Japanese mahjong scoring rules
Japanese mahjong scoring rules are used for Japanese mahjong, a game for four players common in Japan. The rules were organized in the Taishō to Shōwa periods as the game became popular.
The scoring system uses structural criteria as well as bonuses. Player start scores may be set to any value. Usually, it is set to 20,000 to 30,000 points. Scores are counted using sticks of 10,000 points, 5,000 points, 1,000 points and 100 points. A game often ends when all the points of a player are lost, which is a situation called hakoten, dobon, buttobi, etc. However, some settings allow the game to continue, even if a player's score dropped below zero.
There are two criteria for determining the winning points: han and fu, which correspond to a [|points table]. Han is the unit for the value of yaku, which are particular patterns or conditions of a hand, as well as dora, which are tiles given bonus points for the round or as marked on the tile. Fu is the value of melds, waits and "going out". Hands with enough fu and/or han may be considered limit hands; limit hands use predefined values to determine the winning points.
Steps of calculation
The payment to the winner of a hand is calculated as follows:In the case of a draw, points are transferred according to the nō-ten bappu rule. In the event of a penalty, such as claiming a win with an illegal hand, then points are transferred via the chombo rule.
Counting [|''han'']
The total number of han of all the kinds of yaku in the hand is summed up. Each dora increases the han value of a hand. Dora are not regarded as yaku, and no hand can be won without a yaku even if there are some dora tiles.If there is more than one way to arrange the winning hand, the arrangement with the highest han is used. For example, a hand could be either ryanpeikou or chītoitsu, but since ryanpeikou is three han where chītoitsu is two han, ryanpeikou should prevail. Some yaku have their han value reduced by one if the hand is not closed.
If a hand has five han or more, it is always counted by mangan as a unit and it is not necessary to calculate fu or [|basic points].
Counting [|''fu'']
Fu or minipoints are counted in the order below and then rounded up to the tens. There may be variations of rules for counting it. Three han with 70 fu or more and four han with 40 fu or more yield more than mangan and there is no need to calculate basic points.Winning with yaku which include seven pairs is counted as 25 fu altogether. No more fu can be added and the value is not rounded up to the tens.
Any other winning hand starts with 20 fu, and is then checked for the following bonuses:
- An additional +10 fu is added if the winner had a closed hand and won by claiming a discarded tile.
- Fu is added for each component of the hand. Different melds are worth different amounts of fu points; the sum value of all five components are awarded. The value of each component is listed in this table :
Sequence
+0 fu Open triplet of simples
+2 fu Open triplet of honors or terminals
+4 fu Closed triplet of simples
+4 fu Closed triplet of honors or terminals
+8 fu Open quad of simples
+8 fu Open quad of honors or terminals
+16 fu Closed quad of simples
+16 fu Closed quad of honors or terminals
+32 fu Pair of dragons, the seat wind, or the round wind
+2 fu Any other pair
+0 fu - If the winning tile was either part of the pair, the middle tile of a sequence, or a simple tile in a sequence also containing a terminal, the hand is awarded +2 fu.
- If the winning tile was self-drawn, and the hand does not have the pinfu yaku, +2fu is awarded.
- At this point, if the hand has not accumulated any fu past its starting balance of 20, and it is an open hand, it is awarded +2fu.
- Finally, if the running tally of fu is not a multiple of 10, it is rounded up to the next highest multiple of 10. This is the final result.
Scoring the hand
The method of calculating a winning hand's score from han and fu is somewhat tedious, so it is easier to use a pre-computed lookup table. Expert and professional players have this table memorized and can thus tell the value of a hand at a glance. Each of the table's point values is derived from the scoring equation and procedure with each corresponding han and fu value.The formula itself is fu × 2. This produces the hand's "basic" points. If the dealer wins, they are owed 6 × basic; a non-dealer winner is owed 4 × basic. If it was a win by discard, the player who discarded the winning tile is fully liable. Otherwise, for a self-drawn win, all three other players split the bill. All payments are then rounded up to the nearest hundred. Even if the values of han and fu are the same, the points received for self-draw wins often slightly deviate from those received for discard wins because of rounding.
