Hi. A little quiz to test your mahjong skills.
Assume that you're playing HK Old Style. It's round 5 in the hand, and all Circles are raw. You draw C5, and this is now your hand:
C-22345566777888
Questions:
1. Are you out? (If yes, skip the rest of the questions.)
2. What tile should you discard?
3. What tiles are you calling after the discard?
"Live life with Heart."
Alan Kwan / tarot@notme.netvigator.com
http://home.netvigator.com/~tarot
(hard-core game reviews) (remove anti-spam section "notme." from mailing
address)
On Tue, 19 May 1998 01:49:55 GMT, tarot@notme.netvigator.com (Alan Kwan) wrote:
>Hi. A little quiz to test your mahjong skills.
>
>Assume that you're playing HK Old Style. It's round 5 in the hand,
>and all Circles are raw. You draw C5, and this is now your hand:
>
>C-22345566777888
>
>Questions:
>
>1. Are you out? (If yes, skip the rest of the questions.)
>
>2. What tile should you discard?
>
>3. What tiles are you calling after the discard?
>
>"Live life with Heart."
>Alan Kwan / tarot@notme.netvigator.com
>http://home.netvigator.com/~tarot
(hard-core game reviews)
>(remove anti-spam section "notme." from mailing address)
Hé, there's a nice quiz!
I should say:
1. No
2. discard 3
3. wait for 2, 4 or 7
what did I win???
| The world of Mahjong:
| http://surf.to/mahjong
On Tue, 19 May 1998 04:46:29 GMT, mrep@xs4all.nlNOSPAM (Martin Rep) wrote:
>H‚, there's a nice quiz!
>I should say:
>1. No
>2. discard 3
>3. wait for 2, 4 or 7
Hi. The lastest modification to the question removed the dependency of the best anwser on the payoff of "Four Concealed Triplets" relative to "Pure One-Suit". But even if 4CT pays twice or even 4 times that of P1S, I think one should not discard C3 in this situation.
"Live life with Heart."
Alan Kwan / tarot@notme.netvigator.com
http://home.netvigator.com/~tarot
(hard-core game reviews) (remove anti-spam section "notme." from mailing
address)
I need to add something.
On Tue, 19 May 1998 01:49:55 GMT, tarot@notme.netvigator.com (Alan Kwan) wrote:
>Hi. A little quiz to test your mahjong skills.
>
>Assume that you're playing HK Old Style.
Also assume that the limit is two laak, and Pure One-Suit is two laak.
> It's round 5 in the hand,
>and all Circles are raw. You draw C5, and this is now your hand:
>C-22345566777888
>
>Questions:
>
>1. Are you out? (If yes, skip the rest of the questions.)
>
>2. What tile should you discard?
... so as to maximize your chance of going out?
>3. What tiles are you calling after the discard?
"Live life with Heart."
Alan Kwan / tarot@notme.netvigator.com
http://home.netvigator.com/~tarot
(hard-core game reviews) (remove anti-spam section "notme." from mailing
address)
>From: tarot@notme.netvigator.com (Alan Kwan)
>>Assume that you're playing HK Old Style.
>
>Also assume that the limit is two laak, and Pure One-Suit is
>two laak.
>
>> It's round 5 in the hand,
>>and all Circles are raw. You draw C5, and this is now your hand:
>
>>C-22345566777888
>>
>>Questions:
>>
>>1. Are you out? (If yes, skip the rest of the questions.)
>>
>>2. What tile should you discard?
>
>... so as to maximize your chance of going out?
>
>>3. What tiles are you calling after the discard?
If I discard 2, I need a 1, 4, or 7 ("three chances"). The 1s are "raw" (there are four, and people tend to discard terms), and there are two 4s out there but only one 7. 7 tiles I might draw or take.
If I discard 3, as Martin says, I need a 2, 4, or 7 ("three chances"). There are two 2s, three 4s, but only one 7 out there. 8 possible tiles I might draw or take. Alan has already said that this is not the answer, though.
Discarding 4 puts me farther from going Out (not only needing one more tile to go Out). Would also need to discard the 3 and then I need two from the following: 2, 5, 6 for All-Pong hand.
