Which tile is most efficient in Mahjong?
An advanced strategy guide that delves deep into the potential value of all individual tiles in Mahjong
We have thus far touched on the honours and terminal tiles, which in most circumstances, are not favoured especially if we only have one lone copy of these tiles. The other tiles, which is what I will cover in this blog post, are the tiles that we will tend to keep. This is because these tiles have much higher chances in forming a group of 2 that can eventually meld into a group of 3. However, it is important to note that these tiles are also more dangerous to discard, especially when late in the game, as other players will likely be waiting or keeping these tiles.
Which number suit is more tile efficient? If there is, how efficient is each tile? Let’s analyse this in greater detail. To evaluate the values of each tile, it is rational to first analyse the potential of each lone tile to form into a group of 2.
As covered previously, among the numbers, 1 and 9 have lowest possibilities, with a total of 11 possibilities to form a group of 2.
Numbers 2 and 8 have slightly higher possibilities, with a total of 15, as shown below:
Numbers 3 and 7 is even higher, with a total of 19 possibilities:
Using the same logic, numbers 4, 5 and 6 has also a total of 19 possibilities as well.
In summary, based on the above probability analysis, the value of the single tiles in descending order are as follows:
3 = 4 = 5 = 6 = 7 > 2 = 8 > 1 = 9
The question now is, are 3–7 suits really the same efficiency? Let’s analyse this even deeper.
To keep the discussion simple, we will focus our analysis on the 3, 4 and 5 suits (since 6 and 7 are mirrors of 3 and 4 so the same reasoning applies). Let’s analyse for 3 Wan.
Forming a group of 2 for 3 Wan will require you to draw 1, 2, 3, 4 or 5 Wan. Drawing another 3 Wan forms a pair which can be the “eyes” or meld into a triplet. Drawing 2 Wan and 4 Wan gives you the highest chance to meld into a group of 3 as you can have a 2-sided wait of 1 and 5. However, if you draw 1 Wan, this will be a bad one-sided wait of 2 Wan. Similarly, drawing a 5 Wan is also a one-sided wait for 4 Wan.
But if you think deeper, maybe drawing a 5 Wan is not as bad as drawing 1 Wan… This is because you can potentially draw a 6 or 7 Wan later to improve your hand to a 2 sided wait!
Now let’s analyse for 4 Wan. The situation is similar to 3 and 7 Wan, where drawing another 4 Wan forms a pair, drawing 3 or 5 Wan allows you to have a 2-sided wait and drawing 2 or 6 Wan makes a 1-sided wait. However, drawing a 6 Wan allows for a possibility of a 2 sided-wait if we draw a 7 or 8 Wan.
Let’s analyse for 5 Wan now:
Do you see a difference?
You are correct if you noticed that now the potential 2-sided possibilities is increased with 5 Wan. Same logic applies, drawing 5 Wan gives you a pair, 4 or 6 Wan gives a 2-sided wait and 3 or 7 Wan gives a 1-sided wait. However, if you have 3 and 7 Wan, drawing another 1 or 2 Wan will mean you have a 2-sided wait. Likewise, if you have both 5 and 7 Wan, drawing another 8 or 9 sou will mean you also have a 2-sided wait. Hence, 5 is more efficient as compared to 3, 4, 6 and 7 because the potential for a 2-sided wait is higher! With more opportunities for a 2-sided wait, the value of 5 is the highest. The value of cards can thus be ranked as follows:
5 > 3 = 4 = 6 = 7 > 2 = 8 > 1 = 9
If 5 suit is indeed the highest value, then in an expert game where everyone knows that the value of 5 suit is highest, most players will tend keep the 5 suit tile. Hence, the value of 3 and 7 will likely be higher than 4 and 6, as they may end up with the possibility of a one-sided 5 suit wait if players draw 6 and 4 suit respectively. In addition, having a 2–3 pair or 7–8 pair allows you to wait for 1-4 or 6-9 respectively, which is easier to win as 1 and 9 are terminal tiles which are of lower value (Thanks to Flanmyuu from Reddit for pointing this out).
Therefore, based on these analyses, then the ranking of tiles is as follows:
5 > 3 = 7 > 4 = 6 > 2 = 8 > 1 = 9
The concept may seem quite convoluted, so you may read this another time to better understand the concept. However, an important point to note is that we have not considered the possible interaction with other tiles. Nonetheless, this information provides you with the fundamentals of the individual tile values, which will likely help with decision making when discarding tiles. In addition, you can also make inference that a player is likely to be assembling close to a winning hand if a player discards the higher value cards.
Did you guess the most efficient tile correct? Hope this was useful to you! This article is written with feedback from Kuan Chuan Chan. Stay tuned for more mahjong strategy articles!
Kuan Rong Chan
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