[Retros] request for real definition of PRA

[andrew buchanan]

Dear Retro chums,

I would really appreciate a *definition* of PRA (aka RV, aka "Ceriani
Ethics").

It's all very well to hear "well it sort of works like this in *this*
problem". I get a hint of a whiff what it might be about. But that
gives me little predictive power when it comes to the next PRA problem.
So I thought I would send this email once and then I will know.
Hopefully.

Here is my best guess so far as to what PRA might be.

Suppose we have a position. There are a number of game state variables
(who has the move, which castlings rights are retained, what en
passants might be on). These variables give a set of vectors, e.g. they
might be:

W,C1Y,C2Y,E1N
W,C1Y,C2N,E1N
B,C1N,C2N,E1Y
...

where the first one means there is a proof game which results in the
position, with White to play, both castlings OK, but en passant not
working. Etc.

Now some subset of this set is the twinset. How do we pick them? I
think we define a relation ">" (pronounced "dominates") on the vectors.
We say that u>v if every piece in v has all its powers (and possibly
more) in u. (So in the list above, the first vector dominates the
second.)

The PRA twins are those vectors which are not dominated by any other.
So in the above list it would be the first & third vectors.

Am I right so far?

Note that this definition of PRA is independent of words like
"castling" & "en passant". Hence it can be applied to fairy chess with
state as well.

My questions are:

(1) What about "who has the move"? Is that really just another element
of the vector (although u>v only if the same player has the move)? In
the (very vaguely described) example in the Retro Corner, there is no
consideration of the possibility that Black has the move. But an email
I got tonight from someone else says that "the move" is something which
can vary between PRA twins. I never knew this before. Well, obviously
it can't be so in the Langstaff example. Black can evade mate with e.g.
1...Rf8. Nor was there ever the intention that this should happen in
Langstaff. So what gives?

(2) What are the retro consequences of moving from the overall position
to considering a twin? Are we allowed to assume that the proof game
must be one which results in the dominant vector? [This is in contrast
to what I believe (but I've never seen written down anywhere, that for
the conventional castling & en passant conventions, there are no retro
implications. You are *permitted* or *not* *permitted* to castle or ep
in the forward game, but the game state for that position is not
altered.] Can someone please confirm? 

If it's sometimes one and sometimes the other, then the notation
*needs* to show it. Just as Madrasi Rex Inclusiv & Exclusiv would make
absolutely precise which version of Madrasi we are talking about.

(3) And for castling, are we looking at actual castling rights (or
practical ability in the current position, given blocking pieces and
attacks)? I presume that it is the former. [And I think is in common
with the conventional conventions.]

Why with all these mega math/legal brains in retro, why are the
definitions of the conventions so allusive, vague & murky everywhere?
And in the end, the best hints I've ever got were from a professional
*hillwalker*! (Ronald Turnbull). Do we want to create even greater
barriers to entry to our tiny hobby? Or are there books I should be
reading which contain the truth, and I just haven't read them?

If someone can correct my errors here, then I would be happy to turn it
into a page for the Retro Corner Glossary.

Thanks,
Andrew.