Some random thoughts on scoring

Hey, this is UmaiKeiki once again. I think it’s cool when people who play mostly internet mahjong take time to learn how to score hands, even though the computer does it all automatically. Here are a few things that I learned during my own quest to figure out the scoring system; I hope they’ll be useful to you as well.

First off, here are a few resources you’ll want to have at hand:

Guide to scoring

This post won’t be a guide to scoring itself as there are already plenty of those. However, you will need one, and despite its age, Wei-hwa Huang’s Japanese Mahjong Scoring is still the best English language guide on the internet.

http://www.ofb.net/~whuang/ugcs/gp/mahjong/mahjong.html

The best part about this guide is that it includes the Japanese terms plus several common English terms for everything, so you’ll be better prepared to understand what other people are talking about in their own guides.

If you’re a beginner, you might be interested in printing some kind of reference sheet that you can look at during games. The EMA have a sheet based on their custom rules, which are somewhat different than most common Japanese Mahjong rules. Since their sheet has caused so much confusion for beginners, I can’t recommend it. You’ll be better off playing against CPU opponents, so you can take your time while playing and study an in-depth rules guide like the one above. Here’s a good CPU game:

http://gamedesign.jp/flash/mahjong/mahjong_e.html

Score chart

Once you have figured out how Fu and Han are multiplied to get the final score, you might wonder how people calculate their hand scores so quickly. The answer is that they don’t calculate but rather memorize a score chart. You’ll definitely want to obtain a good, concise score chart as soon as possible. Here’s my favorite chart which I found on the website of Henachoko Mahjong Club.

If you’re wondering how to memorize points higher than Mangan, try to think of them as multiples of Mangan. For example,

Haneman = Mangan x 1.5
Baiman = Mangan x 2
Sanbaiman = Mangan x 3
Yakuman = Mangan x 4

Sometimes people refer to double yakuman as “baiyakuman” and triple as “sanbaiyakuman”, and so on, to maintain the pattern.

A challenger appears! Check out this coloured chart by CRiX!

Score quizzes

Yeah, shameless plug time!

The best way to memorize the yaku is to see them in use, and the best way to learn scoring is to score many hands. Playing live games is a good way to do this, but for those without this luxury, I made some applets that generate random hands for you to practice on. You can find them among the tools on Tenhou documentation site.

http://arcturus.su/tenhou/

The Yaku Quiz is for beginners who are trying to memorize the yaku. It gives you a big checklist and all you have to do is check off what yaku you can see. Don’t be intimidated by the size of the list. There are just a lot of yakuman (and character tiles are expanded as well.)

The Score Quiz is mainly for people who play internet mahjong that want to figure out scoring before they go to a real game. This one covers Han, Fu, and payments. For those trying to practice counting Fu, you can enter the exact (unrounded) number if you want.

It uses basically the same rules as Tenhou, but with double Yakuman and two additional yaku: Dai Sha Rin and Open Riichi (because it’s awesome.)

Also be warned that it counts Shanpon waits won by Ron as concealed (an kou), which is an oversight and not an actual scoring rule. (Suu an kou shanpon still has to be a tsumo though.)

Terminology

You’ll probably notice that most english guides use their own English terms for everything. When everyone makes up their own terms to describe the same thing, it can get pretty creative, but not very helpful. The only constants are the Japanese terms, so you might want to learn as many of those as you can to avoid confusion.

Yaku vs. Han confusion

There are a lot of times when people confuse Yaku with Han. Sadly, the first two sites I linked make the same mistake. Here’s clarification:

Yaku are scoring patterns in the hand. For example, Tanyao is a yaku, and Toitoi is a yaku.
Han are units that measure the value of the yaku. For example, Tanyao is worth 1 han, and Toitoi is worth 2 Han.

Pretty simple. Toitoi is 2 han, but it’s not 2 yaku.

Kui-sagari

Kui-sagari is the property of some yaku that makes them worth 1 less Han when open. For example, Hon Itsu is normally worth 3 Han but is reduced to 2 Han if you have called any tiles. What I find funny, though, is that a lot of English guides present this the other way around: they’ll tell you that Hon Itsu is normally worth 2 Han, but gets +1 when closed. It’s as if they know that most games with westerners are going to be pon palace!

Jokes aside, the numbers are the same so it doesn’t matter how it’s presented. However it may help your play style if you think of there being a penalty for an occasional open hand rather than a bonus for an occasional closed hand.

Scoring Chii toi tsu

The “seven pairs” hand might be intimidating to beginners because it uses 25 fu instead of a round 10, some charts do not include a row for 25 fu, and some rulesets score it as 1 han, 50 fu.

Fear not! We can make it really simple. Just score your chii toi tsu as if it were worth 1 han, 50 fu and you’ll get the exact same results (below mangan)!

As proof, here’s a score chart comparing 25 vs. 50 fu payments.

