Aotenjou

Aotenjou 「青天井」 is a rarely used scoring system where all limits are removed, meaning that scoring is entirely exponential.

Rule overview

Han is factored into the scoring equation as follows:

Basic points = fu × 2^{(2 + han)}

In the regular scoring system, this equation is capped at 2000 basic points (mangan), with higher hands being multiples of mangan.

In aotenjou, this mangan cap is removed, meaning that each han will double your score indefinitely. Due to the exponential nature of the scoring system, this can produce astronomically large point values. The modifiers for tsumo, ron, and dealer seat are then applied as normal, increasing the score further. For example, an 8 han 30 fu ron, worth 16,000 normally, is worth 122,880 in aotenjou. A yakuman ron (40 fu) is 32,000 normally and 5,242,880 in aotenjou.

In addition, yakuman are treated as 13 han yaku in aotenjou, so they can stack with regular yaku and dora. As with regular yaku, any yaku that are implied by the completion of a yakuman are not scored. For example, a suuankou hand does not score sanankou or toitoi, because these are prerequisites for suuankou.

Extreme scoring examples

Kokushi musou

+

This hand is scored as 13 han 40 fu (ron) or 14 han 30 fu (tsumo, counting mentsumo). By dealer, it is worth 7,864,400 (ron) or 1,966,080 all (tsumo).

Shousuushii + Tsuuiisou

Agari:

or

With aotenjou, every aspect of this hand is considered, not just the yakuman patterns. This hand also includes the regular yaku of toitoi and sanankou as well as two or three yakuhai, depending on the seat. This hand stands at 31 han and 50 fu via tsumo:

13 han from shousuushii
13 han from tsuuiisou
2 han from sanankou
3 han from the maximum number of yakuhai possible
Basic points: 4.29 × 10¹¹

Any dora to these examples definitely increases the hand even further.

Upper limit

Because a finite-sized hand can only score so many han and fu, there is a maximum score that a single hand can obtain in aotenjou.

In a hypothetical ruleset where double yakuman exist and are scored as 26 han, the maximum scoring hand would be as follows:

, tsumo agari dora uradora

Assume the player is dealer, it's the East round, and has the yaku of riichi, ippatsu, tsumo, haitei.

This hand's fu value would be calculated as:

base fu: 20 fu
pair wait: 2 fu
tsumo: 2 fu
composition of hand:
- closed quad: 32
- closed quad: 32
- closed quad: 32
- closed quad: 32
- yakuhai pair: 2

Total 154 fu, round up to 160

The han value of this hand would be calculated as:

tsuuiisou: 13 han
suukantsu: 13 han
suuankou tanki: 26 han
riichi: 1 han
ippatsu: 1 han
tsumo: 1 han
haitei raoyue: 1 han
double east: 2 han
dragons: 2 han
shousangen: 2 han
40 dora: 40 han

Total 102 han

The base points value of this hand would be 3.25 × 10³³ and the dealer would receive 6.50 × 10³³ points from each player, for a total of 1.95 × 10³⁴ points.

The highest possible fu count is 170, as in the following example for the south player in the south round:

Ron:

base fu: 20
closed ron: 10
pair wait: 2
composition of hand:
- closed quad: 32
- closed quad: 32
- closed quad: 32
- closed quad: 32
- double wind pair: 4

Total 164, round up to 170

Yakuman/Yaku Compability

Main article: Yaku compatibility

Certain yakuman imply certain yaku, and thus they cannot be scored together:

Suuankou: Sanankou, toitoi
Kokushi: Honroutou
Daisangen: The three dragon yakuhai
Tsuuiisou: Honroutou, chanta
Daisuushii: Shousuushii, round wind, seat wind, toitoi
Chinroutou: Honroutou, junchan, chanta, toitoi
Ryuuiisou: Honitsu, If hatsu is forbidden: chinitsu
Chuuren poutou: Chinitsu, honitsu
Tenhou and chiihou: Mentsumo
Suukantsu: Sankantsu, toitoi

These may be subject to further rule variation. For example, if daichiishin (Tsuuiisou + chiitoitsu) is considered an entirely separate yakuman, then regular tsuuiisou cannot score toitoi. The same applies to suuankou + mentsumo if suuankou tanki is its own yakuman.

External links

青天井ルール

青天井 in Japanese Wikipedia