (x). This provides an easy way to visualize fast-speed banks. When the aim is correct, the aim point on the banking rail is exactly between 50% (1/2) and 25% (1/4) of the distance from the pocket on the opposite rail, which is very easy to visualize without any diamond counting or math.
The following illustration compares the two systems. The systems provide very close to the same lines of aim for small-to-medium-angle banks. At larger bank angles, above the (5+1/3)-to-2.5 line, the "1/3-more than twice" system aim will tend to make the ball bank a little short of target (in which case you can make a small adjustment).
In addition to being able to use the aiming systems above, there are advantages to using fast speed with bank shots. For more info, see: advantages of fast speed.
from John Gaynor (via e-mail):
I found a way to simplify the calculations for the Ralph Eckert system for banking with speed. First, I use 10 as the distance between diamonds. So the 3 to 1 track becomes 30 to 10. Then every point on the target rail that is a multiple of 3 leads to a convenient reference track since the crossing point on the near rail is 8/3 times the point on the target rail. So reference tracks are 8 to 3, 16 to 6, 24 to 9, 32 to 12, 40 to 15, 48 to 18, etc. Calculating between the reference tracks is easy. For example, if you're between the 24 to 9 track and the 32 to 12 track, the tracks are 26&2/3 to 10 and 29&1/3 to 11, or with slight rounding 27 to 10 and 29 to 11.
kick shot drills
What are some good drills for practicing kick shots?
Seekick shot drills.
magic spot three-rail mirror-image kick shot aiming system
How do you find and use the "magic spot" for three-rail kick shots?
See the following document from Marcel Elfers: Pool Magic Spot.
Plus System for aiming two-rail kicks off a short rail
How does the Plus System (AKA Plus Two System, AKA "Plus 2 System") work?
It is described and illustrated in detail in the following instructional articles:
"VEPS GEMS - Part VIII: Plus System Intro" (BD, August, 2010).
"VEPS GEMS - Part IX: Plus System Adjustments" (BD, September, 2010).
"VEPS GEMS - Part X: Plus System Examples" (BD, October, 2010).
Here's a video demonstration and explanation:
shallow-angle contact-point-mirror-image kick-shot aiming system
How do you aim shallow-angle kick shots where the object ball is close to the rail?
When the object ball is close to a ball away from the rail, the following mirror system, from Disc IV of the Video Encyclopedia of Pool Shots (VEPS) is very effective:
The following video, from Disc IV of the Video Encycopedia of Pool Practice (VEPP), demonstrates a good way to practice these shots:
For more information, see: "VEPS GEMS - Part VII: Contact-Point Mirror Kick" (BD, July, 2010) and "VEPP - Part X: Shallow One-rail Kicks," (BD, January, 2013).
Sid System for aiming steep two-rail kicks off a short rail
What is the "Sid System" and how does it work?
The following resource explains and illustrates the Side System fairly well:
from Bob Jewett (from AZB post):
For those who are wondering what "System Sid" is, here is the diagram from Walt Harris's book, "Billiard Atlas". To hit a spot on the second cushion, multiply the number for the spot by how many diamonds the cue ball is from point X. In the example, the target is 2.5 and the cue ball (Q) is 3 diamonds from X so the target is 7.5 on the short rail. Note that the short rail (M) is numbered 10 to the diamond, the second rail has a variable numbering that you have to memorize, and the rail you are shooting from (O) is numbered in units to multiply with. Harris recommends renumbering the O rail according to the second rail number, so in the example it would be numbered 0, 2.5, 5.0 and 7.5 starting from X.
If you work out the geometry in detail, the numbers on the second rail are off a little but as listed they are easy to remember.
spin-transfer bank shots
Is spin transfer required to make certain bank shots?
Yes. See NV B.20 for two important examples. For more information, and another example, see "Throw - Part VIII: spin transfer" (BD, March, 2007). Many more examples of spin-transfer shots can be found here:
spot-on-the-wall kick shot aiming system
How do "spot-on-the-wall" kicking systems work?
