Mxplainer: Explain and Learn Insights by Imitating Mahjong Agents

Abstract

People need to internalize the skills of AI agents to improve their own capabilities. Our paper focuses on Mahjong, a multiplayer game involving imperfect information and requiring effective long-term decision-making amidst randomness and hidden information. Through the efforts of AI researchers, several impressive Mahjong AI agents have already achieved performance levels comparable to those of professional human players; however, these agents are often treated as black boxes from which few insights can be gleaned. This paper introduces Mxplainer, a parameterized search algorithm that can be converted into an equivalent neural network to learn the parameters of black-box agents. Experiments on both human and AI agents demonstrate that Mxplainer achieves a top-three action prediction accuracy of over 92% and 90%, respectively, while providing faithful and interpretable approximations that outperform decision-tree methods (34.8% top-three accuracy). This enables Mxplainer to deliver both strategy-level insights into agent characteristics and actionable, step-by-step explanations for individual decisions.

1. Introduction

Games play a pivotal role in the field of AI, offering unique challenges to the research community and serving as fertile ground for the development of novel AI algorithms. Board games, such as Go [1] and chess [2], provide ideal settings for perfect-information scenarios, where all agents are fully aware of the environment states. Card games, like heads-up no-limit hold’em (HUNL) [3,4], Doudizhu [5,6], and Mahjong [7], present different dynamics with their imperfect-information nature, where agents must infer and cope with hidden information from states. Video games, such as Starcraft [8], Minecraft [9], and Honor of Kings [10], push AI algorithms to process and extract crucial features from a multitude of signals amidst noise.

Conversely, the advancement of AI algorithms also incites new enthusiasm in games. The work of AlphaGo [11] in 2016 has had a long-lasting impact on the Go community. It revolutionized the play style of Go, a game with millennia of history, and changed the perspectives of world champions on this game [12]. Teaching tools based on AlphaGo [13] have become invaluable resources for newcomers while empowering professional players to set new records [14].

Mahjong, a worldwide popular game with unique characteristics, has gained traction in the AI research community as a new testbed. It brings its own flavor as a multiplayer imperfect-information environment. First, there is no rank of individual tiles in Mahjong; all tiles are equal in their role within the game. A game of Mahjong is not won by beating other players in card ranks but by being the first to reach a winning pattern. Therefore, state evaluation is more challenging for Mahjong players, as they need to assess the similarity and distance between game states and the closest game goals. Second, the game objective in Mahjong is to become the first to complete one of many possible winning patterns. The optimal goal can frequently change when players draw new tiles during gameplay. In fact, Mahjong’s core difficulty lies in selecting the most effective goal among numerous possibilities. Players must evaluate their goals and make decisions upon drawing each tile and reacting to other players’ discarded tiles. This decision-making process often involves situations where multiple goals are of similar distance, requiring trade-offs that distinguish play styles and reveal a player’s level of expertise.

Several strong agents have already been developed for different variants of Mahjong rules [7,15,16]. However, as illustrated in Figure 1, without the use of explainable AI methods [17,18], people can only observe the agents’ actions without understanding how the game states are evaluated or which game goals are preferred that lead to those actions.

In Explainable AI (XAI) [17], black-box models typically refer to neural networks that lack inherent transparency and thus rely on post hoc explanation tools for interpretability [18]. Existing XAI techniques, such as LIME [19] and LMUT [20], struggle to provide both high-accuracy policy approximation and human-intelligible explanations in domains with immense state spaces and non-Markovian characteristics, a gap that becomes critical for analyzing strategic agents in games like Mahjong.

In this paper, we present Mxplainer (M ahjong Explainer), a parameterized classical agent framework designed to serve as an analytical tool for explaining the decision-making process of black-box Mahjong agents, as shown in Figure 1b. Specifically, we have developed a parameterized framework that forms the basis for a family of search-based Mahjong agents. This framework is then translated into an equivalent neural network model, which can be trained using gradient descent to mimic any black-box Mahjong agent. Finally, the learned parameters are used to populate the parameterized search-based agents. We consider these classical agents to be inherently explainable because each calculation and decision step within them is comprehensible to human experts. This enables detailed interpretation and analysis of the decision-making processes and characteristics of the original black-box agents.

Through a series of experiments on game data from both AI agents and human players, we demonstrate that the learned parameters effectively reflect the decision processes of agents, including their preferred game goals and tiles to play. Our research also shows that by delving into the framework components, we can interpret the decision-making process behind the actions of black-box agents.

This paper pioneers research on analyzing Mahjong agents by presenting Mxplainer, a framework to explain black-box decision-making agents using search-based algorithms. Mxplainer allows AI researchers to profile and compare both AI agents and human players effectively. Additionally, we propose a method to convert any parameterized classical agent into a neural agent for automatic parameter tuning. Beyond traditional approaches like decision trees, our work explores the conversion from neural agents to classical agents.

The rest of this paper is organized as follows: We first review the related literature. Next, we introduce the rules of Mahjong and the specific variant used in our study. Then, we provide a detailed explanation of the components of our approach. Following this, we present a series of experiments demonstrating the effectiveness of our method in approximating and capturing the characteristics of different Mahjong agents. Finally, we discuss the implications of our work and conclude with future research directions.

