Knowing that the Georgian Shuffle has some close relation to claymotion moves (and is used in some of the moves), I wanted to take a closer look at this trick. I also wanted to do some research into other "shuffle" moves and see if there are any other related tricks that would crossover into the style of claymotion. Here are some of the observations I have made, as well as a number of variations of the tricks.
First off, I am not going to do a tutorial on how to learn the Georgian Shuffle. If you don't know the trick and want to first learn how to juggle it, go to Adrian Kirk's excellent tutorial on learning the Georgian Shuffle. Todd Strong also has a Georgian Shuffle tutorial on his web site.
Georgian shuffle variations I have seen a few different varieties of the Georgian Shuffle depending on how the balls are thrown and caught. This video demonstrates a few of them. I first start with grabbing the multiplex ball underneath, then I grab it from above, then I start throwing the multiplex balls under the opposite arm, and lastly I throw a stacked multiplex and grab the bottom ball.
Bare bones georgian shuffle
Here is the bare bones throws and catches that are done in the Georgian Shuffle. The siteswap for this trick is: ([4x4],0)(0,4x)(2,4)
There are two moves that "make" the Georgian Shuffle.

The first move is which one of the multiplex balls thrown is caught (or grabbed) by the same hand. So in the first three examples in the video above notice that the hand throwing the multiplex reaches up and grabs the multiplex ball on the opposite side of the hand that threw it.

A right hand multiplex throw will reach up and grab the multiplex ball on the left side.

A left hand multiplex throw will reach up and grab the multiplex ball on the right side.

The second move is the "fake" that is done by the non-multiplexing hand. All that you do is throw the ball and catch it with the same hand (you can also raise the empty hand for some extra movement). This gives time for the multiplex hand to load both balls for the next multiplex throw.

To me those are the keys to what makes the Georgian Shuffle such an interesting trick.

Ok, another observation that you may have made is that the Georgian Shuffle is not a symmetric trick. Meaning that once you do one cycle of the trick the mirror image of it is not repeated on the other side. So that begs the question, can we reverse the Georgian Shuffle so that the trick is symmetric?

Bare bones georgian shuffle reversal The answer is yes, and here is the bare bones throws and catches for what that looks like.

The siteswap for the Georgian Shuffle Reversal is: ([4x4],0)(0,4)(4,2)*

Georgian shuffle over and under
Here are a couple variations of the Georgian Shuffle Reversal. Similar to the Georgian Shuffle variations above, one grabs the multiplex ball underneath, and another grabs it from above.
Now this is where the Georgian Shuffle Reversal gets interesting. When I started looking into a few of the other "shuffle" tricks, and breaking them down to their basic throws and catches, many of them are the exact same siteswap as the Georgian Shuffle Reversal. Two of the shuffle tricks that are the same are the Singapore Shuffle and the Davenport Shuffle.
Singapore shuffle At the right is the Singapore Shuffle.

In the Singapore Shuffle every throw is an under the arm throw. Also, the hand that does the multiplex throw under one arm will uncross and then reach over the arm and claw one of the multiplex balls that was just thrown. I have found it easier to claw the outside ball.

According to Todd Strong's website the Singapore Shuffle was created by Loh Koah Fong who wanted to create a symmetrical version of the Georgian Shuffle. Which in fact it is, as you can see from the above siteswap and video, but it doesn't really resemble the Georgian Shuffle when juggled. Todd Strong also a page with Loh Koah Fong demonstrating the Singapore Shuffle.

Davenport shuffle And here's the Davenport Shuffle.

The Davenport Shuffle is basically the Singapore Shuffle except that after the under arm two ball multiplex throw, the next single ball throw is a reverse cascade throw (rather than an underarm throw).

So, the Georgian Shuffle Reversal, Singapore Shuffle, and Davenport Shuffle are all based on the same moves, it's just the different throws and catches that make them unique. So, lets start taking some different throws and catches and see what other patterns we can come up with.
Georgian shuffle crossed arm reverse
Here is a variation where you throw the 2 ball multiplex under arm, the single under the arm, and then the reversed self is done while crossed arm. I then do the same trick with the catches and self throw as a claw.
Georgian shuffle crossed arm drops
Here's a variation where the arms stay crossed until the self throw, which throws on top of the crossed arm and catches underneath. I then do the opposite of that where the self throw is done under the crossed arm and then caught on top.
Now lets add in some body throws. It's easiest to think of these moves being based off of the Davenport Shuffle. Most of them are different ways of throwing and catching the self throw.
Georgian shuffle reversal under leg
Under the leg. Self throw is under the opposite leg of the throwing arm.
Georgian shuffle reversal behind head
Behind the head. Self throw is crossed arm behind the head back to same side as arm thrown. The two ball multiplex is caught crossed arm with self throw hand on top.
Georgian shuffle reversal under arm around the back
Under arm around the back. Self throw is under the opposite armpit and behind the back The two ball multiplex is caught crossed arm with self throw hand on bottom (this is a little more difficult).
I had a behind the back version as well, but somehow it didn't make on the tape. I'll end this section here, and I have some more observations to post in the near future.

Ok, so we took the Georgian Shuffle and figured out the reversal of the trick to make the pattern symmetrical. So another question to ask yourself is, "Is there a four ball version of the Georgian Shuffle?" Since the rest of this page is more than a paragraph with "no" at the end, we know that we can create a four ball variation.
Four ball georgian shuffle
Here is the siteswap for the four ball Georgian Shuffle: ([4x4],2)(0,[4x4])(2,4), along with a video of the trick.
Four ball georgian shuffle variations
Now what kind of variations can we do with the four ball version?
Four ball georgian shuffle reversal And of course this begs the question, since we have a four ball asymmetric version, can we make a symmetric version? Sure enough, and here is the siteswap for the symmetric version: ([4x4],2)(0,[4x4])(4,2)*, along with a video of the trick.
Four ball georgian shuffle reversal variations
And some variations.
Four ball singapore shuffle The four ball symmetric version of the georgian shuffle is also the same siteswap as the four ball singapore shuffle (just as in the three ball version). Here is a video doing just an under arm version and then the full under arm with the claw.
Five ball splits and singapore shuffle Finally, there is the five ball version of the singapore shuffle. Which if you break it down to the siteswap it's the same thing as a synchronous version of 5 ball splits!
5 ball splits sync siteswap: ([4x4],2)*
5 ball splits async siteswap: [54][22]2
Here's a video with 5 ball splits (cascade and reverse cascade), underarm 5 ball splits, and then a clawed version for the singapore shuffle trick.
Four ball quick reversal
There is also a variation to the symmetric version of the four ball georgian shuffle above. This results in a quicker version of the trick whose siteswap is: ([4x4],2)(0,[4x2])*, and the corresponding video.
I might cover this trick a bit more in the future since it has an interesting multiplex throw of [4x2]. This is where a hand holding two balls only throws one ball. Many (if not most) multiplex throws, you will throw all the balls in the hand. So a [4x2] throw can be a bit tricky at first because you may want to launch both balls when you do the throw. There are also a number of nice variations you can do with the above siteswap.