Crack the 2024 National Mah Jongg League Card

Hands That Lead to Victory!

As we pass the halfway mark in the American Mah Jongg year, it's a great moment to take stock of how the NMJL's 2024 card is shaping up!

In this article, we'll dive into a mid-year analysis of the NMJL 2024 card, offering statistical insights that enhance our understanding of Mah Jongg strategy and gameplay. Specifically, we've analyzed winning hands to answer key questions, such as:

• What percentage of games result in a win vs. a wall game?
• Which sections of the card have achieved the most wins?
• Which hands have proven the most successful?
• Which groupings/patterns have been the most successful?
• Which numbers are driving the highest win rates in hands containing like-numbers?
• Which numbers are driving the highest win rates in hands containing consecutive numbers?
• Are big odds outperforming little odds?
• Which numbers are achieving the most wins for "flexible" hands?

Our analysis is based on data from millions of games played on the I LOVE MAHJ platform, using the NMJL 2024 card, between late March and mid-October 2024. This includes games played by both human players and computer bots. It's important to note that bot-played games offer a unique advantage - they introduce no bias towards "favorite" hands or card sections, allowing for a more objective look at winning trends. We'll explore this point in more detail later in the analysis.

Notation/Convention

Before we dive in, let's clarify the way we'll represent hands in this article.

Hands will be labeled as <section>/<line>.

• The section will be abbreviated by its initials (e.g. 2024, ALN, CR)
• When the card shows 2 versions for a particular hand, the first will be marked "a" and the second "b"

For example:

• ALN/1 represents Any Like Numbers, line 1
• CR/3b represents the second version of Consecutive Run, line 3

Wins vs Wall Games

So far this year, 93% of games have ended in Mah Jongg, with only 7% resulting in a wall game. In comparison, wall games in previous years typically hovered around 10-11%, so we've seen a noticeable drop in wall games when playing with the 2024 card.

This aligns with our predictions in the 2024 Card Analysis article, published in April. The 2024 card offers a significantly higher number of playable hands (1683 playable hands, compared to 756 in 2023) and increased flexibility, allowing players to switch strategies more easily during the game. As a result, we conclude that the 2024 card is easier than those from previous years, which explains the higher rate of Mah Jongg wins and the lower occurrence of wall games.

Section Popularity

Let's start with a high-level overview by examining the popularity of each section of the card. Below, we break down the overall proportion of winning hands from each section, presented as percentages. First, we'll display the raw data in a table for clarity, followed by a graphical representation to help highlight trends and patterns in a more visual format.

Percentage of Wins per Section of the NMJL 2024 Card

As in previous years, the Consecutive Run (CR) section led the pack with the most winning hands, accounting for 28.6% of the total. This dominance is likely due to the flexibility these hands offer. Coming in second, the Winds-Dragons (WD) section contributed 21.1% of winning hands during the analysis period, while Any Like Numbers (ALN) claimed third place with 19.2%.

What's particularly interesting this year is the smaller percentage gap between the top section and the next two. Stats for the top 3 sections of the 2023 card were as follows: CR=45%, WD=16.4%, 13579=9.8%. This narrowing gap can be attributed to the fact that both the WD and ALN sections include less challenging hands with improved switchability on the 2024 card. The ALN section, in particular, has grown significantly in popularity (19.2% vs. 5.9% in 2023), as all hands are played open on the 2024 card, unlike in 2023, where the final hand was concealed.

The Singles & Pairs section had the fewest winning hands, which comes as no surprise given the notorious difficulty of completing hands in this category.

In the middle of the pack were the 13579 and 2468 sections, contributing 10% and 8.8% of wins, respectively.

Interestingly, Addition Hands accounted for only 0.9% of total wins. While it's possible that human players may be overlooking this section, as noted earlier, bots are free from such biases. It seems that the requirement for three same-suit kongs, with numbers that can't easily switch to other sections of the card, makes these hands more challenging than their 25-point value would suggest!

Hand Popularity

Now, let's dive a little deeper and examine the specific hands that players have won with most frequently. Topping the list is ALN/1, which accounted for 11% of overall wins - somewhat surprising since the top winning hand is typically found in the Consecutive Run section. Following closely, CR/7b (the two-suited pung-pung-kong-kong hand) came in second at 9.8%, which is logical due to the hand's flexibility.

