Tetris/Pieces

There are seven distinct Tetriminos that you must direct and place within the Matrix. They are typically named after the letter of the alphabet that they most closely resemble. In order to become an expert Tetris player, good familiarity with all seven pieces is required. You must know the best ways to utilize each piece, as well as how to prepare for their eventual arrival.

O piece
The O piece resembles a 2x2 square. This is the only piece that looks the same no matter how you rotate it. Because every side consists of two squares, it is also the only piece that cannot fit in a single square gap. As a result, it's a very good idea to plan for this piece's arrival by having a two-square platform for it to be placed on without creating any holes or gaps.

S piece
When rotated once, the S piece looks different, but when rotated a second time, it returns to its original appearance. It has two edges which are two squares long, but it has two other edges that are only a single square, making this a fairly adaptable piece. Use it to plug up single gaps, or lay it down flat when there is a single block sticking up on the right side. S pieces are good for filling up 1-2 staircase gaps when the staircase is rising to the left.

Z piece
The Z piece is the mirror image of the S piece. It has very similar properties, in particular the fact that it looks the same after it's been rotated twice. Since it has the opposite profile of the S piece, look for situations where the S piece isn't quite suited, and try to place a Z piece there instead. Z pieces are good for filling up 1-2 staircase gaps when the staircase is rising to the right.

T piece
The T piece is a very versatile piece. It can be used in a variety of situations. The only time when it's not useful is when you need to fill exactly two squares. Other than that, it can fill in many single square gaps, and it can be rotated to fit a situation just right. This piece has a special property that allows you to rotate it into place beneath a gap to fill in a hole by spinning it after it has landed on top of something. This maneuver is called a "T-Spin" and many more recent versions of Tetris award a bonus for performing it. Note that if you have a flat enough surface, T pieces make excellent foundations for series of S and Z blocks.

L piece
The L piece is another quite useful piece. It has one edge with three squares, one edge with two squares, and two different edges with just one square. It can be safely used in a variety of situations. It also stacks quite nicely with itself when you rotate one 180 degrees. Use this piece to fill in two square holes, or to complete three lines in one shot.

J piece
The J piece is the mirror image of the L piece. It has many of the same properties, including the ability to nicely stack with a rotated version of itself. Its single block occurs on the opposite side of the piece from the L, so take note of locations that aren't perfect for the L piece, and see if you can place a J piece there instead.

I piece
The I piece is perhaps the MVP of Tetris pieces. Horizontally, it isn't very useful unless you have a nice four-square flat surface to drop it on. However, it is incredibly helpful when placed vertically. It is the only piece that can be dropped down vertically without creating any gaps or holes on either side of it, and more importantly, it is the only piece capable of clearing four lines at one time, known as a Tetris, which awards you the largest number of points.

Randomization
The order in which the pieces appear throughout your game is fairly random. But there are actually a variety of random systems which different versions of Tetris employ to present these pieces to you.
 * Purely random: A purely random system picks a number from 1 to 7 every time, and presents you with whatever piece is chosen, regardless of anything, including how often that piece has been presented in the past. Although in the long run, the presentation of pieces are statistically equal, it is possible to get into situations where one particular piece is presented more often throughout an individual game than any other.
 * Single bag random: In a single bag random system, all seven pieces are placed in a "bag" and presented to you at random, until all of the pieces have been selected. Then the pieces are placed back in that "bag" and selected at random again.  This ensures every piece will appear at least once for every seven pieces that you are given.  The worst case scenario for the number of turns you must wait for any one particular piece is thirteen pieces.
 * Multiple bags random: A multiple bag system works almost identically to a single bag system, except that more than one bag of seven pieces is available for selection. For example, in a three bag system, all seven pieces are present in all three bags.  All three bags must be emptied (21 pieces) before the system resets itself and places all seven pieces back in each of the three bags to be selected over again.  This system allows for much more repetition of pieces than a single bag system, while still ensuring that the number of appearances for each piece is more or less statistically equal.
 * History based random: Some games don't use a bag, and instead roll a number from 1 to 7, but reroll up to a certain number of times (usually 4 or 6) if the piece is one you have seen recently (usually within the last 4). This makes duplicate pieces much more unlikely, but doesn't guarantee the appearance of any piece.  Fair, but harder to predict then bag.
 * Unique: A few games (most notably the early Bullet Proof Software versions of the game, including the ones for the NES and Game Boy) employ an odd system of randomization utilizing binary math operations that are intended to produce truly random sequences, but actually result in statistical differences in the likelihood of particular pieces appearing compared to others.