This post is one of many of the latter.
So often we are fixated on attaining a winning hand that we often forget to keep track of not only how many tiles we are away from winning, but also how many the opponent potentially could be.
Shan Ten (上天) is basically the practice of keeping track of that. The ideal Shan Ten is Zero Shan Ten, because obviously when you need zero tiles to win, you win. Then the most familiar Shan Ten is One Shan Ten, which is Tenpai. The pattern follows as such; Two Shan Ten would be two tiles away from a winning hand, Three Shan Ten would be three tiles away ... up to Thirteen Shan Ten (Which is ridiculously rare, but I won't bore you with the math).
Why keep track of such a mundane thing? By knowing how close (or far, if you will) you are from winning, it allows you to play the round in an appropriate style to suit the situation. This is most prominent at the beginning, when you construct your hand from the wall.
Keeping track of your own Shan Ten is child's play; I'll do an example right now:
Note that most (if not all) Mahjong games will arrange your tiles automatically for you, thus making it all the more easier to keep track.
At first, it may be hard to tell how many tiles you are from a winning hand; the best way is to construct melds with the available tiles. The only possible melds for this opening hand would be 4-5-6 Pin (Dots). Next, we construct partial melds; 2 out of 3. There are many here:
- 4-5 Man
- 4-4 Pin
- 3-4 Sou (Bamboo)
- 6-7 Sou
Finally we list our possible discards (The remaining tiles basically):
- 9 Man
- 9 Pin
- South Wind
- North Wind
As an aside, notice that our discards will most of the time (in this case, all of them) be terminal and honour tiles. A probability-based explanation is necessary to elaborate this logic, but that can be another post.
Now we work backwards. Since we have 4 potential discards, that is our initial Shan Ten number. 4 Shan Ten is therefore our maximum, and therefore we are four tiles away from winning. Granted with every new draw the Shan Ten number fluctuates, as of now, this is our Shan Ten number.
This is easy to prove; simply remove the discards, and replace them with tiles that would make melds. For example, I replace them with 6 Man, 7 Pin, 2 Sou, and 8 Sou. This results in an All Simples hand.
It is worth noting that you cannot always assume the number of discards is equal to the Shan Ten number. That is because the Shan Ten number that gives us is the minimum; by changing our melds and partial melds, it changes the potential discards, and therefore gives us a new, higher Shan Ten.
An example here would be our 4-4-5-6. We have listed 4-5-6 Pin as our only complete meld, but we have also listed 4-4 Pin as a partial meld. Since these events are mutually exclusive (Both can't occur simultaneously because if you do stick with the 4-5-6, then the 4 becomes an outlier and therefore a discard) the overall result increases the Shan Ten number to 5 Shan Ten.
But this is a bad example in the sense that you could redo our listing to include 4-4 Pin and 5-6 Pin as partial melds. However, this only simplifies the list; and doesn't change the maximum Shan Ten.
Finally, I'd like to note that after all this, we still have not considered Winning Conditions. Shan Ten does not take that into consideration; if we did however, we would, in most cases, get a higher Shan Ten number. But once again, the minimum Shan Ten doesn't change.
Now that we know we are 4 Shan Ten (Which by the way, is the most common number for a starting hand, with 3 being a very close second), we can draw a few tiles to see if our situation improves.
Unfortunately, the overall situation does not improve, as one player has already declared Riichi after their fourth discard. What can we conclude from this image? Well first let's find our new Shan Ten, without all the explicit work. This may seem harder, with a lot more options to choose from for discards, but just use common sense and pick discards based on the construction of your hand.
After a quick scan, I choose my double 9 Man and my 3 Sou as my discards, thus making it a 3 Shan Ten hand. This hand would still be All Simples, but would allow me to declare Riichi if it remained fully concealed.
We are far from winning (Yes, 3 tiles is still a long ways to go). But someone is already Tenpai. It would be best to play defensively, and hoping in the end that no one plays into their hand, they do not draw the winning tile, and through all that chaos, still get your hand to Tenpai or even win.
Reading the discard and reading your opponent's hand based on the discard will be obviously another post. But for now just note that it is hard to tell what the opponent is aiming for, mainly because their discard pile is so small, and that half of the discards are honour tiles. The safest route to take would be to get rid of double 9 Man, which also helps me get closer to Tenpai.
Indeed the 9 Man were safe bets for discards, but in the end, they managed to Tsumo. No matter how skilled you are in the game, you will always lose to luck. But at the end of the day, luck comes and goes, while skill stays with you until the end.
Next week I will probably expand more on Shan Ten and conclude.
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