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Dual Avoidance Themes

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PostPosted: Thu Oct 16, 2014 12:04 am    Post subject: Dual Avoidance Themes Reply with quote

When there is more than one first (key) move that solves a problem, that problem is said to be cooked and considered worthless. If after a correct, unique, key move there are two or more continuations for white that result in mates, the problem is said to contain duals. These are considered to lessen the value of the problem and hence should be avoided.
Dual avoidance is thus a theme that prevents apparent duals in some specific way. In a way all good problems are dual avoidance problems, but sometimes this aspect is so pronounced, that it merits a named theme. This tutorial presents four such themes:

(1) Fleck theme is probably the most well-known dual avoidance theme. In its most simple form white threatens at least 3 different mates after the key. However black has a counter for each of them, that allows only one of the threats to mate, while avoiding others. This process is called the separation (of threats). See a descriptive example below:

H.Laaksonen,1944 #2

After the key 1.Qe5! white has 3 separate mates 2.Qa5#,2.Qb5# and 2.Qd4#.
However, black defences separate the threats as follows:
1...a3 2.Qa5# (Qb5?,Qd4?)
1...b3 2.Qb5# (Qa5?,Qd4?)
1...Kb4 2.Kd4# (Qa5?,Qb5?)
So only one mate after each defence - no duals. This kind of problem, where more than two mate threats are produced directly from key is called a primary Fleck and the above type a Total primary Fleck specifically as black has only three legal moves and each of them performed separation.

This suggests that there are also partially separated Flecks and something else than primary - possibly secondary ?- Flecks as well. This indeed is the case.

D.Shire, 1980 #2 provides a nice example.

There is a waiting key 1.Bc6! with no threats. After the key king has no moves and any move by Ba6 will fail to 2.Q(x)b5#. It is up to knights to demonstrate the dual avoidance. We divide any knight move to two parts: A departure effect (= removing the piece from its current square) and an arrival effect (= setting the piece on a new square). A secondary Fleck arises from these two events, if the departure effect creates 3 or more mates and the arrival effect separates them - avoiding duals.
If in the Shire problem black removes the Nb4, then mates 2.Nb2#,Ne3# and Qc3# appear, but these get separated with the arrival of Nb4 to a specific square:
1...Nxc2 2.Qc3# (Nb2?,Ne3?)
1...Nxc6 2.Ne3# (Qc3?,Nb2?)
1...Nd5 2.Nb2# (Qc3?,Ne3?)
There is also another equivalent mechanism with the Nf2- knight. Often the departure effect is also called 'random error' and the separation process indicated as below:
1...Nf2 random 2.Nd2#,Ne5#,Qxc5#
1...Nxd1 2.Qxc5# (Nd2?,Ne5?)
1...Ne4 2.Ne5# (Nd2?,Qxc5?)
1...Nfd3 2.Nd2# (Ne5?,Qxc5?)
So, the Shire problem can be labelled as Partial, secondary (2x3) Fleck-theme.

There are also two line themes with special emphasis on dual avoidance:

(2) Java -theme may be simpler of the two. Here one of the black king's field squares (= those squares where bK may step) is taken by two white line pieces from different directions. Black defends against mate and at the same time closes one of these lines. White now has apparently two mating moves, but must carefully select one that does not accidentally close the other of his original control lines. Java variations usually exist in pairs, demonstrating the dual avoidance after black closes each of white's 'java-lines' in turn. Below is a relatively simple example of a Java, composed by a world-class grandmaster of his time:

P.Keres, 1934 2#

After the key 1.Rh4! the bK's field b4 is controlled by both Bf8 and Rh4 and the mate Rb4# is an immediate threat.
with 1...Be5 black blocks the rook's line to b4. Then 2.Nd4#, but not 2.Nc5? blocking the Bf8.
with 1...Ne7 black blocks the bishop from b4. Then 2.Nc5#, but not 2.Nd4? blocking the Rh4.
Hope, this clarifies how the dual is avoided in each of the Java variation.

(3) Herpai -theme is the other line theme promoting dual avoidance. In a Herpai black's defence move against a white threat interferes with two (or more) of his own line pieces allowing apparently more than one mate. However this defence move also contains some beneficial element that eliminates the dualistic mates. Perhaps an example explains this better:

M.Lipton, 1955 2#

The key 1.Qd5! aims for 2.Qd7#. The variations 1...Rc7 2.Rxc7#,1...Rcd6 2.Qb7# and 1...Red6 2.Nxe7# are just non-thematic by-play.
But 1...Nd6 interferes the mutual guard of the rooks. However, only 2.Qxc6# is possible as 2.Qxe6? is not a mate due to line opening of Bg8.(Benefit of the knight move)
Similarly the other Herpai interference 1...Bd6 allows only 2.Qxe6# as 2.Qxe6? allows black to benefit from the bishop move via further 2.Bc7!.

And finally there is still another dual-avoidance theme of self-block nature:

(4) Stocchi -theme or Stocchi Block . This theme concerns of a white man standing on one of the black king's field, where it can be captured by multiple (Theme demands more than 2) black pieces.
If this offending white piece was replaced by a black "dummy", then white would have several dualistic mates.("Dummy"= piece that has only 'mass' ie. can prevent line pieces to move through it, but cannot itself move or threaten anything at all - no 'radiation'). However, when this imaginary dummy is replaced with an actual black piece capturing the white offender, it also separates these dualistic mates so that only one actual mate is possible. Here we have an example:

P.Bekkelund, 1947 2#

After the key 1.Ne4! there is a threat 2.Rb8#, which can be defeated by capturing the offending Nb4 from the black king's field. For a moment think that Nb4 is replaced with a black dummy.
If dummyxNb4, then 2.Rc5#,Nc3#,Bc4#,Nd6# i.e. four mates possible. With actual captures:
1...axb4 2.Rc5#
1...Rxb4 2.Nc3#
1...Bxb4 2.Bc4#
1...Nxb4 2.Nd6#
Only one mate (out of dummy 4) is possible in each case. Study how the others fail!

The tutorial puzzles # 1734 - # 1743 contain Dual Avoidance themes.
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