2. Related Works

Explainable AI (XAI) [17] is a research domain dedicated to developing techniques for interpreting AI models for humans. This field encompasses several categories: classification models, generative AI, and decision-making agents. A specific subfield within this domain is Explainable Reinforcement Learning (XRL) [21], which focuses on explaining the behavior of decision-making agents. Explanations in XRL can be classified into two main categories: global and local.

Global explanations provide a high-level perspective on the characteristics and overall strategies of black-box agents, answering questions such as how an agent’s strategy differs from others. Local explanations, on the other hand, focus on the detailed decision-making processes of agents, elucidating why an agent selects action A over B under specific scenarios.

XRL methods can be classified into intrinsic and post hoc methods. Intrinsic methods directly generate explanations from the original black-box models, while post hoc methods rely on additional models to explain existing ones. Imitation learning (IL) [22,23] is a family of post hoc techniques that approximate a target policy. LMUT [20] constructs a U-tree with linear models as leaf nodes and approximates target policies through a node-splitting algorithm and gradient descent. Q-BSP [24] uses a batched Q-value to partition nodes and generate trees efficiently. EFS [25] employs an ensemble of linear models with non-linear features generated by genetic programming to approximate target policies. These methods have been tested and excelled in environments such as CartPole and MountainCar, and others have excelled in the Gym [26]. However, they rely on properly sampled state–action pairs to generate policies and may not be robust to out-of-distribution (OOD) states, which is particularly crucial for Mahjong with its high-dimensional state space and imperfect information.

PIRL [27] distinguishes itself among IL methods by introducing parameterized policy templates using its proposed policy programming language. It approximates the target $\pi$ through fitting parameters with Bayesian Optimization in Markov games, achieving high performance in the TORCS car racing game. Compared to TORCS, Mahjong has far more complex state features and requires encoding action histories within states to obtain the Markov property. Additionally, Mahjong agents must make multi-step decisions from game goal selection to tile picking. Similarly to PIRL, we define a parameterized search-based framework and optimize parameters using batched gradient descent to address these challenges.

3. Mahjong: The Game

Mahjong is a four-player imperfect information tile-based tabletop game. The complexity of imperfect-information games can be measured by information sets, which are game states that players cannot distinguish from their own observations. The average size of information sets in Mahjong is around ${10}^{48}$, making it a much more complex game to solve than Heads-Up Texas Hold’em [28], for which its average information set size is around ${10}^3$. This immense complexity arises from the vast number of possible tile distributions, hidden player hands, and the long sequence of interdependent decisions involving drawing, discarding, and claiming tiles over multiple rounds. To facilitate the readability of this paper, we highlight terminologies used in Mahjong with bold texts, and we distinguish scoring patterns (fans) by italicized texts.

In Mahjong, there are a maximum of 144 tiles, as shown in Figure 2A. Despite its plethora of rule variants, Mahjong’s general rules are the same. On a broad level, Mahjong is a pattern-matching game. Each player begins with 13 tiles only observable to themselves, and they take turns to draw and discard 1 tile until one completes a game goal with a 14th tile. The general pattern of 14 tiles is four melds and a pair, as shown in Figure 2C. A meld can take the form of Chow, Pung, and Kong, as shown in Figure 2B. Apart from drawing all the tiles by themselves, players can take the tile just discarded by another player instead of drawing one to form a meld, called melding, or declare a win.

Official International Mahjong

Official International Mahjong stipulates Mahjong Competition Rules (MCRs) to enhance the game’s complexity and competitiveness and weaken its gambling nature. It specifies 80 scoring patterns with different points, called “fan”, ranging from 1 to 88 points. In addition to the winning patterns of four melds and a pair, players must have at least eight points by matching multiple scoring patterns to declare a win.

Specific rules and requirements for each pattern can be found in  [29]. Of 81 fans, 56 are highly valued and called major fans since most winning hands usually consist of at least one. The standard strategy of MCR players is to make game plans by identifying several major fans closest to their initial set of tiles. Then, depending on their incoming tiles, they gradually select one of them as the terminal goal and strive to collect all remaining tiles before others do. The exact rules of MCR are detailed in Official International Mahjong: A New Playground for AI Research [28].

4. Methods

We first introduce the general concepts of Mxplainer and then present the details of the implementations in the following subsections. To facilitate readability, we use uppercase symbols to indicate concepts, and lowercase symbols with subscripts indicate instances of concepts.

Figure 3 presents the concept overview of Mxplainer. We assume that the search-based nature of F is explainable to experts in the domain, such as Mahjong players and researchers. Within F, there are parameters $\mathsf{\Theta }$ that control the behaviors of F. To explain a specific target agent $\mathsf{\Psi }$, we would like the behaviors of F to approximate those of $\mathsf{\Psi }$ as closely as possible. In order to automate and speed up the approximation process, we convert a part of F that contains $\mathsf{\Theta }$ into an equivalent neural network representation, and we leverage supervised learning to achieve the goals.

