saam1 jiu1), this occurs in 13-tile variants when the winning hand consists of one of each one, nine, wind, and dragon, and a 14th tile. Because the hand is so greatly divergent from the standard hand, this hand is generally considered the highest scoring hand of any kind, although it is not the hand that is least likely to occur - the nine gates (1112345678999 in one suit, going out on any other tile in that suit) is said to be some 450 times more rare, barring criteria that are probabilistic in nature. Thus, in scoring systems where a maximum point value is imposed, this is often an automatic limit hand. Scoring table The largest group of criteria concern the contents of the winning hand. Typically, a hand that is more improbable will score higher than one that is more common, but this may not be the case. In variations with scoring minimums, it is generally accepted that, barring improbable high-scoring hands (such as the Heavenly Hand described below, even if the winning hand is otherwise scoreless), at least one point must be from this set of criteria. It is not uncommon for players to define minimum fan requirements for declaring a winning hand (typically 1 or 2), and at times a maximum fan cap or ceiling (for example at 7 or 8 fan). Also note that generally speaking in Hong Kong mahjong, 13 fan is considered the absolute limit for fan. Notes A double wind, where a certain wind is both the winner's seat wind and the prevailing wind, counts as 2 fan. It is possible to obtain the maximum fan (13) from only bonuses. For example, a player draws the second last tile from the wall, declares a Kong and wins on the replacement tile. Depending on variation, there may also be the additional requirement of winning by self-pick, in which case, this is known as men qing zi mo, or purely concealed self-drawn hand. Point translation function The point translation function is, as stated above, typically an exponential function. The function itself is subject to variation, typically to set an upper bound: In the traditional style, there is a four-point maximum: a hand worth more than four points pays exactly the same as one worth exactly as a four-point hand. Thus, a limit hand scores 16 times the value of a scoreless hand. In some styles there