Combinatorics Table Posted

[Torgo]

http://mahjong.wikidot.com/analysis:combinatorics

That\'s a link to a table I created that shows the number of possible ways to make many of the scoring patterns used in some popular mahjong styles.

Because I\'d like to make the table better and even more useful and clear, I would appreciate questions, comments, concerns, and ideas for improving it.

Many thanks

(Oh, it has a few riichi hands on it too!)

[WorTeX]

In the end, these numbers are useless, since you can\'t compute these in your head, or put them to any real use.

[Torgo]

If that\'s what you believe, then you are at a disadvantage.

[WorTeX]

If you like you can give me few examples, but I still doubt it will be of any use (atleast for me).

[Shirluban]

If you assimilate the number of combinations to the scoring pattern difficulty, it can be used to compare the relative difficulty of one hand versus on other.
Of course, it ignores all game mechanisms like calling or other players\' defense, so it\'s all bullshit hardly reliable in a real play.

For example, the table said Big Three Dragons have 16,137,216 combinations and Three Similar Pungs have 103,947,264. So Big Three Dragons is 6.4 times harder than Three Similar Pungs and reward 32000/2000 = 16 times more! In conclusion, Big Three Dragons is more profitable than Three Similar Pungs so if you have to choose between them, it\'s better to go for Big Three Dragons.

What! You already know that?!
And even if BTD should be less profitable than TSP, you\'ll go for the yakuman hand instead of the cheap one anyway?
Ok, ok, bad example.

There are some strange points in the given combinations:
- Only one kind of tiles can be use for BTD, but TSP can be made with 9 different kinds (tiles number 1, #2, #3, ..., #9), so why the table say there are only 6.4 more ways to make TSP than BTD and not 9 ?
- Three Identical Chows and Three Pure Shifted Pungs are basically the same hand, so how Three Identical Chows can have more combinations than Three Pure Shifted Pungs ???
(279,401,280 for TIC, and 278,299,266 for TPSP)

[Torgo]

B3D vs 3SP: I\'m not very sure about this, but my guess is that 3SP takes 9 numbered tiles out of the mix, and those tiles can make a LOT of chows... like 3000 by themselves, and many more when combined with their neighbors. Do that 27 times, and it could be in the millions.

As for 3IC vs 3PSP, that threw me for a while too, so I examined it more closely.

Consider: 456d 456d 456d 333d RR. Sure you could get TIC or 3PSP, but you could instead get FOUR Pure Shifted Pungs, so it is not counted for 3PSP.

And one example for at the table: I know I\'m going to be trying for more Seven Pairs and 13 Orphans hands.

[Fat Dragon]

@ Torgo

Thanks for posting! I like your table. Keep on the good work.

FD

[drob]

Edit by moderator:
Drob, can you please argument your point of view and not just laugh at people nor insult them.

[Shirluban]

Consider: 456d 456d 456d 333d RR. Sure you could get TIC or 3PSP, but you could instead get FOUR Pure Shifted Pungs, so it is not counted for 3PSP.

Yes, but it\'s still a 3PSP hand, so I don\'t see any reason to not count it among other 3PSP.

If you want to do so it\'s your right, but you need to say explicitly what is count for one pattern and what is not.
Your Methodology chapter confuse me:
"Four Consecutive Pungs" hands are always "Three Consecutive Pungs" and "All Pungs". But you count 4CP for AP and not for 3CP. I don\'t see the logic behind this: either 4CP is AP and 3CP, either 4CP count for none of them. Not a mix of that!

And one example for at the table: I know I\'m going to be trying for more Seven Pairs and 13 Orphans hands.

Ok, if you didn\'t already know 13 Orphan is the easiest of yakuman hands, the table teach it to you. But the real question is: "When to go for 13 Orphans?"
When you have 12 isolated terminals and honors? When you have 11? 10? 9? 8? ...?
Same problem with Seven Pairs: How many pairs you need in your staring hand to go for it?
This kind of tables, as good it can be, are mute here.

Answer:
With 10 terminals and honors you have good chance to make 13 Orthans. With only 9 you can try it too, depending on the rule (it\'s a case of draw hand in reach mahjong) and situation (current score, ...).
8 is too few.

With 5 pairs, the gates of Seven Pairs are wide open. With 4 pairs you should thing about it, but don\'t neglect All Pung or chow hands.
If one or two of these pairs are pung in fact, consider All Pung.

[Torgo]

... you need to say explicitly what is count for one pattern and what is not.
Your Methodology chapter confuse me:
"Four Consecutive Pungs" hands are always "Three Consecutive Pungs" and "All Pungs". But you count 4CP for AP and not for 3CP. I don\'t see the logic behind this: either 4CP is AP and 3CP, either 4CP count for none of them. Not a mix of that!

You make an excellent point. I will update the table to add the exclusions I\'m using, and when I get some time I\'ll give more thought to testing each one separately.

Big Three Dragons is also Two Dragon Pungs, but you never get to score both, and that is why I excluded patterns that are explicitly implied.

All Pungs is a bit of a different matter: You can score both AP and 4CP in Zung Jung, but not MCR.

But the real question is: "When to go for 13 Orphans?" ... This kind of tables, as good it can be, are mute here.

I\'m hopeful that others will step up and make more tables to help with strategy that do take into account game play and other factors.

I\'ll keep looking at ways to improve the table itself, how it gets used, and most especially that it says what people think it says.

Thank you for your very insightful comments.

[Fat Dragon]

The fact that we have a discussion going on about overall strategy in Riichi just through the point that somebody made something is very positive. Thanks Torgo and thanks Shirublan for your posts.

It\'s something I miss here beside the everyday routine of threads like \"Is Pinfu this... and Furiten that...\" Sure these questions are important for everyone who takes a step to learn this game. But it\'s also good to have something for people who are beyond the level of taking the very first discard in a round.

[Torgo]

I have added a list of exclusions I used to the methodology section.