In third and fourth place were WD/3a and WD/3b, both featuring a consecutive number element, which likely contributed to their popularity and success.

At the other end of the spectrum, the least-winning hand was SP/6 (commonly referred to as the "Big Hand"), representing only 0.01% of total wins. However, this is still a notable improvement compared to previous years' "Big Hands" (0.005% in 2023), as the 2024 version only requires two sets of year tiles instead of three, making it somewhat easier to achieve.

Below, we've listed all the hands from the 2024 card, ranked from the highest to the lowest number of wins. This data reflects 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 variation of each hand.

Percentage of Overall Wins by Hand, Ranked Most to Least

As we observe each year, there remains a clear disconnect between the point value assigned to each hand and the actual difficulty of achieving Mah Jongg with that hand. If we use the percentage of overall wins as an indicator of a hand's ease of completion, it becomes apparent that not all hands are created equal.

In theory, hands that are allocated the same number of points on the card should represent similar levels of difficulty. However, the data tells a different story. This variation raises interesting questions about the balance between point value and hand complexity, further highlighting the nuances of strategy when playing Mah Jongg.

The following examples illustrate this inconsistency: 

• ALN/1, ranked as the #1 winning hand, and 2468/5 (both versions), ranked at #54 and #56, offer a stark example of point-value disparity. Despite both being 25-point hands, ALN/1 accounts for 11% of overall wins, while 2468/5a and 5b represent less than 0.4% (2468/5a and b accounting for 0.19% and 0.17% respectively). This difference is significant and raises questions about how well the point values reflect actual difficulty
• Similarly, concealed hands tend to achieve Mah Jongg about ten times less frequently than exposed hands, which suggests that these hands might be ten times harder to complete. Yet, they're only worth 5 or 10 extra points, which does not adequately reflect the difficulty of achieving Mah Jongg with these hands
• Another curious case is Consecutive Run, Line 6, which ranks #15 and has a point value of 30. Despite this, it appears easier to achieve than many 25-point hands. Several other 30-point hands highlighted in the table above also outperformed some 25-point hands, showing that the challenge of the hand doesn't always align with its reward
• Perhaps the most striking point mismatch is with Q/2. Although this hand requires number quints, along with Jokers, its flexibility makes it far easier to achieve than its 40-point value suggests. It ranks #46, outperforming many hands valued at 30 and even 25 points

Pattern Analysis

Next, we delved into the specific hand patterns to identify which ones led to Mah Jongg more frequently. To streamline our analysis, and make the data easier to digest, we grouped similar patterns together. Notably, we disregarded the order of these groupings - for instance, we treated the "pung-pung-kong-kong" pattern from CR/7 the same as the "kong-pung-kong-pung" pattern from WD/2.

For the purpose of our analysis, the patterns on the card have been organized based on the number of quints, kongs, pungs, pairs, and singles involved. The results of our analysis are presented below.

Wins by Pattern Type

Our analysis reveals that the "2 kongs + 2 pungs" pattern stands out as the most successful, accounting for nearly 58% of overall wins. This high success rate is not surprising, given the prominence of this pattern on the 2024 card and its relative ease of completion; players can call discards and utilize Jokers across all groupings.

In second place is the "1 kong + 2 pungs + 2 pairs" pattern, which captures 17% of overall wins. While this pattern is also commonly featured on the card, it poses a greater challenge due to the necessity of incorporating pairs.

The "3 kongs + 2 singles" pattern accounts for around 6% of winning hands. Interestingly, this pattern appears to be slightly easier to achieve than the "3 kongs + 1 pair" (5.4%). This difference may stem from the fact that acquiring two different number tiles is often less challenging than securing two identical tiles. Ultimately, the ease of completing these patterns will depend on whether a player has their singles or pairs sufficiently covered when pursuing these hands.

Like-Number Hands

Now, let's turn our attention to hands that feature like numbers. While we previously examined which individual hands achieved the most wins, it's also important to consider whether specific numbers contribute more significantly to achieving Mah Jongg for a given hand. Below, we present the results for all hands containing identical numbers, highlighting which numbers have proven to be the most successful in securing wins.