If I discard 5, I need a 2, 6, or 9. There are two 2s, two 6s, and four 9s (they're raw and people tend to discard terms). 8 possible tiles. So I think I'd go with this one (if I understand what Alan's getting at, which I may not) or the "1, 4, 7" one (discarding a two).
If I discard 6, I need a 2, 4, or 7. There are two 2s, three 4s, and only one 7 out there. 6 tiles.
If I discard 7, I need a 2, 5, or 8. There are two 2s, two 5s, and only one 8 out there. 5 tiles.
If I discard 8, I need a 6 or 9. There are two 6s, and four 9s. 6 tiles.
SO...
1. No (or is this some kinda trick question). 2. Discarding a 5 gives you a SLIGHTLY better chance than discarding a 2 (8 possible tiles, and one of them is a "raw" terminal). 3. You're calling 2, 6, or 9.
Tom Sloper, Activision
Senior Producer, Shanghai
tsloper@activision.com
Actsearch@aol.com
Now available: SHANGHAI: DYNASTY -- check our website for a preview and free demo:
http://www4.activision.com/games/dynasty/
>From: tarot@notme.netvigator.com (Alan Kwan)
>Assume that you're playing HK Old Style. It's round 5 in the hand,
*** So we're in "overtime" after the North round, eh? Sudden death?
>and all Circles are raw.
*** What does "raw" mean?
> You draw C5, and this is now your hand:
>
>C-22345566777888
>
>Questions:
>
>1. Are you out? (If yes, skip the rest of the questions.)
>2. What tile should you discard?
>3. What tiles are you calling after the discard?
1. No.
2. 8.
3. 9 or 6 for Pin Huu.
Tom Sloper, Activision
Senior Producer, Shanghai
tsloper@activision.com
Actsearch@aol.com
Now available: SHANGHAI: DYNASTY -- check our website for a preview and free demo:
http://www4.activision.com/games/dynasty/
On 19 May 1998 07:17:10 GMT, actsearch@aol.com (ACTSEARCH) wrote:
>>From: tarot@notme.netvigator.com
(Alan Kwan)
>
>>Assume that you're playing HK Old Style. It's round 5 in the hand,
>
>*** So we're in "overtime" after the North round, eh? Sudden death?
Oops. Not that "round" I meant; this 'round' means everybody has taken about 5 turns in this hand. About 20 tiles have been discarded.
>>and all Circles are raw.
>
>*** What does "raw" mean?
No circles in the discard pool.
>> You draw C5, and this is now your hand:
>>
>>C-22345566777888
>>
>>Questions:
>>
>>1. Are you out? (If yes, skip the rest of the questions.)
>>2. What tile should you discard?
>>3. What tiles are you calling after the discard?
>
>1. No.
>2. 8.
>3. 9 or 6 for Pin Huu.
I think I made a bad omission when stating the question. This is supposed to be a question on multi-way call. The exercise is to try to get the best call shape with the best chances of going out, without regard to the value of the hand. So, let's start working it out all over again.
"Live life with Heart."
Alan Kwan / tarot@notme.netvigator.com
http://home.netvigator.com/~tarot
(hard-core game reviews) (remove anti-spam section "notme." from mailing
address)
In article <3560e392.40301@news.netvigator.com,
tarot@notme.netvigator.com (Alan Kwan)
wrote:
>
> Hi. A little quiz to test your mahjong skills.
>
> Assume that you're playing HK Old Style. It's round 5 in the hand,
> and all Circles are raw. You draw C5, and this is now your hand:
>
> C-22345566777888
>
> Questions:
>
> 1. Are you out? (If yes, skip the rest of the questions.)
>
> 2. What tile should you discard?
>
> 3. What tiles are you calling after the discard?
Hi,
My answers are:
1. No.
2. What tiles should I discard:
The safer the better and I would discard 8. If Circles are "raw", that means
most likely every players has kept quite some Circles and would try to get more. Since I
have three 7's and three 8's, 8 might be the one with fewer chances that other player
could make use of it.
3. I will then be calling for 6 and 9 and would have better chances to win on 9.
COFA TSUI
cofatsui@aicom.com
5/19/1998
-----== Posted via Deja News, The Leader in Internet Discussion ==-----
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On Tue, 19 May 1998 16:54:44 GMT, cofatsui@my-dejanews.com wrote:
>In article <3560e392.40301@news.netvigator.com,
> tarot@notme.netvigator.com (Alan
Kwan) wrote:
>>
>> C-22345566777888
>>
>2. What tiles should I discard:
>The safer the better and I would discard 8. If Circles are "raw", that means
>most likely every players has kept quite some Circles and would try to get
>more.
