Introduction

Bernard Parham I has been a fixture in Indiana chess for many years and is perhaps known for his innovative approach to playing and teaching chess. With his successful "Matrix System" approach, he has taught an estimated 3000 students this method and has perhaps spurred a debate on his unconventional methods.

Part of the Matrix System is the rapid deployment of the Queen in order to "deliver the earliest possible checkmate." While coaches and advanced players would frown upon these tactics, the theory has merit and deserves analysis.

Parham's ideas certainly can find a wider application to chess theory.  Many times it is not the creator of the system who will find the best application. Thus, what Parham has  done is revolutionary in its essence.

Bernard Parham with his signature 2.Qh5 move.

Matrix Revolution Begins!

Back in the 60s, an inquisitive young teen named Bernard Parham strolled through Indianapolis'  Douglass Park and something he saw intrigued him. There were men playing chess who he would come to learn were "street hustlers."  After watching over a period of time, young Parham noticed that the player who brought the Queen out the earliest won an overwhelming majority of the games.  He would return to the park on a regular basis and watched their play with interest. Parham began copying down accounts of these games. A few years later, he would formally learn chess, but those lessons he learned in the park left an indelible impression.

Parham would graduate from Crispus Attucks High School and win a scholarship to Purdue University to study math and physics. It was in a physics class that he recognized a connection between chess and vector analysis. He was 18 years old at the time and would begin to refine his thoughts and eventually came up with a system of chess understanding called the "Matrix System." Three years later, he would then burst onto the scene and win the 1967 Indiana State title with his  revolutionary  ideas. He later became a National Master known widely for the "Parham Attack" and brute tactical style.

What is the Matrix?

Parham's Matrix System entails a system of play and notation that views the 8X8 matrix as a Cartesian plane on which chess pieces form vectors leading to attack routes toward the enemy King. The "Parham Attack" is characterized by the early Queen sally 2.Qh5 (or even …Qh4 with black) and is designed to create swift threats at the enemy's weakest point or what he calls "coincidences."

When asked if this works in Fischer Random chess (960 positions), he stated, "Wherever the King is, you would then aim the Queen at the square where the earliest mating sequence is defined… then strip the defenders away from this square." Of course this "undermining" concept is well-known is chess. While Parham states that the four-move "Scholar's Mate"  has been around since at least 300 B.C., his system of play has taken on scientific relevance.

Based on his theory, the Queen is the first to move, followed by the bishop, the knight and finally the rook. Ironically, in the Matrix System, the Queen is only worth six points  because it moves "cartesianally" like either-colored bishop and the rook forming a spoke. Thus, the Bishop and Rook have a value of two points since both move in two directions on the Cartesian plane.

The Matrix Pieces and Board

Another shocker to chess players is the fact that Matrix students are taught that Knights DO NOT move in "L" shapes. Since the Knight  has eight points, four lines can connect these points to create a diamond. Perhaps one of the most unique aspects of the Matrix System is its method of representing pieces on the Cartesian plane. Each piece is identified not by chess symbols or letters, but by symbolizing their geometric movements. Below is a diagram illustrating the Matrix Pieces.

One very interesting point about the notation of the Matrix pieces is the ability of the pieces to be rotated 180 degrees on the board without any loss of orientation. This system makes it easier to play over games without the use of a board. The Matrix Notation System™ appears to make this task a lot easier to follow since the geometric movements can be identified easily when combined with the appropriate squares on the 8X8 matrix. See illustration below.

That's Not How I Was Taught!

The Matrix System has its detractors, but Parham looks at it in a pragmatic way. "There was a time when many of today's popular openings were considered nothing." One may even ask what makes the Parham Attack any different than the Center Counter (1.e4 d5!? 2.exd5 Qxd5). Of course chess history buffs will note that certain players like Aron Nimzovich brought a hypermodern approach to the games. This meant that you yielded the center to your opponent and relied on flank counterattacks. Openings such as the Benko Gambit and the King's Indian have become the most feared weapons against 1.d4. 

