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Comments by Kenneth Regan

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Tandem-Pawn Chess. Pawns are tandems of two pawns, which can move or capture as a unit, or decouple into two pawns. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]
Kenneth Regan wrote on 2013-01-04 UTC
Thanks for feedback.  To answer George Duke, the main distinction I see from the "modest" and other variants is that mine aims most to lengthen the horizon of planning in the middlegame.  I contributed a comment in the "Future" thread about the influence of the depth of search on the complexity, compared to the branching factor.  

To be sure, I haven't played a game of this to check it out.  Basically I'm doubling down on Philidor's dictum "Pawns are the soul of chess", and figuring that having twice as many souls lessens the influence of soul-less computers :-).

I like "T" for "tandem", though in algebraic one could also capitalize the file of a source square, thus E4 D5 Exd5 Qxd5 for the "tandemized" Scandinavian.  (Note that without the rule that a tandem cannot use just one pawn to take a tandem, ...D5?? would be a blunder.)  For diagrams I would use a pawn printed double with a slight horizontal displacement---for Black you need just the silhouette, while for White you could print one over the other or have one shade the other for some 3D texture.  This should be hackable for existing chess-TeX packages.  

The idea of using checker pieces is also neat, and would work for magnetic sets with button-style pieces.  Another idea is to put a fat ring around the neck of a pawn to make a tandem, though this needs a separate supply of pawns when they decouple.

The Future[Subject Thread] [Add Response]
Kenneth Regan wrote on 2013-01-04 UTC
The horizon of action, also called the depth d, has more influence than the
branching factor b.  The overall complexity is b^d (b raised to the power
of d), which can be re-written as 2^{d*log(b)}.  A doubling of the
branching factor adds only 1 to log(b), and hence adds d to the exponent. 
Whereas, a doubling of d adds d*log(b) to the exponent.  OK, for b as low
as 2 this makes no difference, but for a healthy b like 30 it does.  

Anyway, my intuition for why Go is so much more difficult points to the
long horizon, rather than the up-to-361 branching factor.  Also in Shogi,
storming with pawns and the weaker pieces is much of the strategy, and
takes a long time---especially using paratroops.  That horizon, rather than
the branching of paratroops, explains the greater difficulty for computers,
IMHO.

More simply put, I believe in a common version of Moore's Law for games,
phrased in terms of Laszlo Mero's concept of "depth of a game."  Namely,
say two players are a "class unit" apart if the stronger one takes 75% of
the points in head-to-head play.  Under the Elo system this corresponds to
roughly a 200-point rating difference (was exactly so before a re-basing on
logistic curves).  The depth is the number of class units from "adult
beginner" to world champion.  When I first saw reference to Mero's work
20 years ago, this was reckoned as 11 for chess (600 thru 2800), 14 for
Shogi, and "25-40" (sic!) for Go.  If the CCRL 3200+ ratings for top
programs are accurate, then that corresponds well to computers knocking on
the door of the best Shogi players but being still tangibly behind.  That
is, based on Moore's Law, top programs like Houdini on 8-core hardware are
at "Depth 13".  Use of Monte-Carlo techniques may have computers further
along in Go than this idea would predict, however.

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