This page describes various combinations that you should look for that can lead to a winning Mahjongg hand.
These could be regarded as "primitives" because they are the most fundamental winning combinations possible. They also occur when you have most of your tiles exposed and little left to work with. The advanced arrangements below build on these primitives.
| Completed | Remaining | Need | Chances |
|---|---|---|---|
| 3 combinations, 1 pair | 2 Red Dragons | 1 other Red Dragon | 2 |
| 4 combinations | 1 Red Dragon | 1 other Red Dragon | 3 |
| 3 combinations, 1 pair | 4, 6 Bamboo | 5 Bamboo | 4 |
| 3 combinations, 1 pair | 1, 2 Circles | 3 Circles | 4 |
| 3 combinations, 1 pair | 8, 9 Characters | 7 Characters | 4 |
| 3 combinations | pair of Red Dragons, pair of Green Dragons | 1 more Red Dragon (2), or 1 more Green Dragon (2) | 4 |
These are all awkward arrangements because you are dependant on 1 (maybe 2) specific tile(s) turning up. Note that you get points for all these ways ("One-Shot", "Fishing the Eyes", concealed pung) because they are all difficult to accomplish. You do not want to win like this.
| Completed | Remaining | Need any of | Chances |
|---|---|---|---|
| 3 combinations, 1 pair | 4, 5 Circles | 3 (4), or 6 (4) Circles | 8 |
The "double-ended sequence" doubles (in some cases, more than doubles) your chances of winning over the "awkward" ways above. As an extra benefit, you are not dependant on getting only one specific tile. Note that you do not get any points for completing a double-ended chow, but then again, you do get 20 points for winning...
These are more sophisticated assemblages that build on the "primitives" above. They require that you have more tiles concealed and all of them involve being able to convert a concealed pung into a pair and a chow (if necessary). (Secondarily, these examples demonstrate why a concealed pung is worth more than an exposed pung.) I present them as "formulas" which you can use to help identify these combinations as they occur.
You will also note in all these arrangements how terminals can decrease the chances of winning, a la the one-shot.
Allow me to explain this formula: the 'pair' is, of course, 2 identical tiles; the 'pung' is 3 (different) identical tiles; the expression '[(Chow x N) + 2]' means you have a sequence of 2, 5, or 8 tiles that immediately follow (or immediately precede) the pung.
In all of these examples, I use Red Dragons for the pair, but it could be a pair of anything unrelated to the accompanying pung and sequence. Likewise, I do not specify the suit for the numbered tiles, but it could be any suit, as long as the pung and adjacent sequence are all the same suit.
| Adjacent Sequence of 2 | |||
|---|---|---|---|
| Completed | Remaining | Need any of | Chances |
| 2 combinations | pair RD, 2,2,2,3,4 | RD (2), 2 (1), 5 (4) | 7 |
| 2 combinations | pair RD, 6,7,8,8,8 | RD (2), 8 (1), 5 (4) | 7 |
| 2 combinations | pair RD, 1,1,1,2,3 | RD (2), 1 (1), 4 (4) | 7 |
| 2 combinations | pair RD, 7,8,9,9,9 | RD (2), 9 (1), 6 (4) | 7 |
| 2 combinations | pair RD, 1,2,3,3,3 | RD (2), 3 (1) | 3 |
| 2 combinations | pair RD, 7,7,7,8,9 | RD (2), 7 (1) | 3 |
| Adjacent Sequence of 5 | |||
| Completed | Remaining | Need any of | Chances |
| 1 combination | pair RD, 1,1,1,2,3,4,5,6 | RD (2), 1 (1), 4 (3), 7 (4) | 10 |
| 1 combination | pair RD, 4,5,6,7,8,9,9,9 | RD (2), 9 (1), 6 (3), 3 (4) | 10 |
| 1 combination | pair RD, 2,2,2,3,4,5,6,7 | RD (2), 2 (1), 5 (3), 8 (4) | 10 |
| 1 combination | pair RD, 3,4,5,6,7,8,8,8 | RD (2), 8 (1), 5 (3), 2 (4) | 10 |
| 1 combination | pair RD, 1,2,3,4,5,6,6,6 | RD (2), 6 (1), 3 (3) | 6 |
| 1 combination | pair RD, 4,4,4,5,6,7,8,9 | RD (2), 4 (1), 7 (3) | 6 |
| Adjacent Sequence of 8 | |||
| Completed | Remaining | Need any of | Chances |
| none | pair RD, 1,1,1,2,3,4,5,6,7,8,9 | RD (2), 1 (1), 4 (3), 7 (3) | 9 |
| none | pair RD, 1,2,3,4,5,6,7,8,9,9,9 | RD (2), 9 (1), 6 (3), 3 (3) | 9 |
Explanation: Here you have a pung and a sequence of 1, 4, or 7 tiles that immediately follow (or precede) the pung.