Should one be considering 'safety' in round 5 when he is calling with as big a hand as Pure One-Suit? The other players may have some grouped circles (think about C-135 or C-344); they are likely to unsuspectingly discard the extras as they complete their sets. Therefore, one should be maximizing the number of tiles he can go out on.
Even if everybody is holding their circles (which is unlikely), if I have an excellent call I have a good chance of going out on self-draw.
"Live life with Heart."
Alan Kwan / tarot@notme.netvigator.com
http://home.netvigator.com/~tarot
(hard-core game reviews) (remove anti-spam section "notme." from mailing
address)
tarot@notme.netvigator.com (Alan Kwan)
wrote:
>
> Hi. A little quiz to test your mahjong skills.
>
> Assume that you're playing HK Old Style. It's round 5 in the hand,
> and all Circles are raw. You draw C5, and this is now your hand:
>
> C-22345566777888
>
> Questions:
>
> 1. Are you out? (If yes, skip the rest of the questions.)
>
> 2. What tile should you discard?
>
> 3. What tiles are you calling after the discard?
1. No. (Damn!) The two 2s can only be the pair, which forces 3 to part of a 345 meld, which forces 5 to be part of a 567 meld, which leaves 677888 as two melds. Nope.
2. I would discard 2 in a real game. My gut instinct tells me that this probably leaves a win open for many tiles away from the 2, so others are more likely to discard them. (Gut instinct says that you that you should never leave an AABC... situation, but an ABC... or a AAABC... situation is fine.) In a practice game, I would have the leisure to actually stop and think for a longer time, so let's see:
Discarding 2:
2345566777888
= 234 + 556677 + 7888 Wins on: 6, 7, 9
= 234 + 55 + 66 + 777888 Wins on: 5, (6) = 23456 + 456 + 777888 Wins on: 1, 4, (7) =
(total) wins on 8 ends, 8 centrals
Discarding 3:
22 45566777888
= 22 + 456 + 56777 + 888 Wins on: 2, 4, 7 = (total) wins on 6 centrals
Discarding 4:
223 5566777888
no winning tiles (223 is stuck)
Discarding 5:
2234566777888
= 22 + 345 + 667788 + 78 Wins on: 6, 9
= 22 + 345 + 66 + 777888 Wins on: 2, (6) = (total) wins on 4 ends, 4 centrals
Discarding 6:
2234556777888
= 22 + 345 + 56777 + 888 Wins on: 2, 4, 7 = (total) wins on 6 centrals
Discarding 7:
2234556677888
= 22 + 34567 + 567 + 888 Wins on: 2, 5, 8 = (total) wins on 5 centrals
Discarding 8:
2234556677788
= 22 + 345 + 567 + 678 + 78 Wins on: 6, 9 = (total) wins on 4 ends, 2 centrals
--
Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
Smoking cigarettes are bad for you, so smoking cigarettes is bad for you.
On Tue, 19 May 1998 07:09:50 GMT, tarot@notme.netvigator.com (Alan Kwan) wrote:
>>Hi. A little quiz to test your mahjong skills.
>>
>>Assume that you're playing HK Old Style.
>
>Also assume that the limit is two laak, and Pure One-Suit is
>two laak.
>
>> It's round 5 in the hand,
>>and all Circles are raw. You draw C5, and this is now your hand:
>
>>
>>C-22345566777888
>>
>>Questions:
>>
>>1. Are you out? (If yes, skip the rest of the questions.)
>>
>>2. What tile should you discard?
>
>... so as to maximize your chance of going out?
>
>>3. What tiles are you calling after the discard?
Solution to the quiz below. [Warning: spoiler!]
40
35
30
25
20
15
10
5
0
This is basically an exercise on multi-way call. According to HK Mah-jong Doctor Mr. KAN
Yi-Ching (e.i.s.), apparently some even long-time players of Old Style have not grasped
this skill. When such player luckily runs into a largely concealed Pure One-Suit hand, he
panics and ponders long, giving the opponents hints to the contents of his hand. He may
discard the wrong tile so that his calling shape is largely reduced, or he may not realize
all the tiles he is calling, and miss a discard which he should have gone out on.