To use the table, simply look up the values that correspond to the han and fu counts of the hand. The top numbers in each cell indicate the payout from a player who discards a winning tile. The numbers in brackets indicate the payout for each player in the event the winning tile is self-drawn. If the winner is the dealer, each player pays the same amount. If the winner is a non-dealer, then the other two non-dealers pay the smaller number, while the dealer pays the larger number.
''Mangan''
When it is clear that a hand reaches basic points of more than 2,000, it is limited to full basic points of 2,000 and called mangan. A hand of five han or more is always counted as a multiple of mangan. In those cases, there is no need to calculate basic points.One han cannot reach mangan because 110 fu × 2 = 880 < 2,000.
Two han cannot reach mangan because 110 fu × 2 = 1,760 < 2,000.
When a hand has 120 fu or more, it always has some yaku of three han or more.
Example calculations
Example 1: The player on the right of the dealer goes out by self-draw. The winner's hand is closed and has a closed triplet of Souths. The player also has two Whites as the pair and the winning tile is a White. The yaku are "self-pick" and "honor tiles", and they yield a total of two han. The sum of fu is 20 + 8 + 2 + 2 + 2 = 34 fu, rounded up to 40 fu.The basic points are thus 40 × 2 = 640. The dealer pays the winner 640 × 2 = 1,280, rounded up to 1,300 points. The other two non-dealers pay the winner 640, rounded up to 700 points.
Example 2: The same player goes out by the same hand, except this time the winning tile was discarded by the player on the right. The resulting hand has one han of honor tiles. The number of fu is 20 + 10 + 8 + 2 + 2 = 42 fu, rounded up to 50 fu.
The basic point is thus 50 × 2 = 400. The discarder pays the winner 400 × 4 = 1,600 points. The other two players pay the winner nothing.
One ''han'' [|110 ''fu'']
It is possible for a hand to have one han with 102 fu if the rules allow a pair to have four fu when it is made of wind tiles that are both the seat wind and the prevailing wind. Some rules consider that such a pair is still worth two fu, making the hand have exactly 100 fu.An example of a hand that has one han with 110 fu :
The hand has yakuhai of one han with 20 fu of fūtei, 10 fu of menzen-kafu, 32 fu of ankan, 32 fu of ankan, four fu of minkō, and four fu of toitsu. East is both the player's seat wind and the round's prevailing wind in this case. This is the largest amount of fu that a hand with one han can have.
Exhaustive draws
On plenty of occasions, a hand ends with all tiles drawn and the 14 tiles in the dead wall remain. Yet, no player wins the hand. This is the exhaustive draw. In this case, points may be exchanged barring any tenpai hands vs nōten hands. After each exhaustive draw, the counter increases by one.''Tenpai''
Tenpai means one tile short of a winning hand. To be tenpai, a hand does not need any particular yaku partly because winning by the last discard is yaku itself. When a hand is not tenpai, the situation is called nōten.Players must show their hand to verify that it is tenpai when a hand is a draw and if they declared rīchi or if they declare tenpai. If a hand with rīchi declaration is nōten, a chombo penalty is imposed. In some cases, a player who didn't declare rīchi can declare nōten even when the hand is tenpai to keep their hand concealed.
Point exchange
Players receive or pay points called nō-ten bappu in the following way when a hand ends in an exhaustive draw:- one player is in a state of tenpai, the player gets 1,000 points from each of the other three players and receives total of 3,000.
- two players are tenpai, they get 1,500 each and the other two players pay 1,500 each.
- three players are tenpai, they get 1,000 each and the other player pays 3,000.
- the players are all tenpai or all nōten, no payment is made.