| Adjacent Sequence of 1 | |||
|---|---|---|---|
| Completed | Remaining | Need any of | Chances |
| 3 combinations | 2,2,2,3 | 1 (4), 3 (3), 4 (4) | 11 |
| 3 combinations | 7,8,8,8 | 9 (4), 7 (3), 6 (4) | 11 |
| 3 combinations | 1,1,1,2 | 2 (3), 3 (4) | 7 |
| 3 combinations | 8,9,9,9 | 8 (3), 7 (4) | 7 |
| 3 combinations | 1,2,2,2 | 1 (3), 3 (4) | 7 |
| 3 combinations | 8,8,8,9 | 9 (3), 7 (4) | 7 |
| Adjacent Sequence of 4 | |||
| Completed | Remaining | Need any of | Chances |
| 2 combinations | 2,2,2,3,4,5,6 | 1 (4), 3 (3), 4 (3), 6 (3), 7 (4) | 17 |
| 2 combinations | 4,5,6,7,8,8,8 | 8 (4), 7 (3), 6 (3), 4 (3), 3 (4) | 17 |
| 2 combinations | 1,1,1,2,3,4,5 | 2 (3), 3 (3), 5 (3), 6 (4) | 13 |
| 2 combinations | 5,6,7,8,9,9,9 | 8 (3), 7 (3), 5 (3), 4 (4) | 13 |
| 2 combinations | 5,5,5,6,7,8,9 | 4 (4), 6 (3), 7 (3), 9 (3) | 13 |
| 2 combinations | 1,2,3,4,5,5,5 | 6 (4), 4 (3), 3 (3), 1 (3) | 13 |
| Adjacent Sequence of 7 | |||
| Completed | Remaining | Need any of | Chances |
| 1 combination | 2,2,2,3,4,5,6,7,8,9 | 1 (4), 3 (3), 4 (3), 6 (3), 7 (3), 9 (3) | 19 |
| 1 combination | 1,2,3,4,5,6,7,8,8,8 | 9 (4), 7 (3), 6 (3), 4 (3), 3 (3), 1 (3) | 19 |
| 1 combination | 1,1,1,2,3,4,5,6,7,8 | 2 (3), 3 (3), 5 (3), 6 (3), 8 (3), 9 (4) | 19 |
| 1 combination | 2,3,4,5,6,7,8,9,9,9 | 8 (3), 7 (3), 5 (3), 4 (3), 2 (3), 1 (4) | 19 |
The 2,2,2,3 (or any other such arrangement that contains no terminals) is arguably the best of the advanced arrangements: it is fairly easy to set up, requires very few concealed tiles, and offers exellent winning chances with several different tiles.
This formula is very similar to the previous, with an important difference: you have two concealed pungs and a sequence of 1, 4, or 7 tiles between them. You will notice that having the additional pung at the other end "fills in the holes" of the previous list of needed tiles.
| Middle Sequence of 1 | |||
|---|---|---|---|
| Completed | Remaining | Need any of | Chances |
| 2 combinations | 2,2,2,3,4,4,4 | 1 (4), 2 (1), 3 (3), 4 (1), 5 (4) | 13 |
| 2 combinations | 6,6,6,7,8,8,8 | 9 (4), 8 (1), 7 (3), 6 (1), 5 (4) | 13 |
| 2 combinations | 1,1,1,2,3,3,3 | 1 (1), 2 (3), 3 (1), 4 (4) | 9 |
| 2 combinations | 7,7,7,8,9,9,9 | 9 (1), 8 (3), 7 (1), 6 (4) | 9 |
| Middle Sequence of 4 | |||
| Completed | Remaining | Need any of | Chances |
| 1 combination | 2,2,2,3,4,5,6,7,7,7 | 1 (4), 2 (1), 3 (3), 4 (3), 5 (3), 6 (3), 7 (1), 8 (4) | 22 |
| 1 combination | 3,3,3,4,5,6,7,8,8,8 | 9 (4), 8 (1), 7 (3), 6 (3), 5 (3), 4 (3), 3 (1), 2 (4) | 22 |
| 1 combination | 1,1,1,2,3,4,5,6,6,6 | 1 (1), 2 (3), 3 (3), 4 (3), 5 (3), 6 (1), 7 (4) | 18 |
| 1 combination | 4,4,4,5,6,7,8,9,9,9 | 9 (1), 8 (3), 7 (3), 6 (3), 5 (3), 4 (1), 3 (4) | 18 |
| Middle Sequence of 7 | |||
| Completed | Remaining | Need any of | Chances |
| none | 1,1,1,2,3,4,5,6,7,8,9,9,9 | 1 (1), 2 (3), 3 (3), 4 (3), 5 (3), 6 (3), 7 (3), 8 (3), 9 (1) | 23 |
The last of these illustrates why the "Nine Gates of Heaven" is a limit hand: it is the maximum number of winning combinations you can possibly have, and any tile in the suit will complete a winning hand. It also explains why Nine Gates must be completely concealed: if any sequences are exposed, it does not produce the same winning chances.