Double Runs

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HotelFSR
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Double Runs

Post by HotelFSR » Sun Mar 29, 2009 10:21 pm

This is a follow on from Garthe\'s front page article about Double Runs being undervalued.

It\'s true that certain hands just aren\'t attractive enough to warrant the risk. Personally, I think hand values need to be adjusted along these lines:


Sanshoku Doujun: + 1
Itsuu: + 1
Chanta: + 1
Junchan: + 1

Chii Toitsu: maybe +1 (or at least 30 base points)

Sanshoku Doukou: + 2
San Kantsu: + 2
Ryanpeikou: + 2
Honroutou: + 2


Is that making sense?


Hopefully similar changes will be made to the game someday, much as poker was updated.

We can dream!

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Re:Double Runs

Post by TobiasOlsen » Sun Mar 29, 2009 10:54 pm

From the view of pure probability, a hand like itsuu should be worth more than sanshoku for instance (there are three different ways to make itsuu and 7 different ways to make sanshoku, and since none of them include more than one of a single tile, this translates directly to the ratio of their probablities).

As for the ryanpeiku, I saw a list of how many ways certain of the hands can be made (total number of ways, including the fact that there are 4 of each tile and including the number of ways the rest of the hand can look. The list is at http://mahjong.dk/strategi/kombinatorik/ (it is in danish, though). The number for ryanpeiku is 1.399.137.210 whereas for instance the one for thirteen orphans is 1.308.622.848 and the one for 4 concealed pungs is 2.137.006.080, so ryanpeiku is slightly more likely than thirteen orphans and actually less likely than 4 concealed pungs.

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Re:Double Runs

Post by HotelFSR » Sun Mar 29, 2009 11:59 pm

While that list is very interesting, unfortunately working out the exact probability is much more complicated that one might think.

There are several reasons for this. One is the distribution of the tiles (e.g. if one or two players have many honor tiles, the other two wont and each will find it easier to make certain hands) which that list does not take into account. A related point is the probability that you will actually WIN with a given hand, which depends not only on player skill but also the patterns in which people naturally tend to keep and discard tiles- some hands are harder/easier to make than the numbers suggest! calucating this exactly is very difficult. An extreme example is a hand like Big Four Winds- how likely is it that people will let you steal the tiles you need when they see you going for it?

Finally, you have to take into account the stackability of hands- how well they combine with each other and how likely that is. Not all hands are equal in this way and so, again, it is massively difficult to calculate the exact numbers.

That\'s why I went for a more simple + 1/+ 2 approach!

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Re:Double Runs

Post by gartheee » Sun Apr 12, 2009 4:52 pm

I don\'t think it would be correct to say that what players have will affect which hands are more or less likely. The fact that in holdem, people tend to play pocket pairs should not only make straights less likely, but should also make Full houses more likely as people are playing with cards that make full houses more easily. But that would certainly never be a factor in figuring out which hands were more likely for the purpose of ranking the hands.

The increased values suggested for the hand look good, but another thing to think about is the complication of the scoring system. It\'s already ridiculously complicated with just the point assignments we already have. While it does make the game interesting to have a variety of hands to shoot for, the extreme rarity of hands like, say, 2 Double Runs and 3 Kongs really just makes for a waste of space in every explanation of the rules. If we\'re going to make changes, I\'d think let\'s move towards simpler, not complicateder.

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Re:Double Runs

Post by HotelFSR » Sun Apr 12, 2009 5:06 pm

I hear you Garthe.

On the topic of simplification I would think the base point (Fu) system is by far the most obvious candidate for change! Keep the hands, boost the rare ones if necessary, and lose the Fu.

I tend to teach total beginners only the 30 Fu column (as though Fu did not exist), and I feel like the game could work very happily like that. Some values could be also be rounded off, like 3900->4000.

I do agree that some hands like Three Kans are just too rare, and could be lost, but not all rare ones. I\'ve noticed online that some local variations in Japan accept things like Sanshoku Doukou to be one short (e.g. 555-555-55) for reduced score, which makes going for those hands both slightly more sensible and more probable. Three Kans could be similarly allowed in reduced form (e.g. 9999-7777-444). I\'ve also seen Three Color Itsuu allowed (as opposed to single suit).