Any Like Numbers, Line 1: Broken Down by the Individual Number Used

For those who prefer a graphic representation:

Any Like Numbers, Line 2: Broken Down by the Individual Number Used

Any Like Numbers, Line 3: Broken Down by the Individual Number Used

Consistent with trends from previous years, the number 1 emerged as the standout favorite in winning Mah Jongg hands within the Any Like Numbers category, outpacing all other numbers. The second favorite was the number 9, which also showed strong performance. In contrast, the number 6 lagged behind as the least successful, closely followed by the number 4 in this particular category.

Since Winds-Dragons, Line 7 also adheres to a like-number pattern, we included it in our analysis here.

Winds-Dragons, Line 7: Broken Down by the Individual Number Used

We observe a similar trend with the Winds-Dragons, Line 7 hand, although the results aren't as pronounced as in the Any Like Numbers section. Once again, the number 1 comes out on top as the most successful, followed by the number 9. Conversely, the number 6 remains the least successful, closely followed by the number 4, mirroring the results from the Any Like Numbers category.

Conclusions for Hands Containing Like-Numbers

If you are aiming for a hand that includes like-numbers, our analysis strongly suggests that you'll have a much higher chance of success using the number 1 (or 9, to a lesser extent). The number 6, on the other hand, is the least likely to lead to a win.

A possible explanation lies in tile demand. In our 2024 card analysis from April, we pointed out that the number 6 appears in more hands than any other number (2151 appearances across all hand combinations), whereas the number 1 is in the least demand (appearing only 1446 times). This means there's significantly less competition for 1s than for 6s, making it easier to collect 1s for a winning hand.

Similarly, the number 9 shows up 1704 times across all hands, making it the second least in demand tile.

This insight could be a game-changer, especially during the Charleston phase when critical decisions are made. For example, if you have multiples of 1s and 6s in your hand, leaning towards 1s is more likely to yield a win. Of course, if they're in the same suit, you could always aim for the first line in the Addition Hands section! Likewise, if you're short on 1s but have several 9s, it might be wise to prioritize these for your target hand.

Consecutive Runs

Next, let's shift our focus to hands that feature a run of consecutive numbers (not limited to hands in the Consecutive Run section). Below, we present the results of our analysis, detailing the success rates of these hands.

Consecutive Run, Line 1

Here, we observe that the version of this hand using numbers 5-9 achieves Mah Jongg more frequently than the 1-5 version, with a margin of 12.4 basis points. This mirrors the pattern from last year, but the gap is even larger this time around (there was a margin of 9 basis points in 2023), indicating increased success with higher-numbered tiles.

Consecutive Run, Line 2

Once again, we observe that Mah Jongg is achieved significantly more often when the hand starts with the number 1 or ends with the number 9. This reinforces the trend we've seen across other hands, where these numbers consistently prove to be more successful.

Consecutive Run, Line 3a

Consecutive Run, Line 3b

We again observe that hands starting with the number 1 or ending with the number 9 are more successful at achieving Mah Jongg. The difference is even more pronounced for this particular hand compared to other hands containing a consecutive run. This is likely due to the fact that this hand requires 3 kongs of number tiles, making it easier to complete when using the number 1 or 9, tiles that are less in-demand. 

Consecutive Run, Line 4

The results for the multi-suit hand (CR/4) once again show that including either the number 1 or 9 yields the highest success rates. Interestingly, when comparing the two number sets required for this hand (which involve two same-number runs), using 7-8-9 is significantly more successful than 1-2-3. This difference is likely due to the kong being 9s for the 7-8-9 version, whereas the 1-2-3 version requires a kong of 3s, with only a single 1 needed. 

Consecutive Run, Line 5

At this point, we're starting to sound like a broken record! As you can see, this hand is more likely to be successful if a player includes either the number 1 or 9 in their run. The reason the results are less pronounced here is likely because this hand's groupings consist of pairs and pungs, rather than kongs.

Consecutive Run, Line 6

The results here align well with the trends we've observed in previous charts. This particular hand (CR/6) ends with two pungs of identical numbers, and as expected, ending the run with the number 9 leads to the most successful outcomes. Interestingly, starting the run with the number 1, despite only requiring a single tile, proves to be more successful than starting with numbers 2 through 5. However, the distribution is more balanced compared to other hands we've analyzed. That said, it's worth noting that a run starting with the number 3 and ending in two pungs of 6s is significantly less likely to succeed than other runs.

