[gszes]

Highly relevant to this discussion what would cause opener to reopen
with 4n vs x? We all have ideas on how to proceed after x but the rather
large range of hands p might have for x could be significantly narrowed by
having a clear definition of what a 4n balance would look like.

IMHO 4n would be a highly distributional and mostly (useful) top trick
free hand that is primarily interested in a sac over 4s with long clubs
and a side 4 card red suit void Axxx xx AKxxxxx. x seems horribly wrong
with this type of hand and letting 4s go by also seems horrifically misplaced
at these colors when a sacrifice could easily be a huge winner. 5c could easily
be a winner no matter what partner has but does it really cause any harm to
show the existence of a 2nd side suit in case p hates clubs??

If the 4n reopen is used in this way by opener pretty much any x opener makes
will have a strong tendency to be "more balanced" in nature even if very short in
spades. Strain is very much more important when bidding to make than when
sacrificing so we should cater our responses to handle one and 2 suited hands
(that will not include clubs because we would simply bid clubs or probably
could have bid clubs earlier) that have a reasonable expectation of making at the
5+ level xx Kxxxx Kxxxxx void vs those that are strictly sacrificial in nature
xxx xxxxxxx xx x.

4n = one suited* weak sign off or 2 suited strong
opener bids
5c if they desire slam and responder bids 5d or 5h to show
the weak 1 suited type hand but with the strongish 2 suited hand responder
will bid
5s as a 1st round cue bid (in case opener looking for 7)
opener will then bid 5n or 6s to ask responder to bid their
longer suit at the appropriate level preferring hearts if even.
5n no cue bid both suits even length
6c no cue bid longer dia than hearts
6d no cue bid longer hearts than dia

5d = one suited decent dia hand
5h = one suited decent heart hand (like the problem hand)

* if one has a 2 suited weak hand xx xxxxx xxxxxx responder will have to pretend
to have a weak 1 suited hand and always try to signoff in 5d running to 5h only
if there is a huge sounding penalty x at the table:)

Using this system responder can pass (the original problem hand) and then bid 5h
to show a one suited "strongish" hand for a pass.

Note this :system is hugely different than one I propose if unfavorable since it is designed
to include sacrifice bidding as a viable alternative.