Mid-Year Mah Jongg Statistics (2023 Edition)

The Secrets to Winning More Often!

We're just over half way through the Mah Jongg year, so it's a great time to take a look at how the NMJL's 2023 card is shaping up!

Last year, we published a couple of articles on Mah Jongg statistics. In these articles we investigated the influence of jokers, how stopping the Charleston affects the outcome of the game, along with many other interesting facts that are not card specific. Additionally, we analyzed data relating specifically to hands on last year's card.

After receiving a huge amount of support and interest from our readers, we began focusing on the current year's card. This article covers new and updated NMJL 2023 card analysis, at the mid-year point, providing statistical insights and further enriching our understanding of Mah Jongg dynamics and gameplay. 

In this article, we cover card-specific data relating to the NMJL 2023 card only. In particular, we have analyzed winning hands in order to answer the following questions:

• Which sections of the card have achieved the most wins?
• Which particular hand has achieved the most wins?
• Which hand patterns have achieved the most wins?
• Which numbers achieved the most wins for hands that contain like-numbers?
• Which numbers achieved the most wins for hands that contain consecutive numbers?
• Have there been more wins for big odds vs little odds?
• Which numbers achieved the most wins for "flexible" hands?

Our goal was to analyze winning hands to discover which tile numbers resulted in the most successful outcomes. Our analysis is based on every game played on the I LOVE MAHJ online gaming platform, using the NMJL 2023 card (between the end of March and mid-October 2023). Data includes games played by both humans and bots. This is an important fact, as games played by bots contain no bias towards "favorite" hands or sections of the card. We will touch more on this later in our analysis.

Section Popularity

Let's start at a high level and examine the popularity of each section of the card. Here, we calculate the percentage of time a winning hand came from a particular section. The results are shown as the raw data in a table and then in graphical form.

Percentage of Wins per Section of the NMJL 2023 Card

As expected, the Consecutive Run section contained the most winning hands, by a wide margin (45% of all winning hands). This is likely due to the flexibility these hands provide. The Winds-Dragons (WD) section came in second, with 16.4% of winning hands during the period analyzed. The section with the least number of winning hands is Singles & Pairs. No surprises here, due to the difficulty of these hands.

2468 and 13579 were about the same with ~9.7% of winning hands, while the 2023 section, Any Like Numbers and 369 were around ~5.7%, give or take.

Interestingly, Addition Hands accounted for only 1.5% of total wins. This was a little surprising seeing as these hands are not particularly difficult, and there's good switchability with Any Like Numbers, as well as 2468 or 369 for some options. We suspect human players are just overlooking this particular section of the card, as it's not present every year. However, as we stated above, bots have no such bias. So, overall, there does appear to be a very low likelihood of achieving Mah Jongg when playing Addition Hands. It's not totally clear why this would be, other than the availability of certain numbers, especially as kongs are required for these hands. Looking at the ‘Percentage of Overall Wins by Hand' table in the section below (Hand Popularity), Addition Hand, Line 1, is the most successful of the four hands in this section of the card (ranked #34). This follows a pattern we will see throughout this article, when the numbers 1 and 2 are used together, they are more successful at achieving Mah Jongg than any other number combination.

Hand Popularity

Let's dig a little deeper now and take a look at which hands have won the most often. By far, Consecutive Run, Line 2 is the hand that has achieved the most success, with 21.1% of overall wins. This makes sense due to its flexibility. This total can be broken down into the two versions of this hand. The two suit version of this hand achieved 12.7% of wins vs the one suit version, with 8.3% of overall Mah Jongg wins. Unsurprisingly, Singles and Pairs, Line 6 (the "Big Hand") has won the least often, at just 0.005% of overall wins.

Below, we've noted all the hands listed on the card, starting with those with the most wins all the way down to those with the least wins. This data includes both human and bot wins (more on the importance of this later). The section titles are abbreviated and the letters a and b represent the first or second version of a hand, respectively.

