Aotenjou: Difference between revisions

Latest revision as of 18:51, 10 August 2024

Aotenjou 「青天井」 is a rarely used scoring system where all limits are removed.

Per the scoring equation, han is factored exponentially in the equation:

Basic points = fu × 2^{(2 + han)}

Normally, the point equation has a cap applied at mangan (2000 base points), with higher hands being multiples of mangan.

In aotenjou, this cap is removed - 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.

In addition, yakuman are treated as 13 han yaku, 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.

The points can get very large quickly. 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. For this very reason, the limits of mangan and yakuman are applied in standard rules; the numbers are simply too large for practical use.

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

@@ Line 1: / Line 1: @@
 [[Image:Aotenjou.jpg|thumb|250px|right|Example aotenjou score.]]
-'''Aotenjou''' {{kana|青天井}} is a non-standard [[Scoring|scoring system]], by which all caps and limits are removed.  Per the scoring equation, [[han]] is factored exponentially in the equation:
+'''Aotenjou''' {{kana|青天井}} is a rarely used [[Scoring|scoring system]] where all limits are removed.
+Per the scoring equation, [[han]] is factored exponentially in the equation:
 : '''Basic points = fu × 2<sup>(2 + han)</sup>'''
-Normally, the point equation has a cap applied at [[mangan]], where the basic points is artificially maxed at 2000 points.  Subsequent point values are then multiples of mangan for higher scoring hands.
+Normally, the point equation has a cap applied at [[mangan]] (2000 base points), with higher hands being multiples of mangan.
-With aotenjou, there is essentially no limit.  The basic points have the freedom to be valued as high as possible, as the mangan limit is removed.  Under aotenjou, scoring produces some ridiculously high numbers.  Points are even much higher in conjunction with the multipliers applied for the dealer, non-dealer, and ron vs. tsumo wins.  All yaku retain their original values.  In additionally, [[yakuman]] patterns are defaulted at 13 han and are treated like normal yaku when determining the overall han and fu values.  Furthermore, any han applied by [[dora]] counts as well to further increase the point values.
+In aotenjou, this cap is removed - 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.
-Hence, for this very reason, the scoring limits imposed by both mangan and yakuman are normally used.
+In addition, yakuman are treated as 13 han yaku, 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.
-Under aotenjou rules, yaku that are implied by the completion of another yaku are not counted as additional han for the purposes of scoring. For example, suuankou's 13 han is not combined with sanankou's 2 han because sanankou is a prerequisite for suuankou.
+The points can get very large quickly. 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. For this very reason, the limits of mangan and yakuman are applied in standard rules; the numbers are simply too large for practical use.
 == Extreme scoring examples ==
 * [[Kokushi musou]]
 : {{#mjt:19m19p19s1234567z}}+{{#mjt:1p}}
-: This hand is then scored as 13 han 30 or 40 fu.  By dealer, it is worth 7,864,400 (ron) or 1,966,080 all (tsumo).
+: 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]]
 : {{#mjt:1112233777z}} {{#mjt:4'44z}}  Agari: {{#mjt:2z}} or {{#mjt:3z}}
-: 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]] when applicable.  This hand stands at 31 han and 50 fu via tsumo:
+: 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
@@ Line 28: / Line 30: @@
 ===Upper limit===
-The exponential basic points equation does have an upper limit, imposed by the maximum possible han and fu combination.  This cap only exists due to the maximum capacity with the finite tile count per hand.  Per the [[rule variations]], the rules are applied to produce the maximum hand possible.
+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:
+{{#mjt:5z}} {{#mjt:0110z}} {{#mjt:0330z}} {{#mjt:0660z}} {{#mjt:0770z}}, tsumo agari {{#mjt:5z}} dora {{#mjt:54444z}} uradora {{#mjt:52222z}}
+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:
+** {{#mjt:1z}} closed quad: 32
+** {{#mjt:3z}} closed quad: 32
+** {{#mjt:6z}} closed quad: 32
+** {{#mjt:7z}} closed quad: 32
+** {{#mjt:5z}} 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
+* [[yakuhai|double east]]: 2 han
+* [[yakuhai|dragons]]: 2 han
+* [[shousangen]]: 2 han
+* 40 dora: 40 han
+Total 102 han
+The base points value of this hand would be {{sciencenotation|3.25|33}} and the dealer would receive {{sciencenotation|6.50|33}} points from each player, for a total of {{sciencenotation|1.95|34}} points.
+The highest possible fu count is 170, as in the following example for the south player in the south round:
+:{{#mjt:2z}} {{#mjt:0440z}} {{#mjt:0z99s0z}} {{#mjt:0660z}} {{#mjt:0z11m0z}} Ron: {{#mjt: 2z}}
+* base fu: 20
+* closed ron: 10
+* pair wait: 2
+* composition of hand:
+** {{#mjt:4z}} closed quad: 32
+** {{#mjt:9s}} closed quad: 32
+** {{#mjt:6z}} closed quad: 32
+** {{#mjt:1m}} closed quad: 32
+** {{#mjt:2z}} double wind pair: 4
+Total 164, round up to 170
+==Yakuman/Yaku Compability==
+{{Main|Yaku compatibility}}
-In a hypothetical ruleset with double yakuman, the maximum scoring hand would consist of the following, assuming the player is dealer, it's the East round, and with the yaku of riichi, ippatsu, tsumo, haitei.
+Certain yakuman imply certain yaku, and thus they cannot be scored together:
-{{#mjt:3z}} {{#mjt:0110z}} {{#mjt:0550z}} {{#mjt:0660z}} {{#mjt:0770z}}, tsumo agari {{#mjt:3z}} dora {{#mjt:04444z}} uradora {{#mjt:02222z}}
+*[[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]]
-This hand's fu value would be calculated with:
+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.
-* 32 fu for closed terminal/honor kan * 4 kan = 128 fu
-* 2 fu for pair of terminal/honor = 130 fu
-* 2 fu for tanki wait = 132 fu
-* 2 fu for menzen tsumo = 134 fu, for a total of 140 fu.
-The han value of this hand would be calculated with:
-* 13 han for [[Daisangen]] = 13 han
-* 13 han for [[Tsuuiisou]] = 26 han
-* 13 han for [[Suukantsu]] = 39 han
-* 26 han for [[Suuankou|Suuankou Tanki]] = 65 han
-* 1 han for [[Riichi]] = 66 han
-* 1 han for [[Ippatsu]] = 67 han
-* 1 han for [[Menzenchin_tsumohou|Tsumo]] = 68 han
-* 1 han for [[Haitei_raoyue|Haitei Raoyue]] = 69 han
-* 2 han for [[Yakuhai|Double Ton]] = 71 han
-* 24 han for 24 [[Dora]] = 95 han
-The basic points of this hand would be {{sciencenotation|2.22|31}} and the dealer upon tsumo would receive {{sciencenotation|1.33|32}} points.
 == External links ==