Setting up pool balls

What is the maximum number of changes you could make to a pool triangle to get the balls set up correctly?

Obviously the strict answer is infinite (:smack: ) but I mean taking into account that you are trying to set the balls up correctly and not just try and move them around until you die!!

The minimum is 0 as by chance you have put all the balls into the triangle and by chance they have the correct formation.

The reason I ask is that I play a lot of pool and from time to time you see someone struggling desperately to set them up (especially as the night wears on :wink: ) and I half always wondered the maximum number of times balls should be moved even if the triangle was set up as badly as possible.

Thanks

Well, since technically the “correct” formation for 8 ball as stated by the American Poolplayers Association specifies no specific ball placement except for the 8 being in the center, the maximum would be 1. (ref. http://www.poolplayers.com/8-9-ball-Rules.pdf)

We were taught in pool class that in addition to the 8 in the center, you must have one stripe and one solid in either rear corner, not the same type in both. This would only raise the maximum to 2.

In nine-ball, the only restrictions are that the 1 be in front and the 9 be in the center. Again, maximum changes would be 2.

I assume, however, that you mean what is the maximum number of changes to get the balls in numerical order. I shall work on this problem and return with the answer unless someone beats me to it.

Ok, I’ve thought about it.

Let’s begin with some assumptions.

  1. One move consists of switching the position of two balls.
  2. On each move, a ball must end up in its final postiton (this counters the argument that you could keep moving them forever).

I believe the maximum moves to get all the balls in numerical order (except the 8 which goes in the center), is 14. Here’s why:

On each move, one ball ends up in its final position, meaning you never have to move it again. On the fourteenth move, both balls end in their final positions.

Consider this setup (I think one of the “worst” possible):



........(15)........
.......(1)(2)......
....(3).(4).(8)....
..(5).(6).(7).(9)..
(10)(11)(12)(13)(14)


Forgive the lopsidedness. If you switch the 1 and the 15, then the 2 and the 15, and so on, you will end up switching 14 times.

I think that’s the maximum number possible for 8 ball.

I think the same strategy would be applicable for 9 ball, yielding 8 switches necessary.

Firstly - Garfield226 - wow - only 22 minutes thinking!!! This has been bothering me for ages :slight_smile: !

Secondly I wanted to just clarify something. I understand that ‘American’ pool and ‘English’ pool have some differences but I believe that we stick to a similar set up convention (unfortunately I am unable to access the PDF you reference in your reply).

In US pool you have ‘spots’ and ‘stripes’ or ‘overs’ & ‘unders’ I think. In the UK we have reds and yellows. Assuming these naming conventions are interchangeable it means that they don’t have to be set up in a specific order. They just have to conform to this pattern:

http://www.arseweb.com/rupe/pool/uk_rules.html [image at the top]

I’m not sure if that changes the maximum number of changes or not but I suspect it does so, given your past performance, you now only have 11 minutes to think it out!!! If I am mistaken (again because I can’t reach the PDF) I would still much appreciate a reply concerning English pool.

Any other replies gratefully accepted!!

To clarify further maybe this link will be more useful :

since there are two setup images at the top!!!

Note to self : check posts before hitting “Submit” :smack:

Hm. Does the rack need to be set up EXACTLY as in the picture?

If not, if the only requirements are as in American 8 ball (i.e. 8 in the center, one of each red and yellow in each corner), then the maximum remains 2.

Start the timer on my 11 minutes, if the rack must be exactly as in the second linked pic.

Ok. I think I’ve got it.

Consider that EACH ball except the 8 is the opposite color from what it should be. For now, the 8 remains in the middle.

Simply switch the positions of any two different colored balls (taking care not to move the same one twice). This yields 7 switches.

Now, back in the original set up, if the 8 ball is switched with, say, a red ball, and the 8 ball is in a position that the red ball should occupy at the end, this FORCES a yellow ball to begin in its final position. It therefore still yields only 7 switches.

However, if the ball in the 8 ball’s space is NOT the same as the one which needs to occupy the 8 ball’s beginning location at the end, it adds on an extra switch at the end, yielding 8.

I think this should hold true for any setup using this set of balls in which the pattern is mandatory. Someone should be along to prove me wrong shortly.

[Hijack for minor stupid question not worthy of its own thread]

I’m pathetic at breaking and would like to be able to send all the balls hurtling all over the table. Is it better to rack the balls tightly or loosely?

[/Hijack]

I see you’re in Chicago. The rules for American 8 ball state that either a ball must be pocketed or at least four (4) object balls must contact a cushion for a break to be legal.

The best way to accomplish this (at least in my experience) is to rack the balls tightly. This avoids the problem of the cue ball glancing off the one and barely moving any of the other balls, since in a tight rack, any energy transferred to the 1 will more than likely be distributed throughout the other ones too.

Also note that the rules state that the cue ball must not contact a cushion before striking the one. I’ve found that it’s usually better to hit the cue ball from slightly off center, aiming at the center of the cue ball and using as much power as you’re able while still maintaining control.

Of course, there is more than 8-ball, although that is the most popular game in the USA. In straight pool (international rules), the triangle apex must be on the foot spot, 1 ball on the racker’s right corner, 5 ball on the left, the rest arranged randomly, essentially giving 13! possible combinations.

One local 8-ball variant rack is “King’s Hat”, wherein the corner balls are moved to the front sides to form a “crown” shape. I have only seen this in friendly Indiana games, and it’s not universally known within Indiana.

Garfield226 said :
>Hm. Does the rack need to be set up EXACTLY as in the picture?

Yes and no. It is generally accepted that the reds and yellows can change places as it makes no difference to the break. However some people do insist on it being that way.

Generally as long as the colours alternate as in the order

     1
    2,3
   5,*,4
  6,7,8,9

14,13,12,11,10

[please try and imagine this as a triangle!!]

with the exception of balls 10 and 11 which are always the same colour (giving you the ‘c’ shaped band of colour in the bottom right) the setup is considered good.