The correct discard is C2, leaving this hand:
C-2345566777888
which is a 6-way call for C-145679, or 16 outstanding tiles. Considering the potency of this calling shape, there should not be a strong enough reason to discard otherwise.
Grouping 234 and 888 leaves 5566777, which is a common 4-way call for 4567 (which a skilled mah-jong player should know by heart). By extension via 234, you're also calling for 1. Grouping 234 and 556677 leaves 7888, which is a common 3-way call for 679. Putting these together gives a 6-way call for 145679.
"Live life with Heart."
Alan Kwan / tarot@notme.netvigator.com
http://home.netvigator.com/~tarot
(hard-core game reviews) (remove anti-spam section "notme." from mailing
address)
>From: tarot@notme.netvigator.com (Alan Kwan)
>The correct discard is C2, leaving this hand:
>
>C-2345566777888
>
>which is a 6-way call for C-145679, or 16 outstanding tiles.
>Considering the potency of this calling shape, there should not be a
>strong enough reason to discard otherwise.
>
>Grouping 234 and 888 leaves 5566777, which is a common 4-way call for
>4567 (which a skilled mah-jong player should know by heart).
Dang! Guess I'd better learn this then! Maybe I can use it tonight... (^_~)
Tom Sloper, Activision
Senior Producer, Shanghai
tsloper@activision.com
Actsearch@aol.com
Now available: SHANGHAI: DYNASTY -- check our website for a preview and free demo:
http://www4.activision.com/games/dynasty/
Alan Kwan wrote:
> Grouping 234 and 888 leaves 5566777, which is a common 4-way call for
> 4567 (which a skilled mah-jong player should know by heart). By
> extension via 234, you're also calling for 1. Grouping 234 and 556677
> leaves 7888, which is a common 3-way call for 679. Putting these
> together gives a 6-way call for 145679.
Where do you find this kind of information that every mah-jongg player should know?
On Tue, 19 May 1998 20:26:34 GMT, "Perhaps a Princess..." <sarah@eskimo.com>wrote:
>Alan Kwan wrote:
>
>> Grouping 234 and 888 leaves 5566777, which is a common 4-way call for
>> 4567 (which a skilled mah-jong player should know by heart). By
>> extension via 234, you're also calling for 1. Grouping 234 and 556677
>> leaves 7888, which is a common 3-way call for 679. Putting these
>> together gives a 6-way call for 145679.
>
>Where do you find this kind of information that every mah-jongg player
>should know?
Here.
tiles in hand call for
2223 134
2224 34
2223344 2345
2223334 2345
2223444 12345
2223456 14736
22234 RR 25 R
I think every skilled mah-jong player should know these by heart. More complex call shapes are mostly extensions of these.
"Live life with Heart."
Alan Kwan / tarot@notme.netvigator.com
http://home.netvigator.com/~tarot
(hard-core game reviews) (remove anti-spam section "notme." from mailing
address)
>From: tarot@notme.netvigator.com (Alan Kwan)
>tiles in hand call for
>
>2223 134
>2224 34
>2223344 2345
>2223334 2345
>2223444 12345
>2223456 14736
>22234 RR 25 R
>
>I think every skilled mah-jong player should know these by heart.
>More complex call shapes are mostly extensions of these.
Alan,
I'm printing this out several times and putting copies in all my Mah-Jongg sets -- and
I'll keep one beside me whenever I play until I learn them REAL GOOD!!! Thanks my friend!
Tom
On 20 May 1998 18:17:59 GMT, actsearch@aol.com (ACTSEARCH) wrote:
>>I think every skilled mah-jong player should know these by heart.
>>More complex call shapes are mostly extensions of these.
>
>
>Alan,
>I'm printing this out several times and putting copies in all my Mah-Jongg sets
>-- and I'll keep one beside me whenever I play until I learn them REAL GOOD! !!
You are welcome. I think these are really worth memorizing, especially the 7-tile ones. It speeds up your play a lot. If you have to figure those out during play, you'll slow down so much that everyone at the table knows that you've got 'something'.
