Japanese mahjong scoring rules
Japanese mahjong features a very complex scoring system. Every mahjong hand has a value in terms of han and fu associated with them. The combination of han and fu then corresponds to values indicated from the scoring table, and/or the two numbers of han and fu factor into an equation, by which the scoring table is derived.
By default, most games start players at 25,000 points, with the goal of scoring at least 30,000 to declare victory for the points leader. Point settings may be flexible to vary both the starting score and the goal score.
Scoring factors
Han
Han 「飜」 is the main portion of scoring, as each yaku is assigned a han number. Some may factor being open or closed; for others, this would not matter. Any dora in the winning hand provides one extra han each. In general, an increase of value by one han roughly doubles the number of points, until the cap of mangan.
Yakuman do not have a han value. If a winning hand satisfies at least one yakuman, han and fu are not counted for the hand. Points are awarded based on the yakuman value; and if multiple yakuman are allowed, then the yakuman values are multipled by the number of yakuman patterns in the hand. Finally, any hand that accumulates 13 or more han is counted for a kazoe yakuman.
Fu
Fu 「符」 (pronounced as foo) takes the hand composition into consideration in terms of tile melds, wait patterns and/or win method. Every hand begins with a default start value of 20 fu. To determine the final number of fu, the sources of fu are added up along with the base number and then rounded up to the nearest 10. Even a fu count of 32 gets rounded up to 40. One exception falls on the chii toitsu yaku, which is fixed to 25 fu by default. While fu may be counted for hands worth 5 han or greater, it may no longer be necessary to count fu for human memorization. Hands of this value become solely dependent on the han count, regardless of the fu count. All-in-all, counting fu is most relevant for hands worth 4 han or less.
Scoring procedure
Calculating basic points
To determine the point value of a hand, the following procedure is used:
- If the hand is a yakuman, then hand scores 8,000 basic points × number of yakuman.
- Otherwise, determine the hand's valid yaku.
- Count the han based on the yaku.
- Count any number of dora to the han count.
- If the han count is 5 or more, then counting fu is no longer necessary. Score the hand according to its han value on the scoring table.
- If the han count is 4 or less, then count fu.
- After determining the number of han and/or fu, refer to the scoring table.
For any who prefer to use the equation, basic points for 5 han or less are computed as
- Basic points = fu × 2(2 + han), using basic points = 2,000 if the former exceeds 2,000
Payment multipliers
After determining the basic points, multiply based on the status as dealer and no-dealer as well as the win by ron or tsumo.
- When a non-dealer wins by tsumo, the player earns 1 × basic points from the other non-dealers, rounded up to a full 100. The dealer in this case pays 2 × basic points, rounded up to a full 100.
- When a non-dealer wins by ron, the discarding player pays the winner 4 × basic points, rounded up.
- When the dealer goes out by tsumo, the dealer scores 2 × basic points from all players, rounded up.
- When the dealer goes out by ron, the dealer earns 6 × basic points from the responsible non-dealer, rounded up.
So finally, a hand's point value is finally expressed as:
- Points = Basic points x Payment multiplier
Scoring table
The points derived from the equation and the payment multipliers are arranged in a scoring table. Players have the option of knowing the point scores by either deriving from the equation or brute force memorization.
Honba
In the event of exhaustive draw, abortive draw, or a dealer win, the honba 「本場」 or tsumibou count increases by 1 for the next hand. This count increase for each time either the dealer wins a hand, exhaustive draw occurs (even after a dealer rotation), or any abortive draw. When any non-dealer wins a hand, then the honba count resets back down to zero.
The current dealer indicates the honba count by using 100-point sticks and placing them on the dealer indicator or on the table. These 100-point sticks are merely counters. If a non-dealer player wins a hand, the honba count resets back to zero. If ryuukyoku occurs where the dealer is not tenpai, then the wind seating rotates and the honba count increases by 1. For any time the wind seating rotates, the 100-point sticks are returned to the dealer; and the next dealer assumes responsibility of tracking the honba count.
This count increases hand values by a total of 300 per honba. For ron, the discarder pays the additional 300 points. For tsumo, everyone pays an additional 100 each. These extra points are added to the hand value after the capping as mangan, haneman, etc., so a non-dealer mangan tsumo with 2 honba costs 2,200 for a non-dealer and 4,200 for the dealer.
A custom rule named basengo 「場千五」 may be used, by which the honba value is five times the normal value. With this rule, instead of 300 points per honba, it is 1500 points per honba. This rule is not commonly used; and instead, it can be found under gambling situations.
In the case of sekinin barai, the yakuman tsumo payment is borne entirely by the discarder of the ponned tile, who also has to pay 300 per honba. On a ron, the yakuman value is split between the discarder of the winning tile and the discarder of the earlier ponned tile. Most rules have the winning tile discarder pay for all honba.
Summary
- Determine Han
- Determine Fu
- Refer to the scoring table, or memorize the corresponding point values
- Factor in honba and riichi bets
End game score
At the end of the game, the raw points are used to calculate the end game score. These are the two or three digit +/- numbers used to reflect a player's score. Instead of 30,000 points, a player's score may actually be displayed as +40.0.
Aotenjou
Aotenjou 「青天井」 is the practice of scoring hands without any limit imposed. This practice is rarely used, because without scoring limits, hands can produce ridiculously high point values. Naturally, that is induced by the exponential function of the basic points equation.
External links
- Japanese mahjong scoring rules in Japanese Wikipedia