Percentage of Overall Wins by Hand, Ranked Most to Least

As we noted last year, there is a disconnect between the value assigned to each hand compared to the difficulty of making a particular hand. If you consider the percentage of overall wins for each hand as a guide to how easy that particular hand is to complete, we see that there's quite a difference between individual hands. In theory, hands on the card that have been allocated the same number of points, should be of equal difficulty. However, this doesn't appear to be the case. For example, the data above shows the following:

• Consecutive Run, Line 2b (ranked #1), and Addition Hand, Line 3 (ranked #52), are both 25-point hands, but represent ~13% and ~0.23% of overall wins, respectively.
• Also, if we look at concealed hands, which appear to achieve Mah Jongg 10 times less often, we could surmise that they are 10 times more difficult, yet they are only worth 5 extra points compared to hands with the lowest point value on the card.
• Another interesting case is Consecutive Run, Line 4 (ranked #11), which has a value of 30 points, but appears to be easier to achieve than many of the 25-point hands. We've also highlighted several other 30-point hands in the table above that achieve Mah Jongg more often than many 25-point hands.
• There are also two 45-point hands (ranked #56 and #58), which achieved more Mah Jongg wins than many 30-point and 40-point hands.

One could argue that the popularity of a hand does not necessarily represent its difficulty, as human players have biases towards certain hands they like, and sections of the card they feel more "comfortable" with. While this is true, computer bots are not partial to any particular hand. Bots play based on the tiles they receive, so they match hands objectively, with no emotion, preferences or preconceived notions. This is a very important point, as the inclusion of games played by bots serves to maintain the integrity of the data.

Additionally, since the data used to calculate the overall figures includes an extremely large number of games played by bots (as there is often one human playing against 3 bots), we believe that it is fair to correlate the frequency of a win with a particular hand to that hand's difficulty.

Our conclusion, therefore, is that the National Mah Jongg League should consider assigning point values based on the probability that a hand can be completed. Many players achieving "difficult" hands are, essentially, being short-changed!

Our analysis is certainly not meant to discourage players from attempting the more difficult hands. There's so much more excitement and sheer joy when one completes a Singles and Pairs hand, or even a concealed hand, compared to a more frequently played Consecutive Run hand. If the tiles lead you towards a more difficult hand, by all means, go for it. We find it's way more fun to challenge ourselves when the opportunity arises.

However, you may wish to consider this statistical analysis when playing in tournaments, or when playing for money!

Pattern Analysis

Next, we looked at hand patterns to see which particular patterns achieved Mah Jongg more often. For the purpose of our analysis, and to make the list more manageable, we grouped patterns together. First, we ignored the order of groupings (e.g., we treated the "pung-kong pung-kong" pattern of CR/2 the same as the "kong-pung kong-pung" pattern of 369/6). We also lumped together pairs and single tiles, since these tiles have similar attributes (i.e., a player can't call for an exposure or use a joker). So, we treated the "pair-kong-kong-kong" of CR/5 the same as the "kong-kong-single-single-kong" of 2468/1. Therefore, the patterns on the card are grouped by number of quints, number of kongs, number of pungs and number of single/pair tiles. We also ignored the Singles and Pairs section of the card, as the patterns found here are not statistically significant.

The results are shown below.

Wins by Pattern Type 

Our analysis shows that the "2 kongs + 2 pungs" pattern is by far the most successful (with 52.3% of overall wins). This makes sense since this particular pattern is quite prominent on the 2023 card, plus it is easier to achieve as players can call discards and use jokers in all groupings.

The second most successful pattern is "1 kong, 2 pungs and 4 single or pair tiles" (19.5%). These patterns are also quite popular, but more difficult to achieve due to the single and/or pair tiles required. 

The "3 kongs + (2 singles/pairs)" pattern, represents 17.9% of winning hands. It's interesting to note that, in this particular category of patterns, we find hands that win fairly often (e.g., CR/3, ranked #9 by overall wins) as well as those that are much lower in the rankings (e.g., Addition Hands, ranked #34 and beyond).

Like-Number Hands

Let's now take a look at hands containing like-numbers. We've discussed the individual hands which have achieved the most wins above, but for a given hand, are there certain numbers that are more successful at achieving Mah Jongg? Below are the results for like numbers.

Wins by Hands Containing Like-Numbers, Broken Down by the Individual Number Used

Any Like Numbers, Line 1:

For those who prefer a graphic representation:

Any Like Numbers, Line 2:

As was the case last year, the number 1 appeared in significantly more winning Mah Jongg hands in the Any Like Numbers category than any other number. The next most popular was the number 9. On the other hand, 6 was the least successful number in this category, followed by the number 3. 