"Live life with Heart."
Alan Kwan / tarot@notme.netvigator.com
http://home.netvigator.com/~tarot
(hard-core game reviews) (remove anti-spam section "notme." from mailing
address)
Alan wrote:
I think these are really worth memorizing, especially the 7-tile ones. It speeds up your
play a lot. If you have to figure those out during play, you'll slow down so much that
everyone at the table knows that you've got 'something'.
*** Which is exactly what happens to me all the time!!! Memorizing these patterns would definitely give a player an edge!
Tom Sloper, Activision
Senior Producer, Shanghai
tsloper@activision.com
Actsearch@aol.com
Now available: SHANGHAI: DYNASTY -- check our website for a preview and free demo:
http://www4.activision.com/games/dynasty/
actsearch@aol.com (ACTSEARCH) writes:
>>From: tarot@notme.netvigator.com
(Alan Kwan)
>>tiles in hand call for
>>
>>2223 134
>>2224 34
>>2223344 2345
>>2223334 2345
>>2223444 12345
>>2223456 14736
>>22234 RR 25 R
>>
>>I think every skilled mah-jong player should know these by heart.
>>More complex call shapes are mostly extensions of these.
>Alan,
>I'm printing this out several times and putting copies in all my Mah-Jongg sets
>-- and I'll keep one beside me whenever I play until I learn them REAL GOOD! !!
>Thanks my friend!
In that case, you may be interested in this comprehensive analysis of winning tiles. I'm copying this out of a book; please use a fixed-width typeface for viewing.
Notation:
We denote each tile by the number of times the number appears. For instance, C-222 is
denoted as "3", as is C-555. C-22344 is denoted as "212", while
C-33566 is "2012".
If there is no requirement for the groupings to be in the same suit, we separate them by the symbol "*". For instance, "2*12" might mean C-22788, or D-33 C-344, or even B-56666.
We place a period on top of the calling numbers.
[x,y] means that there are x winning numbers for y tiles.
For this analysis, the matter of end tiles is ignored; the actual player can figure out how to change the calculations as necessary.
Now, there are four basic ways to be calling: (1) Danki or atama, completing the pair. (2) Penchan or ryoumen, Completing a sequence by extending a sequence of two. (3) Kanchan, completing a sequence by the middle tile. (4) Shanpon, completing a triple. Note that you will always be waiting with "two pairs" if you are calling in this fashion.
Using our notation, these four basic calling methods are written this way: .
(1) 1 [1,3]
. .
(2) 2 * 11 [2,8]
.
(3) 2 * 101 [1,4]
. .
(4) 2 * 2 [2,4]
Note that although the pair is irrelevant in cases (2) and (3), we write it anyway -- we always have 1, 4, or 7 "unmelded" tiles when calling.
Now, the more complicated calling schemes result when three-tile melds get added to these basic methods, and create more callable tiles. A three-tile meld is of the form "3" or "111", and adds callable tiles. Essentially, they take the form "If X is a callable tile, then by adding the meld, Y becomes a callable tile." These are very important to remember. They are:
,.,
(u) 3 [only for type (4)]
.,,.
(v) 3 [only for type (4)]
, .
(w) 111 [for all types]
. ,
(x) 111 [only for type (1)]
. ,.
(y) 3 [only for type (1)]
.,
(z) 3 [only for type (1)]
If any of these are extended on longer chains of the form . . . .
111111111111 etc,
then they will also add further spaces at intervals of three.
For instance,
. . .
1111111 [3,9]
when added to
. ,.
3
becomes
. .. .. ..
31111111 [7,23]
a formidable configuration indeed (although practically the number is decreased because
there are only nine values in each suit).
[This might need some further explanation. Here's an example of what (x) means:
Suppose you are calling C-4, and you have a C-456 meld (not accounted for in the call).
Then you are also calling C-7. (y) can mean:
Suppose you are calling C-4 by forming the pair, and you have a C-333 meld. Then you are
also calling C-2 and C-5. In the last example, if you had C-3456789 you are waiting for
C-3, C-6, and C-9. But if you also have C-222, then your C-2223456789 is waiting for C-1,
C-3, C-4, C-6, C-7, C-9, and a theoretical C-10 if it existed.
