Board Game Arena

I think you are wrong springiest since I believe it's a difference between convention's sets.
I will rewrite it nicely:

Played: r1
Bob: b1-x-x-x
Cathy: ?-?-?-?
Donald: x-r3-r1-x
Alice clue 3 to Donald.
Bob plays b1.
What should Cathy do?
What should assume Donald if Cathy doesn't play?
What should assume Donald if Cathy play?

both very easy questions!

if cathy does nothing, donald assumes he has r3 exactly.
if cathy plays (say a g1), donald assumes he has any 3 except r3 or g3.

Why Donald wouldn't assume he has b2-b3-x-x ?
It should look like a self-finesse for blue 1 + 2 + 3, from their point of view. (At least, on BGA.)

b1 doesnt connect to 3 (it only connects to b2), so alice's clue is a bluff rather than a finesse if possible. Cathy's Connecting Principle explains this idea a bit more clearly. for r3 a bluff is possible, for other 3s it is not possible (because no other 3 is a valid bluff target).
this is why, even if donald indeed has `b2 b[3] x x` cathy must STILL blind-play! otherwise donald just assumes he has r3 (which is the only valid bluff target) and does something else.

OK, this is what Romain explained.

You describe the H-group convention, which is not very played on BGA.

All of your examples make much more sense with the H-group convention.

i included that link just to better explain what "connect" means, in case i wasnt doing it clearly enough. it might direct u to a Hgroup document, but that doesnt negate anything i said previously.
i have played a lot of games on various websites (including BGA) where bluffing out an different-colored 1 by clueing "3" to a one-from-playable 3 is allowed. the only thing not allowed on BGA is 3 Bluffs - those are only allowed in Hgroup.
its clear that many people who dont know Hgroup very well have this misconception that clueing "3" to a card to bluff out a 1 (or k5) is a 3 Bluff. that is incorrect - the 3 being clued needs to be two-from-playable for the bluff to be called that! (dont worry, this is a common misconception even for Hgroup players who are just learning 3 Bluffs! )