1 han 2 han 3 han 4 han 5 han
25 N/A 1600 3200 6400 Mangan
50 1600 3200 6400 Mangan

The only difference between the two is that the 2-han 25-fu version will reach Haneman faster.

Associative property

The reason that 25 fu, 2 han is equal to 50 fu, 1 han is because:

25 * (2 * 2 * 2 * 2) = (25 * 2) * (2 * 2 * 2).

You might have noticed that this isn’t limited to Chii toi tsu. In fact we can generalize this into two theories:

(1) Doubling the Fu is equivalent to increasing Han by 1.

(2) Halving the Fu is equivalent to decreasing Han by 1.

Here’s how to put this into practice. Let’s suppose you have memorized the hand values for 40 Fu at all Han. Without a chart, how can you give the value of 80 Fu at 2 Han?

Start at 40 Fu, 2 Han. Since you can’t double the Fu, instead increase Han by 1. This gives 40 Fu, 3 Han which is equal to 80 Fu, 2 Han!

Now how can you get the value of 20 Fu, 2 Han? Again, start at 40 Fu, 2 Han. This time, subtract Han by 1. This gives 40 Fu, 1 Han which is equal to 20 Fu, 2 Han!

If you’re confused, take a look at this table.

1 han 2 han 3 han 4 han 5 han
20 N/A 1300 2600 5200 Mangan
40 1300 2600 5200 Mangan
80 2600 5200 Mangan

Knowing how to use the associative property will save you a LOT of time, as it means you only really need to memorize the charts for 30, 40, and 50 Fu to cover most situations.

The smallest possible score

Many charts won’t have a value for 20 Fu, 1 Han. That’s because you just can’t make a hand that cheap.

What happens if you make an open Tanyao using Shuntsu only, a Ryanmen wait, and win by Ron? Should be worth 20 Fu, 1 Han right?

Actually, such a hand is called “kui-pinfu” or open pinfu, and will be scored as 30 Fu, 1 Han. Since a kui-pinfu is the only way to get 20 Fu, 1 Han, we can thus say the lowest possible score for a hand is 1000 points.

Unrelated to kui-pinfu is the 30 Fu, 1 Han hand won by Tsumo. Such a hand is called “gomi”, because of the payments (500, 300 = 5, 3 = go, mi), and because “gomi” means “trash”.

The highest possible score

What’s the highest possible score you can get? While this probably won’t have any real life application, ever, here’s a cool example that I once found on Japanese Wikipedia. When I went back to find it again, I discovered that it had been deleted due to being “original research”. Pfft! It was amusing enough to me, so here I have reproduced it:

Round wind: East
Seat Wind: East

3z 1z1z1z1z 5z5z5z5z 6z6z6z6z 7z7z7z7z

Ron: 3z

Dora indicators: 2z4z2z2z7m

Uradora indicators: 4z4z2z3s4z

Not shown: All 8 flower tiles extracted from the hand.

Here’s how it works. This is using a rule known as “aotenjuu” (one reading of 青天井). It means “no limits” and eliminates Mangan, Yakuman, etc. So for example if you have a 30 Fu, 5 Han hand, it’s worth 15400 points instead of being capped at 8000. Yakuman are worth 13 Han and can be combined with normal yaku. In addition, Wareme is also in effect, meaning that the payment for this hand is doubled.

So here’s what the above hand gets:

Dai san gen: +13
Tsuu ii sou: +13
Suu an kou tanki wait: +26
Suu kan tsu: +13
Renhou: +13
“Flower Yakuman”: +13
Open riichi, win by Ron: +13
8 Ren Chan: +13
Riichi + Double + Open: +3
Ippatsu: +1
Toitoi: +2
Yakuhai: +5
Dora: +24
Flowers: +8

Total: 160 fu, 160 han.

(160 x 6 x 2^162) x 2 = 11,224,332,574,701,334,411,804,299,515,261,053,590,957,561,930,055,800 points.

Fun, eh? If you ever get hit by this, you’ll have a debt that can only be paid off by playing restricted Rock Paper Scissors on a cruise ship…

26 thoughts on “Some random thoughts on scoring

  1. >(160 x 6 x 2^162) x 2 = 11,224,332,574,701,334,411,804,299,515,261,053,590,957,561,930,055,800 points.
    Holy crap what.

  2. If you’re using 1cc per 100 points, and assume a human has 5000cc, then that hand could fully drain the earth’s population about 30 decillion (10^33) times.

  3. How is it possible to have renhou as well as riichi and suu kan tsu? Renhou must be completed before the first draw, and it’s not possible to declare riichi or make kan before drawing the first tile.

    Also, which yakuman is “Open riichi, win by Ron”?

  4. There are some local rules which allow east to get renhou from one of the other players’ first discards, but you’re right, most require it to be claimed before the first draw. But would you find that at all strange in a game with such obscure things as flower tiles, Aotenjuu, and Wareme?

