[Retros] "Half proof games"

[Joaquim Crusats]

This is a reprint of a mini article that I've published in the April
2018 *Problemas
*about an idea for extending the PG concept following orthodox rules. Any
*s**u**gg*estion, criti*c or comment is welcome.*

http://sepa64.blogspot.com.es/p/revista-problemas-nueva-epoca.html

*-----------------------*


* HALF PROOF GAMES Joaquim Crusats Problemas, April 2018, n.22, p.617   In
a standard proof game (PG) there is a unique global sequence of moves that
allows to reach the diagram position (DP) in the required number of moves.
Let us define a half proof game (HPG) in the following way: in a HPG both
sides do also cooperate to reach the DP, but the sequence of black moves is
unique if and only if a particular sequence of white moves is played.
[notes 1 and 2] In a HPG there is also only one global sequence of moves
that allows to fulfill the stipulation, otherwise the problem is cooked.
HPGs follow orthodox rules and can be of potential interest compared to
standard PGs as they allow specific motivations for new themes and records.
Examples 1 and 2 illustrate the concept. Problem 1 Joaquim Crusats,
Problemas 2018 1r1k1br1/pp2nppp/2p1p3/3pq1B1/3n4/R2P1b2/1PP1PPPP/QN2KBNR
(15+16) HPG 13.5 (C+ in two parts: moves 1-7 and 8-13.5) HPG problems
require a new approach as White actually needs to be carefully used as a
precision tool to force unique black play. In this problem Black’s moves
are all clear from the beginning, but their relative order is not
unambiguously determined: All possi-ble transpositions and duals have to be
ruled out and, among the thousands of solutions that this diagram has as a
standard PG, only one of them corresponds to the HPG. Solution: 1.Sf3 Sc6
2.Sd4 Rb8! 3.Sb5 Sd4 4.a4 c6 5.a5 Qxa5 6.Ra3 Kd8! 7.S5c3 Qe5 8.d3 d5 9.Sd2
Bg4! 10.Sf3 e6 11.Bg5+ Se7 12.Qa1 Rg8! 13.Sg1! Bf3 14.Sb1! The knights
exchange positions. The knight moves are not motivated by captures, but
rather by the need to block certain strategic squares for a certain period
of moves, and all under a carefully controlled timing and without any
possible transposition of moves. The problem shows how HPGs can provide new
motivations for a well-known PG theme. Problem 2 Joaquim Crusats, Problemas
2018 2r2bnr/pp1kpppp/3p2Q1/q1p5/4P3/3b4/P1PP1PPP/RNB1KBNR (15+15) HPG 8.0
C+ In this case, first of all we have to solve the problem as a usual PG,
and then analyse why the promotion unit is determined. Solution: 1.b4 c5
2.b5 Sc6 3.bxc6 d6 4.c7 Bf5 5.c8=Q! Bd3 6.e4 Rxc8! 7.Qg4 Qa5 8.Qg6 Kd7.
Then we soon realize that 5.c8=Q! is mandatory as only this move makes the
following sequence of black moves unique: with other promotions, Black
might play Qa5 or Kd7 before Rxc8. Notice also that in the solution the wQ
route to g6 must be via g4 and not h5 so as to force the bQ move before
that of the bK: there are no duals in White’s play and the solution is
unique. However, the fact that there is an alternative wQ route via h5 is
essential to rule out a wR promotion on c8, as the existence of this route
would still allow Black to play Kd7 before RxRc8 (note that Black is
cooperating with White, so he would not be able to make the king move if it
prevented reaching the DP owing to an unavoidable check by a wQg4).
Schnoebelen–Q. This HPG problem shows a theme that cannot be accomplished
in a standard PG. Fruitful discussions with Andriy Frolkin and Bernd
Gräfrath during the preparation of this mini-article are gratefully
acknowledged. [Note 1] In a HPG the black side has no choice of play
whatsoever, like in a standard PG. In this sense, this black “half part” of
the problem is indistinguishable from that of a normal PG. However,
although the white side play is also dual-free, this is not dictated by the
DP, but rather by the HPG definition itself and the fact that there must be
a unique solution to the HPG problem that has to be sorted out from the
whole set of dualized solutions that the problem has as a standard PG. This
white “half part” is thus different from that of a normal PG. [Note 2]
Although the related concept that both sides simultaneously only play moves
that make the other side’s play unique in an entangled way is conceivable,
it is too restrictive and unpractical because the whole branched tree of
solutions must be analyzed at every stage, something that can only be done
by a computer. An  HPG, however, is composer and solver-friendly because at
every move one only has to take into account whether or not there is at
least a line of play leading to the DP, as when solving or composing a
standard PG. *
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