Tuesday, May 3, 2011

Chess960: Statistics and insider information on bishops

Ok yesterday I thought it was a pretty good finding to have worked out the deal with knights in Chess960. (Insider information on the Knight Pairs).
But today I really blew my simple little mind on these statistics on the bishop pairs. Check out Naming the Bishop Pairs as well.

Bishops together:
  1. Bishops 0 squares apart = 420 "The Patriarch Bishops"
  2. Bishops 2 squares apart = 300 "The Archbishops"
  3. Bishops 4 squares apart = 180 "The Metropolitan Bishops"
  4. Bishops 6 squares apart = 060 "The Suffragan Bishops"
What this means is that the Patriarch Bishops are getting onto almost half of all Chess960 games! Not only that, but the Patriarch's are evenly distributed throughout the 960 positions. The traditional arrangement of the Archbishops is roughly one third of all games. So with the staggering Patriarch case, it needs to be broken down further:

 The Patriarch Bishops (BB):
  1. Bishops (BB) on AB/GH   = 120 "The Primary Patriarch's"
  2. Bishops (BB) on BC/FG   = 120 "The Middle Patriarch's"
  3. Bishops (BB) on CD/EF   = 120 "The Minor Patriarch's"
  4. Bishops (BB) on DE      = 060 "The Titular Patriarch's"
Why these weird names for the bishop combinations then??? It's quite simple really! Wikipedia defines each of them (Wiki Bishops). If you read the definitions, you will see why I called them what I have. I wanted to combine their Chess960 flavor with the characteristics of their historical Wiki counterparts. Do please excuse me if you find the "male oriented" namings of the Patriarch bishops offensive but I must mention that to be fair, the most powerful piece on the board is a female and so I think the namings balance out :-)

The Pure Forms of the Bishop Pairs
Here are the pure forms, but of some mixing of roles takes place as well:
  • The Patriarch's: "Highest Ranking; Autocratic Authority". In terms of Chess960, these bishop pairs dominate the whole feel of the starting position in nearly half of all Chess960 games. The primary and middle forms of the Patriarch's need actively deployed wing pawn formations to operate that must not allow enemy knights to infiltrate and exchange away half of their dual color dominance. As the patriarch bishops move from primary to middle to minor bishops in the various SP's, they become more likely to split apart and thus more difficult to target.
  • The Primary Patriarch's can work powerfully together to control both colors along only one skewed diagonal trajectory. They are the patriarch's that wield the most autocratic power along the long dual colored diagonals almost instantly and often do not need to move from their seat of power. The primaries have a dual role of active attack but also active defense. They can morph into being staunch protectors of the king by simply transposing a single square inwards becoming important king shields while retaining their long diagonal authority. 
  • The Middle Patriarch's can quickly adopt a similar autocratic authority as the primaries. They can also split apart but are more difficult to justify such splits. Their main weakness is an inability to form a protective shield in creative king defense roles. The sometimes remain seated on their original square, working at a distance like the primaries.
  • The Minor Patriarch's are subtler in how they exercise their authority. They can shift to the long diagonal roles of the primary patriarch's but can also morph into solid king protectors. They have more access to both wings of the chess board and are thus more versatile and ambiguous in operation.
  • The Archbishops: "Importance in history; Also Metropolitan". In terms of Chess960, these clergy are your traditional distance apart as per Chess. They can morph into various diagonal lines of controls and are very flexible and versatile (less so in their shifted forms).
  • The Metropolitans: "In charge of a province". In terms of Chess960, these bishops are far enough apart that they exhibit independent authority over various diagonal combinations but are not as versatile and can be problematic to coordinate within the whole framework of the development phase unless properly thought out. In their shifted forms they morph into complex combinations of the Patriarch's and the Suffragan bishops.
  • The Suffragans: "Subordinate to the Metropolitans; In charge of a specific area". In Chess960, these bishops are the subordinate bishops because they are on the long diagonal and control only one specific long diagonal. In their pure form they never get that control alone on the diagonal because they must face their arch rival on the same line. They struggle to be versatile but can be very powerful if not counter-balanced along their color of influence.
  • The Titulars: "A bishop without a diocese". Yes the amazing Titulars! If you have ever played Chess960 with two BB bishops in the center of the board, you will know immediately what I'm talking about. The two bishops have no defined role to work in. They have to angle about until finally they find out what their purpose is! The ambiguity of deployment is weird but personally I wish there were more SP's with them. Luckily the minor Patriarch bishops have characteristics in common with these philosophical bishops and so there are quite a few SP's with this level of bishop ambiguity.

Ok so here is a bit of insider information then!:
Because of the phenomenon of the Patriarch Bishops in the Chess960 SP's, if you want to win at Chess960, practice how to deploy your Patriarchs over all the other pairings. In approaching fifty percent of all Chess960 games the tactics around them will dominate and you will have the edge!

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