Simpler hand values for zung jung mahjong
Something that always bothered me with Zung Jung is the scoring table, the values are all over the place. Although I understand that Alan Kwan must have calculated all the correct probabilities to reach each value, still the values chosen perhaps could deviate a bit to be more "regular" and overall simpler.
| Pattern | Name | Points |
|---|---|---|
| 1.0 | Trivial Patterns | |
| 1.1 | All Sequences | 1 |
| 1.2 | Concealed Hand | 1 |
| 1.3 | No Terminals | 1 |
| 2.0 | One-Suit Patterns | |
| 2.1.1 | Mixed One-Suit | 8 |
| 2.1.2 | Pure One-Suit | 16 |
| 2.2 | Nine Gates | 100 |
| 3.0 | Honor Tiles | |
| 3.1 | Value Honor | 2 per set |
| 3.2.1 | Small Three Dragons | 8 |
| 3.2.2 | Big Three Dragons | 24 |
| 3.3.1 | Small Three Winds | 6 |
| 3.3.2 | Big Three Winds | 24 |
| 3.3.3 | Small Four Winds | 64 |
| 3.3.4 | Big Four Winds | 80 |
| 3.4 | All Honors | 64 |
| 4.0 | Triplets and Kong | |
| 4.1 | All Triplets | 6 |
| 4.2.1 | Two Concealed Triplets | 1 |
| 4.2.2 | Three Concealed Triplets | 6 |
| 4.2.3 | Four Concealed Triplets | 24 |
| 4.3.1 | One Kong | 1 |
| 4.3.2 | Two Kong | 4 |
| 4.3.3 | Three Kong | 24 |
| 4.3.4 | Four Kong | 100 |
| 5.0 | Identical Sets | |
| 5.1.1 | Two Identical Sequences | 2 |
| 5.1.2 | Two Identical Sequences Twice | 12 |
| 5.1.3 | Three Identical Sequences | 24 |
| 5.1.4 | Four Identical Sequences | 100 |
| 6.0 | Similar Sets | |
| 6.1 | Three Similar Sequences | 8 |
| 6.2.1 | Small Three Similar Triplets | 6 |
| 6.2.2 | Three Similar Triplets | 24 |
| 7.0 | Consecutive Sets | |
| 7.1 | Nine-Tile Straight | 8 |
| 7.2.1 | Three Consecutive Triplets | 20 |
| 7.2.2 | Four Consecutive Triplets | 40 |
| 8.0 | Terminals | |
| 8.1.1 | Mixed Lesser Terminals | 8 |
| 8.1.2 | Pure Lesser Terminals | 10 |
| 8.1.3 | Mixed Greater Terminals | 20 |
| 8.1.4 | Pure Greater Terminals | 80 |
| 9.0 | Incidental Bonuses | |
| 9.1.1 | Final Draw | 2 |
| 9.1.2 | Final Discard | 2 |
| 9.2 | Win on Kong | 2 |
| 9.3 | Robbing a Kong | 2 |
| 9.4.1 | Blessing of Heaven | 32 |
| 9.4.2 | Blessing of Earth | 32 |
| 10.0 | Irregular Hands | |
| 10.1 | Thirteen Terminals | 32 |
| 10.2 | Seven Pairs | 6 |
| 11.0 | Bonus Tiles (optional) | |
| 11.1.1 | Improper Flower/Season | 1 per 2 tiles |
| 11.1.2 | Proper Flower/Season | 1 per tile |
| 11.2.1 | Four Flowers | 2 |
| 11.2.2 | Four Seasons | 2 |
Maximum Limit of a compound hand is now 64 points. With the exception of the 80 and 100 point Listed Limit Hand.
If you use a Minimum Requirement point value, it can now be simply 1 point (or more, up to you).
For Discarder pays for big hands, the threshold is now 5 points. So up to 5 points everybody pays and above that the discarder is responsible to make up the difference. Since the numbers are smaller, payout should be much easier to calculate.
How I came up with those numbers: To arrive at the "new" values I basically divided everything by 5 and then rounded the numbers to the nearest in the following list: **1, 2, [3], 4; 6, 8, 10, 12; 16, 20, 24; 32, 40, [48]; 64, 80 and 100 (~96)**. Now the possible pattern values increases in more predicable steps (+1, +2 after 4, +4 after 12, +8 after 24, +16 after 48). Note that 3 and 48 are not used, and I decided to round 96 to a nice big 100, since this is the max pattern value in the game.
Overall there is very little rounding happening:
- Three Similar Sequences: 7 to 8 (+1)
- Four Concealed Triplets: 25 to 24 (-1)
- Big Three Dragons: 26 to 24 (-2)
PS: If you really, really want, you could now make Seven Pairs be worth 7 points as is traditional in a few styles of Mahjong. It will break the "symmetry", but Seven Pairs is already a break in hand structure anyway...