Consecutive Run, Line 7a

Consecutive Run, Line 7b

The usual pattern emerges again, with runs that end in 9 or start with 1 being the most successful. Using 9s offers a slight edge in achieving success since they form the "kong" element in this hand, whereas 1s are always part of the "pung" element. Runs that begin with numbers 3 or 4 are the least likely to succeed, due to the number 6 falling in the "kong" position, making it more challenging to complete the hand.

Consecutive Run, Line 8

The concealed hand in the Consecutive Run section mirrors the trends seen in previous hands, where a run including the number 1 or number 9 yields the most successful outcome. However, the distinction is even more pronounced in this case, with the number 1 demonstrating significantly higher success. This can be attributed to the hand's pattern: it requires two consecutive pungs followed by a pair. Consequently, a hand starting with the number 1 necessitates two pungs of 1s, while a hand ending in 9s only requires one pair of 9s, complemented by pungs of 7s and 8s.

Since a couple of hands in the Quints category adhere to the consecutive run pattern, we have included them in this section.

Quints, Line 1

This three-number Quint run exhibits the same trend, with runs that include the numbers 1 or 9 achieving the highest success rates.

Quints, Line 3

Quints, Line 3, presents an intriguing anomaly. While the data aligns with the prevailing pattern (where including 1s or 9s yields the most successful outcome), it's important to note that 1s can only occupy the "pair" position, and 9s are confined to the "quint" position for this particular hand. Therefore, it's quite surprising to observe that the combination of "1 and 2" achieves similar success to that of "8 and 9." We would love to hear your thoughts on this unexpected finding!

Winds-Dragons, Line 3a

Winds-Dragons, Line 3b

Both versions of this two-number run exhibit the same pattern we've discussed, yet this time, the number 1 demonstrates significantly greater success than the number 9. Perhaps this suggests that gathering a kong of 2s is somewhat easier than collecting a kong of 8s? What are your thoughts on why the number 1 is the runaway winner for this particular hand?

Winds-Dragons, Line 5a

Winds-Dragons, Line 5b

Once again, hands that include the numbers 1 or 9 prove to be the most successful. Conversely, it's clear that hands featuring both 4s and 6s are among the least successful.

Singles & Pairs, Line 5

This hand (S&P/5) yields an intriguing result. While including 1s or 9s leads to the best outcomes, the 5 through 9 run stands out as the most successful overall. As anticipated, runs that incorporate both 4s and 6s are the least successful.

Conclusions for Hands that Include Consecutive Numbers

While there are some variations in the distributions for each hand analyzed above, the overall shape of each chart exhibits a striking similarity. In every case, both low and high-end runs proved to be the most successful in achieving Mah Jongg. This finding might seem counterintuitive; one might assume that constructing a run in the middle, allowing for the possibility of building on either end, would enhance the chances of success.

This raises an interesting hypothesis: perhaps the increased competition for the same tiles in those middle ranges contributes to their higher failure rates. In contrast, the extreme low and high-end numbers face less demand, leading to greater availability. We'd love to hear your thoughts on this interpretation of the data!

Little Odds vs Big Odds

Most hands in the 13579 section of the card present players with two options: the 1-3-5 combination (little odds) and the 5-7-9 combination (big odds). We analyzed the data to determine which version achieves Mah Jongg more frequently and present the results below.

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

Analysis & Conclusion for Little Odds vs Big Odds

The results of our analysis reveal a mixed performance between little odds (1-3-5) and big odds (5-7-9), with various factors influencing their success rates:

• Line 2: The big odds version performs slightly better, which aligns with expectations. This success can be attributed to the number 9 occupying the "kong" position, making it slightly more advantageous for achieving Mah Jongg. In the little odds version, the number 1 is in the "pung" position, meaning fewer low-demand tiles are required. As a result, more of the high-demand tiles are needed, which could make it more challenging to complete the hand
• Line 3: Here, little and big odds are virtually equal in success rates. This balance can be attributed to the position of the tiles, 1s in the "pair" position creates a more challenging grouping to complete, whereas 9s in the "kong" position facilitates easier completion. Interestingly, the lower demand for the pair tiles in the little odds version may serve as that hand's saving grace, contributing to the similar success rates observed between the two configurations
• Line 5: The little odds version requires only a single 1, while the big odds version does not require any 9s. This suggests that kongs made up of 3s and 5s are more accessible to players than kongs consisting of 5s and 7s
• Line 6: Similar to Line 2, the big odds version fares better, reinforcing the trend that 1s in the "pair" position hinder success compared to 9s in the "pung" position
• Line 7: The big odds version significantly outperforms the little odds version. Both require either a pung of 1s or 9s, indicating their demand for less popular tiles is similar. Both hands also require a pung of 5s. However, the little odds version requires 3s in all three suits (pair, pung, pung), while the big odds version requires 7s in all three suits. 7s appear to be easier to collect than 3s, which is in alignment with our findings for ALN Line 1 and 2

In summary, the success of hands in the 13579 section often hinges on the positioning of numbers and their respective demand, influencing how easily players can form the necessary combinations to achieve Mah Jongg.

Flexible Hands

In our final analysis, we explored hands that incorporate a flexible element, yet fall outside the Any Like Numbers and Consecutive Run sections of the card. These hands often allow for greater adaptability in strategy, as players can opt to utilize a particular number to achieve Mah Jongg. By examining the performance of these flexible hands, we aim to uncover insights into their success rates and the factors that contribute to their effectiveness.

Flexible Hand Analysis: Kongs of 2s or 4s

2024, Line 3 (flexible kongs)

For this particular hand, there is not a significant difference between the two options, kongs of 2s or kongs of 4s, in terms of achieving Mah Jongg. Both options present viable pathways for success, allowing players flexibility in their tile selection.

Flexible Hand Analysis: Pungs of 3s, 6s, or 9s 

369, Line 2 (flexible pungs)

This particular hand allows for the pungs to consist of either 3s, 6s, or 9s, providing players with several options to achieve Mah Jongg. However, as 6s are the most in-demand tile this year, choosing to use 6s would lead to the least successful outcome. However, 9s only just beat 3s to the top spot for this hand.

369, Line 4 (flexible pungs)

Unsurprisingly, 6s are the least successful option. In contrast, 9s consistently prove to be the most successful choice for achieving Mah Jongg with this hand, their relatively lower demand compared to 6s contributing to their success rate.

In summary, while this hand offers flexibility in choosing pungs, the underlying demand for 6s significantly impacts the likelihood of success. Players may find it advantageous to focus on 9s, and to a lesser extent 3s, when attempting this hand.

Take Aways

Key Findings on Winning Hands and Tile Success

Our analysis aimed to identify which tile numbers lead to the most successful Mah Jongg outcomes. It is clear that certain tiles, specifically 1s and 9s, are less in demand and, therefore, easier to gather. Incorporating either of these tiles into a hand significantly increases the likelihood of achieving Mah Jongg. While it's certainly possible to win with other numbers, players should prioritize these tiles to enhance their chances of achieving success before their opponents.

Conversely, hands that include 4s and 6s, when not paired with 1s or 9s, tend to be the least successful. This lower success rate is primarily due to the heightened competition for these numbers among players at the table.

In terms of winning patterns, those featuring 2 pungs and 2 kongs are the most successful, accounting for 52.3% of overall wins. This pattern is particularly prevalent on the 2024 card and is easier to achieve, as players can call discards and utilize Jokers in all groupings. Conversely, hand patterns that include single tiles and/or pairs are less likely to lead to victory.

Conclusion

To maximize your chances of achieving Mah Jongg, leverage the potential of the tiles in your hand. If you hold multiples of 1s or 9s, recognize these as your "superpowers" that can propel your hand toward success. Conversely, be cautious with 6s (and, to a lesser extent, 4s ), as these high-demand tiles may hinder your progress.

It is important to note that many of the results published in this article were predicted in the card analysis we provided in April. Specifically, the demand on each individual tile played a pivotal role in determining the potential success of each hand. This is the reason we continue to emphasize that, when analyzing the card, it is essential to count all possible permutations of playable hands (1683), rather than simply relying on the number of hands printed on the card (73).