]
Using combinations, we can create some of the possible tile formations for four tiles
in one suit. These are ordered by "most likely to go out":
. ..
(a) 31 [3,11] {(1)+(y)}
..
(b) 301 [2,7] {(1)+(z),(3)}
. .
(c) 211 [2,6] {(1)+(w),(2)}
. .
(d) 1111 [2,6] {(1)+(x)}
..
(e) 22 [2,4] {(4)}
. .
(f) 202 [2,4] {(4)}
.
(g) 121 [1,2] {(3)}
These are the most common ones. There are also formations like "2002", "2101" and "2011" which are trivial extensions and therefore not listed.
Here are the tile formations in one suit with seven tiles, ordered first by different types of tiles called, then by total number of tiles called. This covers all ways that can result in three or more calls. This listing is credited to a person named KUSAGA Sanrou, although a good player already knows them by heart or can figure them out quickly:
. .. ..
(A) 31111 [5,17] {(d)+(y),(a)+(w)]
(B) 313 [5,13] {(a)+(y)}
.. . .
(C) 13111 [4,14] {(a)+(w)}
.. ..
(D) 1411 [4,13] {(a)+(x),(d)+(y)}
.. ..
(E) 241 [4,13] {(a)+(w),(c)+(y)]
. .. .
(F) 3211 [4,13] {(a)+(w),(c)+(y)]
....
(G) 331 [4,9] {(b)+(y),(a)+(z)]
....
(H) 322 [4,9] {(e)+(v)} -- important
...
(I) 30103 [3,11] {(b)+(z)}
.. .
(J) 301111 [3,10] {(b)+(x),(d)+(z)}
.. .
(K) 30211 [3,10] {(b)+(w),(c)+(z)}
. ..
(L) 412 [3,9] {(c)+(z),(b)+(x)}
.. .
(M) 3121 [3,9] {(b)+(w),(g)+(y)[note the extension!]}
. . .
(N) 1111111 [3,9] {(d)+(x)}
. . .
(O) 112111 [3,9] {(d)+(w),(c)+(x)}
. . .
(P) 211111 [3,9] {(c)+(w)}
. . .
(Q) 11311 [3,9] {(c)+(w)}
.. .
(R) 2311 [3,7] {(e)+(w)}
...
(S) 232 [3,5] {(f)+(u)}
For ten tiles, the extensions are straightforward. It turns out that there are:
1 configuration that has 8 callable tiles, 7 configurations that have 6 callable tiles, 26
configurations that have 5 callable tiles, 35 configurations that have 4 callable tiles,
54 configurations that have 3 callable tiles.
They will not be listed here for brevity :-), but the beginning of the chart is as follows:
311113 [8,22]
. .. .. .
3111211 [6,19]
. .. .. ..
31111111 [7,23], effectively [6,19]
.. .. ..
142111 [6,19]
.. .. ..
1141111 [6,17]
..... .
313111 [6,16]
.... ..
331111 [6,15]
31411 [6,14]
For interest, it might be interesting to know which hands allow ALL tiles in that suit to
be callable. They are:
311111113
311114110
314111110
011414110
014411110
014111410
031112410
--
Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
Smoking cigarettes are bad for you, so smoking cigarettes is bad for you.
whuang@ugcs.caltech.edu (Wei-Hwa Huang) writes:
> For interest, it might be interesting to know which hands allow
> ALL tiles in that suit to be callable. They are:
> 311111113
> 311114110
> 314111110
> 011414110
> 014411110
> 014111410
> 031112410
This is interesting. Only the first one (Nine Gates) is counted as a limit hand and mentioned in the books I have seen, but I checked some of the others, and they all work. For example, the last:
(1)23,22,456,678,777
(2)22,234,567,678,77
222,(3)3,456,678,777
22,23(4),456,678,777
222,34(5),567,678,77
222,345,(6)6,678,777
22,234,56(7),678,777
222,345,67(8),678,77
222,345,66,777,78(9)
The key to working out patterns like this seems to be the multiple-of-3 rule. Every chow or pung contains tiles which add to a multiple of 3; therefore, you can only go out on a tile if you can make a pair which leaves the rest of your hand a multiple of 3. For example, the tiles in the last hand above add to 63, and thus if you draw a 3, 6, or 9, you need only look for combinations with a pair of 3, 6, or 9. The other hands above all add to 2 more than a multiple of 3, and thus if you draw a 3, 6, or 9, your pair must be 1, 4, or 7.
