# [Retros] Retro-strategy and new AP-type

Rol, Guus G.A.Rol at umcutrecht.nl
Mon Jun 25 13:52:49 EDT 2007

Dear retro-friends,

The solution to the reflexmate problem I posted last week is not
difficult once you get the right AP (a posteriori) idea. Look at the
equivalence with e.p in a formal logical context:

A Posteriori:
1. If "castling right" proves "e.p. right" in all proof games then
"playing e.p". can be justified a posteriori by "castling"
2. If "the right to 0-0" proves "no right to 0-0-0" in all proof games
then "denying the right to play 0-0-0" can be justified a posteriori by
"0-0"

"Denying the right to play 0-0-0" in a reflexmate problem is
demonstrated by refusing to mate through long castling and needs a
posteriori justification as shown in this composition:

Problem:
White: Kd6, Bg7, Sd7, P:b6,c4,f5,g6
Black: Ke8, Ra8, Rh8, Bd8, P:b7,c6,f6,f7.
R#6 (AP = A Posteriori).

Solution:
Note that one of the black castlings is illegal.
1. Sxf6+ Bxf6
2. c5 Rd8+! (black refuses to 0-0-0 and must justify that by playing 0-0
later)
3. Kc7 Rd7+
4. Kc8 (Kb8? Be5+! Kc8 wastes a move) Bxg7
Now white is in zugzwang; black on move would be forced to play Ke7
illegal mate!
5. Pg6xf7+ Rxf7
6. Pf6 0-0 reflexmate!

Black is happy to accomplish his 0-0 justification and white to get his
timely reflexmate. Note that black cannot successfully delay the mate