This chapter is about
your chances to win when you are missing exactly one tile to complete legal
hand. This is defined as “WAIT”. COMPLETE set of tables of combinations and
matching tiles will be provided.

Neglecting __“7
Pairs”__ and __“Knitted”__ ways to complete a hand we are left with
classical “4*Groups + Pair”, or __“4*3+2”__ for short (where
“Group” is 3 tiles for Chow or Pung and 4 tiles for Kong).

Some of 3-Groups may
be already exposed (you CANNOT exposed a Pair!). Some of concealed Groups may
relate to DIFFERENT suits and, hence, have a little space to maneuver. But those
CONCEALED-and-in-one-Suit Groups may be re-shuffled in any expected way to form
new Groups for winning. We will call these available-for-maneuver tiles as
“MANEUVER tiles” later in the text.

We start with
analysis in ONE suit neglecting Honors (only two cases “H+H” and “HH+H”
are available).

All possible cases of
those maneuver tiles were identified and classified. There are 9 possible
combinations (see table):

**Table 1:
Single-Suited Waits Distribution
**

- Columns
represent number of maneuver tiles before and after adding winning tile.
- Rows
represent “Number of Waits”, available for a given maneuver tiles.
- Number
across is number of variants.

Not surprisingly
structure WITHOUT Pair in final hand i.e. 2+1, 5+1, 8+1, 11+1 have very limited
calling power (max 3). On the other hand, others provide up to 9-tile-wait
(famous “Nine Gates” 1112345678999). The explanation is simple: __a Pair
gives flexibility__ -- some tiles may be used either in 3-Groups or in Pair
when adding winning tile (like “444” goes either for Pung or for a Pair + 3^{rd}
tile is used for Chow).

**1+1=2
2+1=3
4+1=5
5+1=6
7+1=8
8+1=9
10+1=11
11+1=12
13+1=14**

__First table__
in each Excel file is showing entire process:

N Tiles Wait Group1
Group2 Group3 Method, where

__N__
= number of waits,

__Tiles__
= tiles in hand

__Wait__
= tiles which legally complete hand

__Group...__
= those pieces which complete hand (Chow, Pung of Pair)

__Method__
= ways how hand is completed, C = Chow, P = Pung, 2 = Pair, Pung are coded prior
to Chows, Pair goes last.

Please, note, that
multiple ways of "breaking" SAME final hand into Groups are considered
as one variant.

__Example__:

66 777 8888 9999
calls for 5, 6 or 7 where after 7 hand could be breaking into:

789*4 + 66, or

678*2 + 789*2 + 99,
or

777 + 888 + 999 + 789
+ 66

For that hand N=3
though number of lines is 5.

__Second table__
simple lists those [unique] variants. In case of last hand there will be one
line featuring:

N=3
Tiles=6677788889999.

On the top of any
cases is “13+1=14” case of “Nine Gates” with 1112345678999 tiles having
9 waits (see __Table 1__). But we can find 8 waits for 2 cases in a column
“10+1=11” which is also a record. What are they?

2223456777 and
3334567888!!

See, the pattern
311113 calls for 8 tiles, all tiles present in hand PLUS 2 on the SIDE. So,
“Nine Gates” pattern 311111113 SHOULD call for 2 more tiles: “0” and
“10” if only those tiles were present in the set! The answer for the
question in the title is __“9G”__ may be called __“11G”__ (if
only!).

P.S. Pattern 313
(like “5556777”) calls for 5 tiles: 3 from the range and 2 from sides.

Click **here**
to see how Single-Suited Waits Analysis works in applications.

The simplest case of
two-suited wait is “XX + YY”, getting Pung + Pair. What peculiarities could
be found here? It’s all about “transformation abilities” for “3X+2”
tiles sets (2, 5, 8 and 11 tiles).

- When
a group of “maneuver tiles” forming COMPLETE “X*Groups + 2” set by
adding wait tile transforms to valid COMPLETE “(X+1)*Groups” set, such
“maneuver tiles” will be defined as
__CHAMELEON__.

So, Two-Suited
waiting hand is simply TWO Chameleons. Waiting tile adds to ONE Chameleon which
hence undergoes conversion, the other Chameleons remains untouched.

In this file 1^{st}
table is complete list of all chameleons, 2^{nd} table lists unique
variants and the 3^{rd} is some kind of summary of Distribution which is
provided below in Table 2:

**Table 2: Chameleon
Waits Distribution
**

We read __Table 2__
in a similar fashion as __Table 1__. As follows, maximum Number of Waits (for
ONE Chameleon) is 3. So, for the waiting hand consisting of 11+2, 8+5 or less
tiles maximum Number of Waits in total is 3+2=5.

B11123456 C34555 à waiting for B1, B4, B7, C2 and C5 (3+2=5 waits).

B34444567888 C77 à waiting for B2, B5, B8 and C7 (3+1=4 waits).

B34555 C55567 à waiting for B2, B5, C5 and C8 (2+2=4 waits).

SS RR à waiting for S or R (note that “Honors” were not included into
Two-Suited Wait Analysis for the same reason as for Single-Suited).

Next logical step to
do is to systemize “patterns” (see “Nine Gates’ paragraph) of maneuver
tiles. Due to 2223444 and, say, 4445666 represent the same animal from the
player’s point of view.