Essentially, I divide the various types of shuffles, by how the cards move within the deck, which we will learn much more about in later sections, but at least for now we will describe a series of situations according to the three basic types of shuffles. Block shuffles, weave shuffles and chaos shuffles.
Block shuffling includes overhand shuffling, Hindu (capitalized when the others are not in order to keep my spell checker happy) shuffling and underhand shuffling (if anyone were actually to perform such a decidedly ridiculous method). It is defined by the fact that cards are rearranged within a small area but not over the course of the larger deck. For example, if you had a card on the top of the deck and one four cards from the top that you wanted to group together, this could easily be performed with a block shuffle (methods will be discussed later). If on the other hand you had a card in the middle of the deck that you wanted grouped with the card on top this could not easily be performed with a block shuffle. That is to say, it would require more than a single shuffle, again, methods will be described in detail later. (A qualification here, it could be performed, but it would involve greatly limiting the shuffling and it would not appear terribly natural).
Weave shuffling includes riffle shuffles, ranging from dovetails to slop shuffles to plain weaves and faros. These are characterized by the ability to bring the middle of the deck to the top of the deck, but not to bring say the fourth card down next to the top card in a single shuffle. (Note, technically it may be possible to violate this rule, but not while at the same time appearing natural and so I remain firm on my definitions.)
The final type of shuffling is what I call chaos shuffling and it is by far the least used and yet the most effective. It is characterized by the ability to move any card from any position in the deck into any other position in the deck. Again, the method will be described later, but it is mostly for the sake of completeness that I have included it as I find it to be a very impractical method, particularly when one is attempting to control cards.
As you have surely surmised, each method presents advantages and disadvantages. Each method will be described in detail later, but for now, I will outline the advantages and disadvantages as follows. Chaos shuffling when well executed is the best for mixing the cards. Weave shuffling is second and block shuffling is the poorest method. To give you some idea, a single good chaos shuffle can fully randomize the deck, it takes seven riffle shuffles to fully randomize the deck and typically many more block shuffles. Weave shuffling is however the best for controlling and culling cards for reasons I will go into more later. Chaos shuffling is not particularly effective for this due to the fact that it presents such logistical nightmares. Block shuffling is the best for certain other types of controls and for blind shuffling (on the subject of blind shuffling it actually depends on the method used, but we will continue on that subject further on in this volume). Blind shuffling with a chaos shuffle is nigh impossible and tends to be a little more suspicious with a weave shuffle.
A note here, I have been mocked for using a chaos shuffle. I recall being at a party playing cards and when I began to mix the cards in a chaotic fashion someone remarked, "What's this? Mr. One-handed shuffle has to shuffle the deck like that". To say the least, it is not the most elegant approach, but it works well for mixing and is very convincing if you can manage it for controlling.
I realize that most of this first section will likely be boring to the majority of my readers who I hope have at least average familiarity with cards and consequently shuffling, but I believe in being thorough and working with the basics. This is in part so that everyone is on the same page when we reach more advanced material and in part so that there is some understanding as to the evolution of thought. For those who find what I will cover now to be too mundane please feel free to skip ahead to the portions you find to be of greater interest. For those of you who feel either the need or the interest to read the basics I outline here I hope you garner at least some crumbs of insight.
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