As Quints, Line 1 also follows a like-number pattern, we analyzed this hand too. 

Quints, Line 1:

We observe a similar pattern for this Quint hand, with the number 1 being the most successful, followed by the number 9. The number 6 is the least successful.

Analysis & Conclusion for Hands Containing Like-Numbers

If you are aiming for a hand that includes like-numbers, our conclusion is that you will be considerably more successful if you use the number 1 (or 9, to a lesser extent). The least likely to succeed is the number 6. 

A possible explanation is related to how in-demand each tile is. You may recall that in our analysis of the 2023 card, published back in April, we noted that the number 6 appears in more hands than any other number (1074 appearances across all combinations of hands on the 2023 card) and the number 1 is in the least demand (appearing only 519 times across all hand combinations). This results in significantly less competition for 1s than for 6s and, therefore, more chances of successfully gathering 1s in order to achieve Mah Jongg.

Additionally, the number 9 makes 765 appearances across all hand combinations and is in third place as the least demanded tile, just behind the number 8 (which makes 762 appearances). 

This is important information as it could significantly aid your decision-making during the crucial Charleston phase of the game. For instance, if you have multiples of 1s and also 6s in your hand and you're trying to decide which way to go, focusing on 1s is definitely more likely to result in a successful outcome! Also, if you don't have 1s but you do have 9s, then it might be in your best interests to use these if you can! 

Consecutive Runs

Let's now turn our attention to hands that contain a run of consecutive numbers (including hands outside the Consecutive Run section of the card). The results are shown below.

Wins by Hands Containing Consecutive runs

Consecutive Run, Line 1

Here we see that the 5-9 version of this hand achieves Mah Jongg more often (by a margin of 9 basis points) compared to the version using numbers 1-5. 

Consecutive Run, Line 2

Once again, for this pung-kong pung-kong hand, we see Mah Jongg being achieved significantly more often when the hand starts with the number 1, or ends with the number 9.

Consecutive Run, Line 3

Even when a hand is constructed of just two consecutive kongs, those hands starting with the number 1 or ending with the number 9 are still more successful at achieving Mah Jongg. An interesting point to note with this particular hand, is that using the combination of numbers 1 and 2 is far more likely to be successful than using numbers 2 and 3. This would suggest that the number 3 is in higher demand and, therefore, not as easy to gather.

Consecutive Run, Line 4

Once again, the results for this multi-suit hand show that including either the number 1 or 9 will achieve the best outcome. Following on from previous results, hands that include the numbers 2, 3 or 6, without also including the numbers 1 or 9, are the least successful.

Consecutive Run, Line 5 - 1-suit version

At this point, we're beginning to sound like a broken record! As you can see above, this three kong Consecutive Run hand (in one suit) is more likely to be successful if a player includes either the number 1 or 9 in their run. Once again, using the numbers 2 and 3, without the number 1, is the least likely to be successful.

Consecutive Run, Line 5 - 3 suit version

Once again, using the numbers 1 or 9, in the three suit version of this hand, has proven to be the most successful at achieving Mah Jongg.

Consecutive Run, Line 6

The pung-kong pung-kong two-number run follows the same pattern, with the numbers 1 and 9 dominating. Also, as seen previously, the data shows that using the number 2, without the number 1, results in the least successful outcome, followed closely by the numbers 3 and 6.

Consecutive Run, Line 7

Well, the results here make total sense when we compare them to previous charts. This particular hand ends in 2 pungs of identical numbers, and ending with the number 9 results in the most successful outcome. However, starting the run with the number 1 is still more successful than any of the other numbers (apart from 7, of course).

Consecutive Run, Line 8

The concealed hand in the Consecutive Run section follows the same pattern as all the others. A run that includes the number 1 or the number 9 results in the most successful outcome. 

Quints, Line 3

The two-number Quint run, also follows the exact same pattern, with runs including the numbers 1 or 9 being the most successful.

Winds/Dragons Line 2a

Winds/Dragons Line 2b

Both versions of this three-number run also follow the same pattern discussed above, with runs that include the number 1 or 9 being the most successful at achieving Mah Jongg, over any other choice of run.

