Analysis of a mahjong hand

or2az · Post by **or2az** » Wed Oct 11, 2017 7:38 pm

Had this multiple wait hand recently and although I didn't see all the possibilities during the game, it looked interesting enough to analyze afterwards. Game was East round only.

It was time to make a discard and call riichi
There were 2 choices. The

or the

.

Discarding the 6bam would leave me with a wait of

.

Discarding the 4dot would leave me with a wait of

.

Coincidentally, if all are available, both have a 13 tile wait.
The

all yield riichi/tanyao while the

adds San Ankou.

The

also yield riichi/tanyao while the

also add San Ankou. The

loses tanyao, obviously.

Since the 1st situation has 3 tiles (4dots) that yield San Ankou and the 2nd situation has 6 tiles (6bams, 9bams) that yield San Ankou, I would think that would be the way to go.

BUT WHAT IF ALL TILES ARE NOT AVAILABLE.
Suppose the 3 tile San Ankou had 12 tiles available for the win while the 6 tile San Ankou had only 8 tiles available for the win. What then?

I assume the answer will be that it depends on how badly you need the points.
With a nice lead, go for the 12 tile available win.
If playing serious catch-up, go for the 6 out of 8 San Ankou win.

But what if the game is close and you are right in the thick of It?
And what if you are sitting EAST for a possible dealer mangan.

How much risk is getting that San Ankou worth for those extra points?

Any and all comments are welcome.

Ignatius · Post by **Ignatius** » Tue Oct 17, 2017 2:07 am

If the player were to be me, I would had tossed away the

.

Just because the wait has more tiles to wait on.

This is, obviously, if we do not consider all the potential conditions you talked about, of course.

Shirluban · Post by **Shirluban** » Tue Oct 17, 2017 12:08 pm

If you discard the

you get more winning tiles and you can kong the

.
(Discarding the

would allow to kong both the

and

but since otherwise they would be winning tiles it's kinda counter-productive.)

Most of the time, when you're East you'd better go for a fast hand to keep the renchan (more hands to win).

If you desperately need points, and you're not East, you can also not riichi and go for sūankō with an extra

(but don't blame me if you lose

).

Iapetus · Post by **Iapetus** » Tue Oct 17, 2017 3:00 pm

Shirluban wrote:If you discard the you get more winning tiles and you can kong the .
(Discarding the would allow to kong both the and but since otherwise they would be winning tiles it's kinda counter-productive.)

The hands have the same amount of winning tiles.

has 4x

1x

3x

1x

4x

for a total of 13.

has 4x

2x

3x

4x

for a total of 13. Tatsumaki waits may be five-way, but they have surprisingly few winning tiles.

3334555's only advantage is the higher chance of tanyao sanankou. If one absolutely needs a massive hand, then it's a better choice (though gunning for suuankou might be even better). Otherwise, the 5556678 has one tile less for tanyao sanankou, but gains 4 tiles for non-tanyao sanankou instead. That's a great trade. It also has the advantage of being able to do two different kans (and no, the kan tiles being winning tiles for the other wait doesn't matter at all), and a 7s tsumo win gets you extra fu. In a generic situation, this hand is 100% 4-pin discard riichi.

So now that we're finally back to something or2az perfectly reasoned on his own, we can talk about ways to deal with wait/value trade-off judgements.

One possible way to compare wait choices is to multiply the scores each wait would gain with the width of that wait. Thinking quickly, it would be the simplest to assume tsumo with no ura dora. Under that assumption, the 3334555 wait's total value is

Code: Select all

3*(riichi tsumo tanyao sanankou = 8000) + 10*(riichi tsumo tanyao = 4000)  = 64000.

For the 5556678 wait, it's

Code: Select all

2*(riichi tsumo tanyao sanankou = 8000) + 4*(riichi tsumo sanankou = 8000) + 3*(riichi tsumo tanyao 40fu = 5200) + 4*(riichi tsumo tanyao = 4000) = 79600.

Now, as tiles disappear, you can edit the formulas accordingly. For example, if someone kanned the

, the 5556678's value would drop to 63600. In a case with similar values, it's usually better to choose the better wait, since ura-dora favors cheaper hands.

(This method is a simplification and has its inaccuracies. I haven't read any books by Japanese experts who've analyzed the statistics to compute the actual expected values.)

I've heard the statistical expected value for an extra turn as dealer is about 700 points. So as dealer, you should put a bit more value on winning, but not too much.

If it's an endgame situation, choose the wait with the best chances of getting what you need. If you're only 2000 below competition, whichever wait has more tiles left is straight up better. But if you need a mangan tsumo to make a comeback, the 5556678 tends to win. If it has to be a mangan direct hit, the 3334555 is better.

Shirluban · Post by **Shirluban** » Tue Oct 17, 2017 6:55 pm

I mean more different winning tiles.
With the same number of total winning tiles, it gives a slight more chances to win.

or2az · Post by **or2az** » Tue Oct 17, 2017 8:06 pm

ways to deal with wait/value trade-off judgements.

Thanks for your explanation regarding the above. Was not familiar with any of that.
Are players actually able to do all that during a game? Pretry time consuming.
I assume a tatsumaki wait is 5 consecutive (or more?) numbers in the same suit.

Oh, a typo below, the 8 should be a 10. (13 tile wait and so the math works)

CODE: SELECT ALL
3*(riichi tsumo tanyao sanankou = 8000) + 8*(riichi tsumo tanyao = 4000) = 64000.

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