--
David Grabiner, grabiner@math.lsa.umich.edu
http://www.math.lsa.umich.edu/~grabiner
Shop at the Mobius Strip Mall: Always on the same side of the street! Klein Glassworks,
Torus Coffee and Donuts, Projective Airlines, etc.
David Grabiner <grabiner@math.lsa.umich.edu>writes:
>whuang@ugcs.caltech.edu (Wei-Hwa Huang) writes:
>> For interest, it might be interesting to know which hands allow
>> ALL tiles in that suit to be callable. They are:
>
>> 311111113
>> 311114110
>> 314111110
>> 011414110
>> 014411110
>> 014111410
>> 031112410
>This is interesting. Only the first one (Nine Gates) is counted as a
>limit hand and mentioned in the books I have seen, but I checked some of
>the others, and they all work. For example, the last:
AFAIR (I will look it up), Millington defines Nine Heavenly Gates as being able to go out on any of nine different tiles, and actually getting one of them. This requires you to have 1112345678999 concealed in your hand (the book claims).
Klaus O K
On 28 May 1998 08:58:58 +0200, klaus@diku.dk (Klaus Ole Kristiansen) wrote:
>David Grabiner <grabiner@math.lsa.umich.edu>writes:
>
>>whuang@ugcs.caltech.edu (Wei-Hwa
Huang) writes:
>
>>> For interest, it might be interesting to know which hands allow
>>> ALL tiles in that suit to be callable. They are:
>>
>>> 311111113
>>> 311114110
>>> 314111110
>>> 011414110
>>> 014411110
>>> 014111410
>>> 031112410
>
>>This is interesting. Only the first one (Nine Gates) is counted as a
>>limit hand and mentioned in the books I have seen, but I checked some of
>>the others, and they all work. For example, the last:
>
>AFAIR (I will look it up), Millington defines Nine Heavenly Gates as being
>able to go out on any of nine different tiles, and actually getting one of
>them. This requires you to have 1112345678999 concealed in your hand (the
>book claims).
According to Mahjong Walker, it is a principle in mahjong that a hand is considered to be calling a tile only if the hand itself has not used all 4 copies of a tile. Thus the other hands are technically not 9-way-call hands, though they provide an interesting study.
"Live life with Heart."
Alan Kwan / tarot@notme.netvigator.com
http://home.netvigator.com/~tarot
(hard-core game reviews) (please remove anti-spam section "notme." from mailing
address)
tarot@notme.netvigator.com (Alan Kwan) writes:
[snip]
>According to Mahjong Walker, it is a principle in mahjong that a hand
>is considered to be calling a tile only if the hand itself has not
>used all 4 copies of a tile. Thus the other hands are technically not
>9-way-call hands, though they provide an interesting study.
Sorry about that. I didn't notice those 4s.
Klaus O K
>From: klaus@diku.dk (Klaus Ole Kristiansen)
>David Grabiner <grabiner@math.lsa.umich.edu>writes:
>>> 311111113
>[snip]
>>This is interesting. Only the first one (Nine Gates) is counted as a
>>limit hand and mentioned in the books I have seen, [snip]
>
>AFAIR (I will look it up), Millington defines Nine Heavenly Gates as being
>able to go out on any of nine different tiles, and actually getting one of
>them.
Yes, this is the one that is worth "the limit," as David says. The others may
be valid calling hands (as he proceeded to prove) but those are not worth "the
limit."
Tom Sloper, Activision
Senior Producer, Shanghai
tsloper@activision.com
Actsearch@aol.com
Now available: SHANGHAI: DYNASTY -- check our website for a preview and free demo:
http://www4.activision.com/games/dynasty/
>From: whuang@ugcs.caltech.edu
(Wei-Hwa Huang)
> you may be interested in this comprehensive analysis of
>winning tiles. I'm copying this out of a book;
>Notation:
> We denote each tile by the number of times the number appears.
> For instance, C-222 is denoted as "3", as is C-555.
> C-22344 is denoted as "212", while C-33566 is "2012".
[etc.]