P.S. The starting hands that other players have does affect the probability that you will WIN with certain hand types. e.g. if you have a starting hand with a lot of honors and terminals, on the path to an outside hand, there is a slightly higher probability (right off the bat) that someone else will win first with an inside hand (since you are using up a bunch of tiles they neither need nor will ever draw). This is before you even consider that the waits toward an outside hand will tend to be inferior.

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Re:Double Runs

Post by gartheee » Mon Apr 13, 2009 6:28 am

Yeah, the \'fu\' system is pretty unnecessary alright and would be the first candidate for simplification. THough of course, having gotten used to it I\'d miss it.

I\'ve seen the variations on 3 Colored Triples (sanshoku doukou), 3 Colored Straight(sanshoku itsuu?), etc, that you mention, but only in Chinese and WSOM rules. Where did you run into them in Japan? Must have been some pretty local rules, I would think.

Also, I understand that the tiles people have will affect how likely certain hands are for that game. But I still fail to see how it matters for the purpose of ranking hands by their basic probability of occurrence right now, before the game starts, which we need to do so we can play the game. Going back to poker as an example, if Jack9 gets into an unfortunate pot against two players who both have pocket 10\'s, he\'s obviously going to need a small miracle to draw out a straight. Still, we\'re not going to rerank straights higher than flushes or full houses that hand. Whatever people start with in a hand in Poker or Mahjong, it still shouldn\'t affect the way we rank hands before the cards/tiles are dealt, yes? Are you suggesting we wait to assign point values to hands until we\'ve seen everyone\'s starting tiles and then we decide which hands are more/less likely and thus worth more?

P.S. That\'s sposed to be a joke. If that sounds like a good idea, I guess the conversation\'s over.

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Re:Double Runs

Post by HotelFSR » Mon Apr 13, 2009 12:19 pm

I don\'t think the effect is anwhere near big enough (particularly because it almost always takes several turns before the hand is formed) to warrant changing the hand values based on it.

That would indeed be ridiculous.

However, if you are calculating probability with the strictest precision you would need to take it into account.

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Re:Double Runs

Post by KawamuraReo » Mon Apr 13, 2009 1:38 pm

http://www.ix3.jp/hiii/02mahken/2-10-1toukei.htm

Statistics:

SAMPLE SIZE: 120589 kyoku
kyoku won: 103737
81507 of those hands were NOT limit hands

5.60% of the won hands were Iipeikou
4.05% of those were Sansyokudoujun
0.07% of those were Ryanpeikou

Anyway, the point of this is that at heart, Mahjong still has a large degree of luck and you have to take into account that you can get combinations of hands. Making rarer hands like Ryanpeikou worth more would not only be silly because stacking them with other winning hands would break the scoring system, but it also encourages players to think harder >_> For example, let us say you have:

2-bam 2-bam 3-bam 4-bam 5-bam 3-crak 4-crak 5-crak 3-dot 4-dot 5-dot 6-dot 7-dot

And you Reach, and get an Ippatsu Ron on 8-dot, and your initial dora is 2-bam, with the reverse dora being 2-crak

Your hand would be Riichi Ippatsu Mentanpin Sansyoku Doradora. That would already be Baiman hand >_>;; If you\'re dealer, that\'s already worth 24000 t__t Note that such a hand would, by probability, be unrealistic to shoot for, but given that Mentanpin is one of the most popular hands, and is already worth 3 yaku (Mentanpin = Riichi/Tan Yao/Pinfu), making hands like Sansyoku which can easily be integrated with other hands (Junchanta, for instance, which when closed is worth THREE yaku) larger is just silly and would break a game which is already fine as it is.

