Unify Bubblegum and Taffy moves. Improve flow of Bubblegum section. [[Issue #1045]]

docs/variant-specific/pink.mdx

@@ -274,7 +274,7 @@ These conventions apply to any variant with a pink (touched by all ranks) suit.
   - In the previous example, we can modify Donald's hand such that he only holds the pink 4 (instead of holding both the pink 4 and the pink 3).
   - In the previous example, Cathy discarded, but in the modified example, Cathy would know that the pink 4 was promised to be playable. And Cathy would not see anyone else having the pink 3, so Cathy would have to respond by playing a pink 3 from her _Finesse Position_.
 
-### The Bubblegum Bluff
+### The Bubblegum Bluff (Standard Form)
 
 - Similar to a _Bubblegum Finesse_, it is also possible to perform a _Bubblegum Bluff_.
 - For example, in a 3-player game:
@@ -291,37 +291,33 @@ These conventions apply to any variant with a pink (touched by all ranks) suit.
 - _Bubblegum Bluffs_ can only be performed on non-pink cards; otherwise, it will look like a _Bubblegum Finesse_.
 - Note that it is impossible to _3 Bluff_ and _Bubblegum Bluff_ at the same time.
 
-### The Bubblegum Bluff, part 2
+### The Bubblegum Bluff (Two-Away-From-Playable Form)
 
-- Note that, as with a standard _Bluff_, the receiver of a _[Bubblegum Bluff](#the-bubblegum-bluff)_ marks their pink card as the lowest-possible logical _Good Touch_ value it could be.
-- However, it is sometimes possible that the lowest-possible _Good Touch_ value is actually _two-away-from-playable_.
+- Normally, _Bubblegum Bluffs_ are always performed by touching _one-way-from-playable_ pink cards.
+- Rarely, it is possible to perform a _Bubblegum Bluff_ on a _two-away-from-playable_ pink card. However, this can only be done in a specific situation where, due to the circumstances of the clue, it would be impossible for the clued card to be _one-way-from-playable_.
 - For example, in a 3-player game:
   - It is the first turn and nothing is played on the stacks.
-  - Alice clues number 2 to Cathy, touching a pink 3 on slot 3. (The pink 3 is currently _two-away-from-playable_.)
+  - Alice clues number 2 to Cathy, touching a pink 3 on slot 3 as a _Play Clue_. (The pink 3 is currently _two-away-from-playable_.)
   - Bob knows that Alice is violating _Pink Promise_.
-  - If he plays slot 1, then Alice will mark it as the matching 2 and will misplay it.
-  - Bob concludes this is a _Bubblegum Finesse_, with pink 1 in slot 2 and pink 2 in slot 1.
+  - If Bob blind-plays his _Finesse Position_ card and it successfully plays, it is guaraunteed to be one of the 1s. If that happened, then Cathy would mark her clued card as the matching 2 and will go on to misplay it.
+  - Thus, Bob concludes this is a _Bubblegum Finesse_, with pink 1 in slot 2 and pink 2 in slot 1.
   - Bob blind-plays his slot 2, but it is a red 1. It is now revealed to Bob that this was a _Bubblegum Bluff_ instead of a _Bubblegum Finesse_.
-  - Cathy knows that if her clued card were really a 2, Bob would have played slot 1. Thus, it cannot be a 2. Furthermore, there are no _Ejections_ that match this situation, so she must be holding a pink 3.
-  - No one is promised the pink 1 or 2, and the team is synchronized on the identity of Cathy's pink 3.
-- _Historical note:_ This was previously named a _Taffy Bluff_.
+  - Cathy knows that if her clued card were really a 2, Bob would have played slot 1. Thus, it cannot be a 2. Furthermore, there are no _Ejections_ that match this situation, so a _Bubblegum_ move must have happened. Normally, a _Bubblegum Bluff_ would be on a _one-away-from-playable_ card, but that would be the pink 2, and due to the circumstances of the clue, it is impossible to be a 2. Thus, it instead must be the _two-away-from-playable_ card, which is the pink 3.
 
 ### The Bubblegum Double Bluff
 
 - Normally, after a _Bubblegum Bluff_, the entire team is synchronized on the identity of the focus of the _Bubblegum_ move.
-- But what if the note the clue receiver would write on their card is still incorrect?
-- The clue-giver must be expecting additional blind-plays to resynchronize the information.
+- But what if the note that the clue receiver would write on their card is still incorrect? In this situation, the clue-giver expects additional blind-plays to resynchronize the information, in the same way that a normal _Double Bluff_ works.
 - For example, in a 4-player game:
   - It is the first turn and nothing is played on the stacks.
   - Alice clues number 3 to Donald, touching a pink 4 on slot 1.
-  - Bob knows that Alice is violating _Pink Promise_. This must mean that he is supposed to play his slot 3 card as pink 1, with pink 2 and 3 promised as playable through his current finesse position.
-  - Bob blind-plays slot 3, and it is a red 1.
-  - From Donald's perspective, he knows that Alice performed a _Bubblegum Bluff_. Donald marks his slot 1 card as a pink 2 (_one-away-from-playable_).
+  - Bob knows that Alice is violating _Pink Promise_. This must mean that he is supposed to play his slot 3 card as pink 1, with pink 2 and 3 promised as playable through his current _Finesse Position_ and _Second Finesse Position_, respectively.
+  - Bob blind-plays slot 3. It is a red 1 and it successfully plays on the stacks.
+  - From Donald's perspective, he knows that Alice performed a _Bubblegum Bluff_. Donald marks his slot 1 card as a pink 2 (i.e. the _one-away-from-playable_ pink card).
   - Next, it is Cathy's turn. Cathy sees that Donald will mark his pink card as a pink 2. However, the card is really a pink 4, so the situation has not yet resolved.
   - Cathy blind-plays her slot 1 card. It is a red 2 and it successfully plays on the stacks.
-  - Donald realizes that if his clued card were a pink 2, then Cathy would not have blind-played. Donald also knows that if the card were a pink 3, Bob would have played slot 1 as a _3 Bluff_. Thus, Donald updates the note on his card to be a pink 4.
-- Note that, in the example, the pink 4 happens to be _three-away-from-playable_. A similar example could be constructed by swapping the clue to be a 4 touching a pink 3 (where Bob plays slot 4), where the pink 3 happens to be _two-away-from-playable_. What matters is that the team is re-synchronized on the identity of the focus of the _Bubblegum_ clue. In both cases, this requires 2 blind-plays.
-- _Historical note:_ This was previously named a _Taffy Double Bluff_.
+  - Donald realizes that if his clued card were a pink 2, then Cathy would not have blind-played. Donald also knows that if the card were a pink 3, Bob would have played slot 1 as a _3 Bluff_. Thus, Donald updates the note on his card to be the next pink card, which is the pink 4.
+- Note that, in the previous example, the pink 4 happens to be _three-away-from-playable_, but that is not relevant for the move to work properly. A _Bubblegum Double Bluff_ can also be performed with a _two-away-from-playable_ card. What matters is that the team is re-synchronized on the identity of the focus of the _Bubblegum_ clue.
 
 ### The Bubblegum Slide