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[[Image:Aotenjou.jpg|thumb|250px|right|Example aotenjou score.]] | [[Image:Aotenjou.jpg|thumb|250px|right|Example aotenjou score.]] | ||
'''Aotenjou''' {{kana|青天井}} is a | '''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>''' | : '''Basic points = fu × 2<sup>(2 + han)</sup>''' | ||
Normally, the point equation has a cap applied at [[mangan]] | 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 == | == Extreme scoring examples == | ||
* [[Kokushi musou]] | * [[Kokushi musou]] | ||
: {{#mjt:19m19p19s1234567z}}+{{#mjt:1p}} | : {{#mjt:19m19p19s1234567z}}+{{#mjt:1p}} | ||
: This hand is | : 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]] | * [[Shousuushii]] + [[Tsuuiisou]] | ||
: {{#mjt:1112233777z}} {{#mjt:4'44z}} Agari: {{#mjt:2z}} or {{#mjt:3z}} | : {{#mjt:1112233777z}} {{#mjt:4'44z}} Agari: {{#mjt:2z}} or {{#mjt:3z}} | ||
Line 26: | Line 30: | ||
===Upper limit=== | ===Upper limit=== | ||
Because a 14-tile 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 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. | 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. | ||
{{#mjt: | {{#mjt:5z}} {{#mjt:0110z}} {{#mjt:0330z}} {{#mjt:0660z}} {{#mjt:0770z}}, tsumo agari {{#mjt:5z}} dora {{#mjt:54444z}} uradora {{#mjt:52222z}} | ||
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}} | |||
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. | |||
The | |||
== External links == | == External links == |
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