Anyway, you probably might not understand the point I\'m trying to make here, and whatever I say here might not really be of much interest to anyone (Yeah, I\'m only 16, big deal), I\'m basically pushing the fact that the point values, the fu system, are perfectly fine as they are. It is up to you to decide how you are going to form your hand, the example I have given earlier is a good way to show that you don\'t rely on just a couple of yaku, you form your hand based on putting forth a multitude of yaku into one single powerful hand. Another classic example is:

1-bam 1-bam 2-bam 2-bam 3-bam 3-bam 7-bam 7-bam 8-bam 8-bam 9-bam 9-bam 9-bam 9-bam

If you have a lot of dora, that could easily take that hand into kazoe yakuman: Menchinjunchan ryanpeikou. On its own, that\'s a sanbaiman or 11 yaku >_>

An interesting page with Local Yaku can be found http://www.ix3.jp/hiii/02mahken/1-10local.htm

Hiii\'s Mahjong Research is a very interesting website for mahjong, so you should probably check it out... If you can understand Japanese, that is.

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Re:Double Runs

Post by zzo38 » Mon Apr 13, 2009 3:34 pm

gartheee wrote:Yeah, the \'fu\' system is pretty unnecessary alright and would be the first candidate for simplification. THough of course, having gotten used to it I\'d miss it.
I don\'t use the table
HotelFSR wrote:I tend to teach total beginners only the 30 Fu column (as though Fu did not exist), and I feel like the game could work very happily like that.
I just ignore the scoring table. Because I do the calculation like this: Calculate fu, round up to multiple of ten, quadruple, double for each han, set to 2000 if higher than 2000, determine if you have enough han for haneman/baiman/etc (ignoring fu), multiply for payment, round up to multiple of hundred. I find this way easier than memorizing the table.

(PS. Why is ALT+S "spoiler" in this forum software? It is "send" in most others!)

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Re:Double Runs

Post by HotelFSR » Mon Apr 13, 2009 3:49 pm

zzo38: that actually sounds more complicated than using the table. the simplest way for beginners is just to ignore fu altogether.

kawamurareo: you don\'t explain why increasing the values breaks the game. if anything, the odds you show suggest that they should be worth more. for example, ryanpeikou is about as likely as some yakuman hands- makes sense that it should have a huge reward. that yaku site is very interesting by the way. I love that some players have apparently invented yakuman hands called \'windows 95\', \'windows 98\' and \'honda\'!

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Re:Double Runs

Post by zzo38 » Tue Apr 14, 2009 4:07 am

HotelFSR wrote:zzo38: that actually sounds more complicated than using the table. the simplest way for beginners is just to ignore fu altogether.
I\'m just saying that I find it easier to calculate than memorizing the table, I\'m not saying everyone does. Either way you will get the same answer, although fixing the fu to 30 fu will simplify it whether the table or calculation is used. I think the modern Chinese system also ignores fu (effectively setting it to 1 fu always).
HotelFSR wrote:I love that some players have apparently invented yakuman hands called \'windows 95\', \'windows 98\' and \'honda\'!
Are you trying to play American Mahjong now?

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Re:Double Runs

Post by HotelFSR » Tue Apr 14, 2009 5:24 pm

No :) Just think it\'s funny. Those hands aren\'t in American MJ... or are they?

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Re:Double Runs

Post by Shirluban » Wed Apr 15, 2009 3:23 pm

HotelFSR wrote:Those hands aren\'t in American MJ... or are they?
Hum... depends on the year.

(No, I\'ve nothing interesting to say right now.)
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Re:Double Runs

Post by Tom Sloper » Wed Apr 15, 2009 3:47 pm

HotelFSR wrote:No :) Just think it\'s funny. Those hands aren\'t in American MJ... or are they?
No, not in what I call American mah jongg (the National Mah Jongg League game). (Note that some people call other variants "American".)

But maybe players of Wright-Patterson or one of the offshoots of British/Western rules might have such hands.

The players in India have some interestingly named hands but I never heard of a Windows 95 hand or a Honda hand. If such hands really exist, I\'d love to hear more about them!
4649おねがいします。

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Re:Double Runs

Post by HotelFSR » Wed Apr 15, 2009 3:56 pm

That site has illustrations for most of the hands.

Windows 95 is a Yakuman, basically a toi-toi composed of all nines and fives. Windows 98 is the same with all nines and eights.

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