The answer to the
question posed in title is the KEY to playing particular hand. In order to win a
player should evaluate chances to finish with particular pattern. (Top 10 wining
patterns you can find here).
And, picking-and-throwing tiles do best to keep alternatives open. At certain
time the decision Where to Go? must be made. Consider, for instance,
having 5 Pairs is worth to
go for All Pungs or Seven Pairs?,
having 2/3 Pairs is it worth
to go for All Pungs or any Chow-based hand?
how many tiles for Knitted
hands is worth to have in order to win?, etc.
First choice is about
to go for Pung-hunt or wait on self-draw. In the second example Chow-based hands
are very flexible though you can pick only from 1 player plus self-draw. The 3rd
strictly suggests self-drawing only until the last tile to pick from anybody.
Underlying idea to go
through is to use cumulative PROBABILITIES to get certain useful tiles (we
will call them MT = Matching Tiles). Extensive calculations
have been carried out in order to get Number-of-Moves to get (at certain
Level-of-Certainty) required tile depending on starting conditions:
Buying Method, Tiles-in-the-Wall and number of Matching Tiles.
Before those results would be provided let clarify ingredients J.
for more on Draws Analysis Ingredients:
Here is table for Matching
Tiles (Excel file for convenience is in filter mode). Please, select
values for the fields:
Method (= Buying
MT (= Matching
to get expected
number of single moves to get required tile. Lets consider typical CHOICE
problems and try to solve them using attached table.
Lets consider 3
Pairs dealt for the start. How easy is to convert that 2221111111 distribution
for All Pungs? The answer depends on how sure we want to be to get it.
First goes Lucky Guy, cumulative probability = 0.5, which means in
equivalent to pick right tile out of two. (Click here
for full example).
Analysis listed above
is only a sample of what MAY happen at the table. Real chances highly depend on:
flexibility of players
portion of luck (Luck
how friendly or not
opponents discards are (Environment Factor).
transformations of several distributions. For simplicity we assume start of the
hand (83 tiles in the Wall) and couple different Luck Factors.
at-the-table when you get next tile toward your hand the following Simplified
Method might be applied.
"Tiles-in-the-Wall" number (for instance, 83 for the start of the
"Tiles-in-the-Wall" onto Matching Tiles" you get number of:
formula is valid ROUGHLY for the "Level-of-Certainty" = 70%
which is slightly lower than "Sure" level and much higher than
"Luck" level. To increases "Level-of-Certainty" simply
multiply estimate by 1.1, 1.2 or 1.3.
9 Knitted for 10-th tile:
MT=28, 83/28=3 TURNS (Method="Draw");
22222111 for a Pair: MT=9,
22222111 for Pung, MT=10,
83/10=8 MOVES ("Full") etc.
It is necessary to
estimate WHEN (meaning how much tiles passed) is good to finish a hand
depending on the hand score. 8 pts. limit for going out increases slightly game
(compared to No Limit rule). Playing level of opponents and their
propensity to compete might give a hint for HOW LONG current hand would be
played. It is crucial to fit within time gap when choosing among the
alternatives. Distribution table of the scores (and Elements) vs. single moves
passed would provide good basis for further analysis.