    There’s also a local rule that says if you intentionally deal into an open riichi, it becomes worth a Yakuman. The fact that it’s an open riichi means that you’ll probably never deal into it, but the guy might have an accomplice who feeds him the tile. In that case the game might be one that is settled by the point difference between two players (think Akagi vs. Washizu where the two side players don’t count.)

  5. You can’t Renhou and Riichi at the same time ^^ – and 8 Ren-chan only applies if you’re dealer. Flowers aren’t used in Japanese Mahjong, and Non-Yakuman criteria don’t take effect once if you already have at least one yakuman you’re using ^^. So it doesn’t happen ^.^; Oh, and it’d only be 4 yakuhai, not 5. But rules vary from place to place.

  6. Thanks for the chart CRiX!

    Kafka, the house rules in question let East get Renhou from one of the other players’ first discards even though he made four concealed Kans and Riichi already. The flowers are treated as nuki-dora and the bonus for getting all the flowers is treated as a Yakuman. And the Aotenjou rule turns all yakuman into ordinary, stackable yaku worth 13 Han. So it is possible, although highly unlikely in real life that all these rules would be in effect at the same time.

    The 4 yakuhai comes up when East counts as a double wind.

  7. Yeah, that’s definitely a bug. I warn people that it counts Shanpon waits won by Ron as concealed (an kou), which is an oversight and not an actual scoring rule. I should probably fix it at some point, but :effort:

  8. Two things:
    1. is it possible to somehow get those quizzes on my phone? Its Java, so it should work on a blackberry 9500, right?
    2. In the Yaku quiz, there was a 小三元 but the quiz still required me to check the 2 役牌 (ハク & チュン). I thought those are already included in the 小三元 yaku? (as in, its 4 han in total, not 6).

  9. Shou san gen is worth 2 han itself on top of the 2 from yakuhai, so it is still 4 han total. Sort of how honroutou is always at least 4 han even if it is only worth 2 itself plus 2 from either toitoi or chiitoitsu.

    I might be lynched for admitting this, but I happen to know J2ME, which means I could in theory make a mobile version. I don’t think there would be much demand for that project, though, which is just as well since I hate looking at my old work. I’d much rather rewrite the whole thing as a server-side script in something other than java which would avoid bogging down browsers with klunky applets and junk. =3=

  10. hm, thanks. I always counted shou san gen as 4 han and ignored the yakuhais, guess I was wrong :D (not that it matters for the actual score)
    and regarding the mobile version: I don’t actually know how different J2ME and Java are, so I don’t know how much you had to change the code…
    and on that note, does someone know a riichi mahjong game for mobile phones? The only thing I can find are those stupid solitaire games or flash-based ones and the blackberry doesn’t support flash, unfortunately :(

  11. Okay, I’m probably a year late, but nonetheless, if anyone cares:

    @Lorizean You can download a cellphone gameboy emulator called “meboy” and just load any gameboy rom mahjong game you want (there are a lot, such as Mahjong Pro Tsuwamono). The AI are kind of stupid, but it’s still very fun to just take the cellphone anyway, and assemble epic hands. I recommend any mahjong player with the will to play on the small cellphone screen to give this a try.

  12. @xKime Thanks alot!!

    @umai:
    Found a bug in the scoring quiz. It does not seem to properly recognize pinfu, i.e. if you got 2233455667788m, ron by 4m, it does not count the Pinfu (which it should, right?). I had another hand where it interpreted a ryanmen as kanchan and therefore didn’t give a pinfu. Both were situations where it could have been a ryanmen (22334 – 556677 – 88, waiting on 14m etc.) as well as kanchan (22 – 33455 – 667788, waiting on 4m only). But if I’m not mistaken, in that situation that counts as ryanmen, therefore Pinfu counts too?

  13. yea that old thing is a piece of junk. I never got around to making it work properly since I stopped using java a long time ago and have no plans to install it again. At least it’s still good for… uhh… generating lots and lots of hands. w

  14. A mobile version of a yaku quiz and/or the scoring quiz would be the most awesome thing ever. I was thinking it would be awesome just the other day.

    The best mobile version for Riichi Mahjong I’ve found is Mahjong Tengokuhai, Janryumon is pretty good too if you like hand animations and a more flashy design.

  15. I realize the article’s several years old, but I just stumbled across it a second time and realized I can improve on the highest possible score: Exchange the 西 and 中 tiles in your scenario (i.e. a kantsu of 西 and tanki wait on 中) then put the remaining two 中 tiles in the dora indicators, replacing the two that don’t contribute anything to the hand. You lose Daisangen (-13) and one Yakuhai (-1) but gain Shousangen (+2) and 40 dora instead of 24 (+16) for a net gain of 4 han.

  16. I like it! The fu even goes up by two, although I don’t recall if it’s enough to round up to the next tier. Add in the assumption that haku pocchi also counts as dora (instead of just an ippatsu wild card) and there’s at least 5 more han attainable. Anyone feel like calculating the score?

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