Rarest Mahjong Hand

[Renita Lukins]

Ialways thought the rarest special hand was the 13 Orphans (1 and 9 of eachsuit, each wind and dragon and one extra tile that makes a pair). Thatperception quickly changed last week when both myself and one of my friendsproduced that hand within a span of about 15 hands!

I think perhaps "heavenly hand" is the rarest in Chinese, Hong Kong, andJapanese. In those forms, the 13 Orphans (Cantonese: "Sup Sam Yiu") isindeed extremely rare, especially when waiting for a 13-way call. Iassume you play Western rules.

13 Orphans is far from being the rarest special hand, because the handrequires only 1 of each tile. In fact, it is one of the more commonones. For example, I have proven that the "Mixed Terminals + 7 pairs"hand (which is not even a limit hand) in Modern Japanese is rarer than13 Orphans. (Please see my homepage for the document. It sheds someinsights as to why "the hand requiring only 1 of each tile" would makeit not so rare.)

When I was much younger I asked my father the exact same question. Hisresponse was a particular hand that I don't think I've ever heardof anywhere else. The literal translation was "Twin Dragons Holding Pearls."

I believe "Twin Dragons Holding" is a Chinese term for two pairs ofidentical sequences. To get the "Pearls" qualifier, the outstandingpair has two be two single dots, and the Twin Dragons have to be theterminal sequences in dots.

I have never spoken to anyone who ever made the Heavenly or the

Earthly Hand. Nor did they know anyone who ever made one of these

hands.

Coming to think of it, this is rather surprising, since *any*

combination will do for this special hand. So any four of pungs and/or

chows, and one closing pair.

How come this hand is yet so extremely rare?Explanation: A Heavenly Hand is when East goes out on the initial deal

Earthly Hand: Depending on what rules you play, South, West or North

make an Earthly Hand either on Easts first discard, or on their first

self-drawn tile, or on any discarded tile in the first round.

Martin Rep

The Independent Internet Mahjong Newspaper

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> Coming to think of it, this is rather surprising, since *any*

> combination will do for this special hand. So any four of pungs and/or

> chows, and one closing pair.

> How come this hand is yet so extremely rare?

I don't know how to compile a logical comparison, but I think this is

reasonable. A hand is delivered at random at start, but a winning hand has

to meet certain set combinations of the pieces. We achieve those set

combinations through several exchanges of pieces during the game play.

(Should the Heaven ever be so frequent, mahjong games could be quite boring

to play with, I guess.)

> Explanation: A Heavenly Hand is when East goes out on the initial deal

> Earthly Hand: Depending on what rules you play, South, West or North

> make an Earthly Hand either on Easts first discard, or on their first

> self-drawn tile, or on any discarded tile in the first round.

> > I have never spoken to anyone who ever made the Heavenly or the

> > Earthly Hand. Nor did they know anyone who ever made one of these

> > hands.

>

> Martin, you probably have forgotten me ;-) I won at least 3 Heaven hands

> ever since I started playing mahjong. I couldn't recall any winning on the

> Earth, though.

The combinatorics of this is a bit nasty, and I don't feel inclined to

work it out (maybe Alan would do it!).

However, I can say that in the few thousand random games

played while testing my xmj program, Heavenly Hand has occurred once.If you don't mind waiting a week or two, I could play a hundred thousand

hands and see what happens!

Our table rules allow the following: flower replacements and kong

replacements do not matter (i.e., if East wins after replacing

flowers, it is still a Heavenly Hand). And our rule for Earthly Hand

is winning before that player makes a discard -- with pungs/kongs and

so on, it is difficult to determine what is a "round".

Personally? No. But I've had the computer make it against me. I don't like it scoring maximum at all, as it's too much of a lucky swing.--

--- John Hwang "JohnHw...@cs.com.no.com"

\--/

A.K.D. F.E.M.C.

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No prize for guessing, but the Big Four Winds/Big Four Blessings winning hand is said to have the lowest probability in a game of mahjong. With a rare 1 in 57,856 chance of happening, this combination must go onto your Instastory!

