As Sherlock have mentioned, part of the solution is to find which fan or combinations of fan related to the winning tile are applicable from the list:

  • fan #44 Last Tile Draw -- 8 pts.
  • fan #45 Last Tile Claim -- 8 pts.
  • fan #46 Out with Replacement Tile -- 8 pts.
  • fan #47 Robbing The Kong -- 8 pts.
  • fan #56 Fully Concealed Hand -- 4 pts.
  • fan #58 Last Tile -- 4 pts.
  • fan #77 Edge Wait -- 1 pt.
  • fan #78 Closed Wait -- 1 pt.
  • fan #79 Single Wait -- 1 pt.
  • fan #80 Self-Drawn -- 1 pt.

Since 8-points fan are most costly, they should be used in the first place. Which combinations of these fan work? Definitely, #44+#46 (whenever kong may be a part of a structure), what else? Key information can be found in "Green Book", p. 3.7.2.3 saying: "the second way to make mahjong is by discard (to make mahjong with a tile discarded by another, including Robbing the Kong)." This means that #45 and #47 are combinable!

The second part of solution is to determine applicability of fans #58 and #77-79 (waits). The third part is to find best-scored hand within the given structure of a hand. Let's look at hand structures one by one.

"Lesser/Greater Honors and Knitted Tiles"

As for the third part, the maximum hand costs 24 points -- for "Greater Honors" it is always the case, for "Lesser Honors" "Short Straight" provides 12 points. Self-drawn or from discard? For self-drawn we have: #44+#56+#58=8+4+4=16 points. From discard: #45+#47=8+8=16 points again, unfortunately, #58 Last Tile is always implied by #47 Robbing The Kong. Since any hand of hand structure considered has 3-sided wait there are no points for the Wait.

Maximum score is 24+16=40 points.

"Thirteen Orphans"

This hand always costs exactly 88 points. Moreover, both type of waits: for single tile or 13-sided is not recognised by "Green Book". Like in "Lesser/Greater Honors and Knitted Tiles" case no Kongs can be included into hand, hence, both #44+#56+#58 or #45+#47 would yield same 16 points.

Maximum score is 88+16=104 points.

"Semi-Regular"

This hand beside fixed three knitted sequences of "Knitted Straight" allows one set in a form of Chow / Pung / Kong plus a Pair. Best choice is to have "All Types". Which pung cost more? Definitely, "double-Wind" where Wind is both Prevalent and Seat one. So, the plan is: concealed hand with Kong, winning after Kong replacement with Suited tile (although wait into any knitted sequence is not recognized by "Green Book" still "Last Tile" will bring 4 points which is more that 1 point for "Single Wait") being the last tile of the wall.

Concealed --  (as Concealed Kong),  +  (Last Tile).

Maximum score is:

  • Knitted Straight -- 12 pts.
  • Last Tile Draw -- 8 pts.
  • Out with Replacement Tile -- 8 pts.
  • All Types -- 6 pts.
  • Fully Concealed Hand -- 4 pts.
  • Last Tile -- 4 pts.,
  • Prevalent Wind -- 2 pts.
  • Seat Wind -- 2 pts.
  • Concealed Kong -- 2 pts.

Totaling 12+8*2+6+4*2+2*3=48 points.

"Seven Pairs"

For "Seven Pairs" hand an increase of hand value comes mainly from choosing what tiles to use to form winning hand. One should use an appropriate tile group or combination of groups. Maximal hand will have "All Green" as the main group and a bunch of supplementary groups with winning on the last tile of the wall and three "Tile Hogs".

Concealed --  + .

Maximum score is:

  • All Green -- 88 pts.
  • Full Flush -- 24 pts.
  • Seven Pairs -- 24 pts.
  • Last Tile Draw -- 8 pts.
  • Reversible Tiles -- 8 pts.
  • Fully Concealed Hand -- 4 pts.
  • Tile Hog -- 2 pts. * 3
  • All Simples -- 2 pts.

Totalling 88+24*2+8*2+4+2*4=164 points.

 

Prizes generously provided by the publishers of Mahjong Collector Magazine, and by Holiday Mahjong Online.