Winds/Dragons, Line 7

In this particular Winds-Dragons hand, including the number 1 in the run will lead to far more success than using any other number. Using the number 9 is the next most successful choice. 

Singles and pairs, Line 2

Well, the chart above really speaks for itself! Including the number 1 in this Singles and Pairs hand is far more likely to result in Mah Jongg than starting the run with any other number. Including the number 9 in the run results in the next most successful outcome, but significantly less often.

Singles and Pairs, Line 5

And, just to really drum this home... in this 7-pair hand, runs that include either the number 1 or the number 9 are going to be the most successful!  

Analysis & Conclusion for Hands that Include Consecutive Numbers

Although there are some differences in the distributions for each of the hands analyzed above, the shape for each chart is very similar. Low and high-end runs ended up being the most successful at achieving Mah Jongg, in every single case. This may be counter-intuitive, since it would seem that building a run somewhere in the middle, and having the opportunity to build on either end, would have more likelihood of achieving success. Perhaps this is actually why these hands end up failing more often? Maybe there is just too much competition for the same tiles. Whereas the extreme low and high-end numbers are less in demand. We'd love to know how you interpret these results!

Little Odds vs Big Odds

Other than lines 1, 7 and 8, hands in the 13579 section of the card offer 2 options: 1-3-5 (little odds) or 5-7-9 (big odds). We delved into the data to discover which version achieved Mah Jongg more often. Here are the results.

Percentage of Overall Wins for Hands in the 13579 Category - Little Odds vs Big Odds

Analysis & Conclusion for Little Odds vs Big Odds

Interestingly, in every case, the 5-7-9 version of the hand was more successful than the 1-3-5 version (often by a wide margin). This would suggest that there is less competition for tiles used for the big odds hands. This makes sense as one of the tiles in little odds, the 3, is specifically used in two other sections of the card: 2023 and 369. Plus, it may be used in the Winds hands that contain the year and potentially in the 3+3=6 Addition Hand. Whereas, for big odds, only the 9 is specifically used in another section: 369. 

Other Flexible Hands

Finally, we analyzed additional hands that contain a flexible element, which did not belong to the Any Like Numbers or Consecutive Run sections of the card.

2468, Line 2 (flexible kongs)

This hand achieves the most success when the number 8 is used for the flexible kongs. This makes sense when we consider that the number 8 is less likely to be required for any other section of the card, so there is just less competition for it. In line with our previous findings, the number 6 is the least likely to achieve success.

369, Line 5 (flexible kongs)

Once again, the number 9 is the front-runner by a wide margin, with the number 6 achieving success the least often. 

Analysis & Conclusion for Hands Containing a Flexible Component

Again, it is interesting to note that hands using 9s in the flexible 369 hand, achieved success the most often. For the flexible evens hand, 8 turned out to be the most successful number, with 6 being the least successful (which is in line with our earlier analysis).

Overall Conclusion

It's very clear from our analysis that certain tiles are in less demand and are, therefore, easier to gather. Namely the number 1 and 9. Using either of these tiles in a hand results in Mah Jongg being achieved significantly more often. That's not to say that Mah Jongg can't be achieved with other numbers, it most certainly can. However, given the opportunity, it's in a player's best interest to utilize these tiles as they are in less demand overall, and will lead to a far higher likelihood of achieving Mah Jongg before an opponent.

Hands that include the numbers 2, 3 and 6, when not accompanied by either the number 1 or 9, are the least successful at achieving Mah Jongg. This is mainly due to the additional competition for these particular numbers between players at the table.

With regards to winning patterns, hands that contain 2 pungs and 2 kongs are by far the most successful (with 52.3% of overall wins). This makes sense since this particular pattern is quite prominent on the 2023 card, plus it is easier to achieve as players can call discards and use jokers in all groupings. Hand patterns that contain singles and/or pairs of any variety are far less likely to be successful (achieving only 19.5% of overall wins, or less). As expected, the flexibility of hands where all parts can either be exposed or contain jokers, certainly helps a player to achieve Mah Jongg more often.

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We hope you've enjoyed geeking out with us again, and that these insights may help inform some of your decisions during the game (and result in more wins!). As usual, we welcome your feedback and suggestions for future articles (please email us at info@ilovemahj.com).

Mahj on, everyone!

Philippe & Julie
ilovemahj.com

November 2023