In some variants of Mahjong, particularly in Asian countries like China and Japan, the dealer may have specific privileges or responsibilities during the game, such as having the first turn to draw a tile from the wall or receiving extra points for winning a hand while in the dealer position.

Otherwise, if everyone is fighting for the same tiles, chances are nobody will throw out any valuable tiles, and the unused tiles will run out. And when the unused tile runs out, the game is considered a draw.

No prize for guessing, but the Big Four Winds/Big Four Blessings winning hand has the lowest probability in a game of mahjong. With a rare 1 in 57,856 chance of happening, this combination definitely needs to go onto your Instastory!

Aiming for this yaku is one of the most basic strategies in Doman mahjong.

If you enter tenpai without calling chi, pon, or kan, you will be given the option to declare riichi. Once you form a winning hand, you will achieve the Riichi yaku.

If a player declares riichi on their first discarded tile, they will be eligible for the Double Riichi yaku.

However, if any player calls chi, pon, or kan on the first turn, this yaku becomes invalid.

A winning hand formed without using any honor tiles or terminals (1 or 9 number tiles).

With kuitan enabled, this can be achieved after calling chi, pon, or kan, which makes it a very easy yaku in this type of match.

Achieved by having the same straight in each suit.

Not only is this yaku compatible with Pinfu, it can also be achieved at the same time as the Tanyao and Outside Hand yaku, so it may be included in several types of high-scoring winning hands.

Formed with three straights of the same suit. Naturally, this is comprised of 1, 2, 3, then 4, 5, 6, and 7, 8, 9.

This is compatible with the Half Flush and Full Flush yaku and some that rely on straights, but since you may often be waiting for several specific tiles at once, you must pay close attention to avoid losing an essential tile.

Made from two sets of Pure Double Chi. Since it is particularly difficult to form, it awards 3 han. Calling chi, pon, or kan invalidates this yaku. If you achieve this yaku, you will not receive additional han from Pure Double Chi.

Another yaku similar to Outside Hand, but all melds are triplets or kan made from terminals or honor tiles.

Calling chi, pon, or kan does not reduce the han awarded, and since it also includes the 2 han from the All Pon yaku, it awards a total of 4 han.

A hand comprised of number tiles from a single suit and honor tiles.

Although calling chi, pon, or kan reduces the han to 2, this yaku can be combined with yaku tiles and the Pure Straight yaku to earn high scores.

Includes only number tiles from a single suit. Being able to quickly identify which tiles are needed to complete the hand after entering tenpai is the mark of an advanced player.

Calling chi, pon, or kan reduces the han earned to 5, which is still very high. Unfortunately, it is easy for your opponents to identify when you are attempting to complete this yaku, which greatly reduces the chances of forming it before they produce a winning hand.

Made from two triplets and a pair of dragon tiles.

Although the yaku itself is only worth 2 han, it includes two triplets of dragon tiles, which are themselves yaku tiles, so a total of 4 han are awarded.

Comprised of three triplets. You may call chi to form a straight or call pon to form a fourth triplet but cannot call pon to complete any of the three concealed triplets. Additionally, calling ron to complete the third concealed triplet invalidates this yaku.

A hand that includes three kan. These can be either concealed or open, and calling chi, pon, or kan does not reduce the han awarded. The kan used add three dora, making it an attractive choice, although this may hand the advantage to your opponents instead.

While most winning hands are comprised of four melds and a pair, there are two yaku that do not follow this format, Seven Pairs being one of them.

As the name suggests, the yaku is made from seven pairs of identical tiles. Although it may not seem to be compatible with other yaku, it can in fact be used in conjunction with a few specific kinds, such as Tanyao, All Terminals and Honors, Half Flush, and Full Flush, often leading to high scores.

It is important to note that in Doman mahjong, four identical tiles do not count as two separate pairs. Each of the seven pairs must be unique.

When a player has called pon, that triplet will be exposed (open) for other players to see. The owner of that triplet can then call kan to add a fourth tile.

However, this tile can be robbed at that moment by calling ron. The player that claims that tile will achieve this yaku.

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