4.1.2 Exact calculation of the hand value                      
                      
                      Instead of calculating manually the value of the hand, the 
tables  are
                      recommended. For completeness, however, the calculation procedure is given here.
                      
                      For hands worth five or more fan, the table for limit hands is used. For hands worth
                      less than five fan, the value is calculated thus:
                      
                      The base value of the hand ( the minipoints rounded up ) are doubled by the number
                      of fan plus 2. This figure is the base figure to be paid by all three opponents in case of
                      self-draw. For East, however, the figure is doubled one more time. East receives double
                      payment, but also pays twice the amount of the base figure in case of an opponent’s selfdraw.
                      
                      Payments are rounded up to the next 100, though never exceeding the value of a
                      mangan.
                      In case of winning on a discard, the discarding player must pay for all opponents,
                      incl. East, i.e. four times the base figure if the winner is not East, and three times the
                      doubled base figure if the winner is East. The payment is rounded up to the next 100,
                      though never exceeding the value of a mangan.
                      
                      In addition to this is the value of counters and riichi bets on the table.
              
              
              
4.1.3 Scoring tables
                      
                      The 
scoring tables are categorized by whether the winner is East or not, and
                      whether the win was on a discard (ron) or on self-draw (tsumo).
                      
                      In the relevant table, use the column that gives the fan value of the hand and the row
                      that gives the minipoint value of the hand.
                      
                      The table East on self-draw (Tsumo) gives the amount that each opponent should pay
                      to East. The table Others on self-draw (Tsumo) gives two numbers; the largest number
                      is the payment from East, the other number is the payment from each of the two other
                      opponents. The tables for winning on a discard (Ron) gives the amount that the discarder
                      should pay to the winner. 
                      
                      The tables for limit hands gives the amount that each opponent
                      should pay to a self-drawn win. In case of winning on a discard, the discarder pays for
                      all, e.g. for a haneman the payment is 18 000 to East or 12 000 otherwise.
                      
                      The value of any counters and riichi bets are added to the value found in the tables.
              
              
              
4.2 Yaku overview
                      
                      Several yaku requires that the hand is concealed. A concealed hand can be won on a
                      discard. If the discarded winning tile finishes a pung, the pung is considered open when
                      scoring the minipoints, but the hand as such is still concealed.
                      The yaku are all cumulative, so several yaku may be combined in the same mahjong
                      hand. E.g. a concealed hand with All Simples and Mixed Triple Chows is worth 4 fan
                      on a self-draw. If the hand is open, it is worth only two fan. No more than thirteen fan
                      can be obtained in this way.
                      
                      Yakuman are not cumulative.