The three-rail Corner-5, two-rail Plus-2, and one-rail kick "spot-on-the-wall" systems are described and demonstrated here:
More information, including guidelines on how far the spot should be from the table, can be found in "VEPS GEMS - Part XIV: 'Spot-on-the-Wall' System" (BD, February, 2011).
There are different "rules of thumb" for estimating the best distance to the spot on the wall, but they don't always match the results in the article very well. Here's a common rule that does a decent job (although, it predicts a distance longer than recommended for a 3-rail shot and a distance shorter than recommended for a 1-rail shot):
from Monte Ohrt:
For any given spot-on-the-wall kick shot, the exact optimal distance from the first rail to the spot is the distance the cueball travels after it hits the first rail to the target. For a one-rail kick, this is simply the distance from rail 1 to the target. For a two-rail kick, it is the distance between rail 1 and 2, and also add the distance between rail 2 and the target point. For a three rail kick, it is the distance between rails 1 and 2, 2 and 3, and 3 to the target point ... and so on for 4 rails, 5 rails, etc. After about 3 rails the point of convergence is so narrow that it normally doesn't make any difference, just pick a spot at least 3 tables away.
through-diamond rolling-cue-ball 2-to-1 one-rail kick and bank shot aiming system
How does the through-diamond rolling-cue-ball one-rail kick system work?
It is described in "VEPS GEMS - Part VI: One-Rail Kicks" (BD, June, 2010). Here's a video demonstration, from Disc IV of the Video Encyclopedia of Pool Shots (VEPS), with a complete explanation:
Here's another useful video, from Disc III of the Billiard University (BU) Instructional DVD series:
The visual equal-distance mirror system is also based on the 2-to-1 system.
two-rail bank shot aiming system off a short rail
Is there an aiming system for two-rail bank shots off the short rail?
You can use the Plus System for aiming two-rail banks off the short rail, but it will require practice to learn how to adjust for the lack of running english and forward roll on the OB into the first cushion which varies with distance and shot speed.
If the OB is fairly close to or frozen to the short rail, the systems below from Freddy Bentivegna work fairly well.
from freddy the beard AZB post:
two-rail parallel-line kick shot aiming system
Dave, I have been practicing the 2-rail parallel line kick shots you show in your
book on pages 229 & 230 and demonstrated in NV
7.9. It works fine if I set up the balls similar to what you show in your
book but I am having difficulty envisioning the same shot from other set ups.
I don't think I fully understand how to determine the center line between the
2 parallel lines. Can you elaborate on this idea?
The following video, from Disc III of the Billiard University (BU) Instructional DVD series, demonstrates the system:
Unfortunately, the action of this shot depends on english, shot speed, and table (especially cushion) conditions. Obviously, when practicing, you need to try to use consistent english and speed on a given table to see how the cue ball responds at different angles.
For more information and demonstrations, see Shots 514 and 515 on Disc IV of the Video Encyclopedia of Pool Shots.
from Patrick Johnson:
You have to aim a little closer to the corner than the measurement suggests - experience will tell you how much, depending on the angle to the first rail and the cleanliness of the table/balls.
In this drawing the blue line is the measured track, but the actual track will look more like the red line:
... the "Amazing Double-mirror Image Method" or ADIM for short ... is explained on the second page of http://www.sfbilliards.com/articles/2004.pdf (July). Mostly, it gives you a very easy way to put up a target ball exactly where the real ball would appear for a perfect mirror system. ... This lets you see immediately how pitifully awful the two-rail mirror system is, but it also allows you to try to find out where it does work and maybe how to modify it so it works for more cases.
two-times-across and three-times across bank shots
What are "two-times" and "three-times" across bank shots, and how do they work?
from Patrick Johnson:
It's a series of spin events:
1. The CB colliding with the OB puts some "holdup" spin on the OB, which shortens the angle off the first rail.
2. The OB colliding with the first rail at an angle reverses the spin that was put on by the CB (just like any ball picks up "running" spin when it hits the rail).
3. The reversed spin throws the OB toward the side pocket off the second rail.
two-times-across Z-kick aiming system
How does Jimmy Reid's two-times-across Z-kick system work?
from Patrick Johnson:
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