Another hallmark of Matrix players is that they avoid the trading pieces and concentrate on combining the geometry of the pieces so they can begin to calculate permutations (!). More on this later. When asked how he convinces his students to go against known methods taught by coaches and leading players, he simply grins and re-emphasizes the merits of how it helps his students become successful in chess and in life. 

There will always be detractors of the application of the theory, but the theory in itself has merit. Perhaps decades from now, someone will find a better application for the theory… this is usually the way theory works. Who ever thought GM Garry Kasparov would defeat a player of GM Viswanathan Anand's caliber in 25 moves with a revived Evans Gambit!? When asked if he would play 2.Qh5 against Kasparov, Parham immediately replied, "Absolutely!"

The Science of Matrix Chess

Parham was challenged on many points. One point was that since chess is played mostly is perpendicular patterns, the rook should be more powerful than the bishop. He explained that in the Matrix system, the Bishop is just as powerful as the Rook because it can support its Queen in delivering the quickest checkmate possible (QED). This may be true if one follows the Matrix credo of keeping the pieces on the board and attacking swiftly.

The 2.Qh5 idea defies all accepted rules of opening play, but when Parham sat down to play strong Master Boris Men (2571 USCF), the game went 1.e4 d5!? 2.e5 c5 3.Qh5 g6 4.Qh4. Men had earlier seen Parham demolish Jim Spalding in 19 moves (after 1.e4 c5 2.Qh5). Men avoided Parham's preparation, but the game ended in a hard-fought 52-move draw. In fact, Parham states that 3.Qh5 drew a 20-minute think from Men.

As the Queen and other pieces move across the board, the permutation of possibilities increase. Parham has created an interesting way of calculating variations on the board. He reduces this concept into two factors: Attackers and Defenders. Thus, the amount of permutations on any given move is defined by the formula (A!D!=P). For example,  (2!2!=4) means when there are two attackers and two defenders then there are four possible move sequences from which a player can pick to attack. Thus, a position in which there are three attackers and three defenders, there are 36 move sequences (3!3!=36).

Enter the Matrix (Editor's Comments)

While sitting in Denny's restaurant with Mr. Parham on the 6th of July (during the World Open tournament), we had a very interesting conversation about his system. Of course, I asked him a number of questions he had never faced before, but  he was  patient and straightforward with his answers.

I also asked him if there was any connection with his system to the message in the "Matrix" movies and he stated that there is a connection, but that information would be revealed later. One connection I see deals with whether Parham's Matrix system breaks down if the pieces on the 8X8 matrix are changed as in Fischer Random.  In the 1st Matrix movie, when the Matrix was altered (remember the déjà vu cat), the system became flawed.

Besides the Fischer Random questions, I asked whether the Matrix System worked in board sports like shogi, checkers, draughts and go. In between bites, he stated that any situation where you're dealing with a Matrix with a defined set of geometric movements, there will be such an application.  Does that then change the value of the Matrix pieces in Fischer Random since another piece (in a given starting position) may be able to deliver a quicker checkmate?

Over the years, I have seen Bernard Parham employ his system, and it never fails to get a quizzical look from the opponent. I remember playing next to "The Matrix Man" at the 2001 Chicago Open while he beat Vlad Dima. It was interesting to notice Dima's confused expression. On a recent visit to Indianapolis, GM Maurice Ashley was asked his opinion of the Matrix System. Parham told me that GM Ashley expressed outright skepticism, but again… chess is so dynamic that there is room for intellectual discourse about new theories and methods of play.

Parham's own son Bernard II, was a successful scholastic player winning the National K-12 Scholastic Championship in 1994. He has employed the Matrix System ever since he learned to play and recently told me he has never studied chess books. He is also quick to state that he has introduced some additions into the Matrix System.  Thus, the Matrix debate rages on!

Interview conducted: 6 July 2003


Other Sources:

The Chess Drum, "Bernard Parham: Creator of the Matrix System," 2 June 2003.

The Chess Drum, "Indiana Jones meets 'The Matrix'!" 22 April 2002.