Sheesh, talk about something that's hard to comprehend! I like pictures of tiles
myself.
Regardless, Wei-Hwa, you can call and bring over a resume anytime (you'd want to talk, and
take a look at Activision, and isn't Caltech in the L.A. area anyway?). Then maybe you can
help me decipher this gobbledygook while we're at it. (^_^)
Tom Sloper, Activision
Senior Producer, Shanghai
tsloper@activision.com
Actsearch@aol.com
Now available: SHANGHAI: DYNASTY -- check our website for a preview and free demo:
http://www4.activision.com/games/dynasty/
Hello,
Back in the newsgroup after a longish absence... been browsing the articles occasionally, but I think I'll have to go through Martin Rep's archives sometime to catch up...
Alan Kwan explained:
: This is basically an exercise on multi-way call. According to HK : Mah-jong Doctor Mr.
KAN Yi-Ching (e.i.s.), apparently some even : long-time players of Old Style have not
grasped this skill. When such : player luckily runs into a largely concealed Pure One-Suit
hand, he : panics and ponders long, giving the opponents hints to the contents of : his
hand. He may discard the wrong tile so that his calling shape is : largely reduced, or he
may not realize all the tiles he is calling, : and miss a discard which he should have
gone out on.
One way to look at such hands that helps me to think fast during gameplay is to trying to identify the most inflexible part of the hand, and discard a tile from that part, making it more useful in different kinds of combinations. In the 22345566777888-example, the pair of C2s immediately stands out as that unflexible part: it is only usable as a the pair of the hand or a potential pong. This is because only one C3 and one C4 are available (with a hand like this, try to notice these "narrow" sequence elements), and using one of the C2s to form a sequence would leave the other completely isolated. Besides, the rest of the hand has a long run of different numbers that ends in concealed pongs, which is a very good sign considering the number of tiles that one can expect to be calling with: hidden pongs with neighboring tiles are extremely flexible as they can be used to make pairs, pongs or sequences. It this case there are actually two consecutive hidden pongs at the end of the long sequence. With a "long" cluster of suit tiles like in the example, the inflexible element can almost always be found at one end of the sequence, so I'd say the ends are the place where to start looking.
This is just my method, but I prefer it to memorizing huge lists of big suit tile elements that allow so-and-so many tiles when calling (and that every mahjongg player should know by heart :)). Though of course the more common ones do become familiar when one plays enough.
Hmm, I wonder if I made any sense...
Oh, and by the way, Alan, I'd like to see the player who gets that hand on the fifth turn (and the player was calling with several tiles on the fourth turn already!).... or, more to the point, please warn me beforehand so I can avoid playing him/her :)
Juha
On 20 May 1998 01:39:10 GMT, jsorva@niksula.hut.fi (Juha Sorva) wrote:
>One way to look at such hands that helps me to think fast during
>gameplay is to trying to identify the most inflexible part of the hand, and
>discard a tile from that part, making it more useful in different kinds of
>combinations. In the 22345566777888-example, the pair of C2s
>immediately stands out as that unflexible part [...]
Yes, Juha. This is the best approach to this question.
> [...] hidden pongs with neighboring tiles are extremely flexible
>as they can be used to make pairs, pongs or sequences.
A very good point. Concealed pongs are the key to most of the complex multi-way calling shapes.
>This is just my method, but I prefer it to memorizing huge lists of big
>suit tile elements that allow so-and-so many tiles when calling (and that
>every mahjongg player should know by heart :)). Though of course the more
>common ones do become familiar when one plays enough.
I was referring to the short list that I just posted in another article. Memorizing those would help one recognize larger elements. It's just like memorizing 1 digit by 1 digit multiplication so that one can do larger multiplications smooothly.
>Oh, and by the way, Alan, I'd like to see the player who gets that hand on
>the fifth turn (and the player was calling with several tiles on the
>fourth turn already!).... or, more to the point, please warn me
>beforehand so I can avoid playing him/her :)
Well, '5th turn' was made up along with 'raw circles' to simplify the question. Which turn it is doesn't really matter, for this question.
"Live life with Heart."
Alan Kwan / tarot@notme.netvigator.com
http://home.netvigator.com/~tarot
(hard-core game reviews) (remove anti-spam section "notme." from mailing
address)