F consists of Search Component $SC$ and Calculation Component $CC$, denoted as $F=SC|CC$. $SC$ searches and proposes valid goals in a fixed order. Next, $CC$ takes groups of manually defined parameters $\mathsf{\Theta }$, each of which carries meanings and is explainable to experts, and makes decisions based on the search results from $SC$, as shown in Figure 4.

$CC$ can be converted into an equivalent neural network N, for which its neurons are semantically equivalent to $\mathsf{\Theta }$. $SC|N$ can approximate any target agents $\mathsf{\Psi }$ by fitting $\mathsf{\Psi }$’s state–action pairs. Since $\mathsf{\Theta }$ is the same for both $CC$ and N, learned $\widehat{\mathsf{\Theta }}$ can be put back into $CC$ and explains actions locally through step-by-step deductions of $SC|CC$. Moreover, by normalizing and studying $\mathsf{\Theta }$, Mxplainer is able to compare and analyze agents’ strategies and characteristics.

The construction of F and the design of parameters $\mathsf{\Theta }$ are problem-related, as they reflect researchers’ and players’ attention to the game’s characteristics and the game agents’ strategies. The conversion from $CC$ to N and the approximation through supervised learning is problem-agnostic and can be automated. In the Mxplainer framework, the Search Component ($SC$) of F is fixed and shared across all agents, while the behavior of the Calculation Component ($CC$) and its neural equivalent N is determined by the parameters $\mathsf{\Theta }$, which are tuned to mimic different target agents $\mathsf{\Psi }$.

4.1. Parameters $\mathsf{\Theta }$ of Framework F

For $\mathsf{\Theta }$, we manually craft three groups of parameters to model people’s general understanding of Mahjong: ${\mathsf{\Theta }}_{tile}$, ${\mathsf{\Theta }}_{fan}$, and ${\mathsf{\Theta }}_{held}$.

${\mathsf{\Theta }}_{tile}$ is used to break ties between tiles, and different players may have different preferences for tiles.

${\mathsf{\Theta }}_{fan}$ is designed to break ties between goals when multiple goals are equally distant from the current hand. There are more than billions of possible goals in Mahjong, but each goal consists of fans. Thus, we use the compound of preferences of fans to sort goals. We hypothesize that there exists a natural order of difficulty between fans, which implies that some are more likely to achieve than others [29]. However, such an order is impossible to obtain unless there is an oracle that always gives the best action. Additionally, players break ties based on their inclinations towards fans. Since the natural difficulty order and players’ inclinations are hard to decouple, we use ${\mathsf{\Theta }}_{fan}$ to represent their products. Consequently, ${\mathsf{\Theta }}_{fan}$ between different fans for a single player cannot be compared directly, but ${\mathsf{\Theta }}_{fan}$ for the same fans between different players reflect their comparative preferences.

${\mathsf{\Theta }}_{held}$ denotes the linear weights of a heuristic function that approximates the probability that a tile is held by other players. The linear function takes features from local game states, including the number of total unshown tiles, the length of game steps, and the unshown tile counts of the neighboring tiles. Unshown tiles are those not visible to the agent, encompassing tiles in the wall and in opponents’ hands. The agent maintains a probability distribution over these tiles, modeled as a dictionary U, where each key is a tile type and its value is the estimated number of remaining copies. The components and the usage of ${\mathsf{\Theta }}_{held}$ will be discussed in detail in the following sections.

4.2. Search Component $SC$ of Framework F

In Mahjong, Redundant Tiles, R, refer to the tiles in a player’s hand that are considered useless for achieving their game goals. In contrast, Missing Tiles, M, are the ones that players need to acquire in future rounds to complete their objectives. Following this, the Shanten Distance is defined as $D=\left|M\right|$, which conveys the distance between the current hand and a selected goal.

Here, we define a game goal as $G=(M,R,\mathsf{\Phi })$, since when both M and R are fixed, a game goal is set, and its corresponding fans $\mathsf{\Phi }$ can be calculated. Each tile $t\in M$ additionally has two indicators, $i_p$ and $i_c$, which determine if it can be acquired through melding from other players. $i_p$ is true if the player already owns two tiles in the Pung, and the same happens to $i_c$ and Chow. Thus, $\forall t\in M$, it has $(t,i_p,i_c)$.

Through dynamic programming, we can efficiently propose different combinations of tiles and test if they satisfy MCR’s winning condition. We can search all possible goals, but not all goals are reasonable to be considered as candidates. In practice, only up to 64 goals, G, are returned in ascending Shanten Distances D, since in most cases, only the closest goals are important for decisions, and they are usually less than two dozen.

However, only the presence of goals is not enough. MCR players also need to consider other observable game information to jointly evaluate the value of each goal G, such as other players’ discard history and unshown tiles. For our framework F, we only consider unshown tiles U, a dictionary keeping track of the number of each tile that is not shown through observable information.

Thus, the Goal Proposer P accepts game state information S and outputs $\left(\right[G],U)$ such that $0<\left|\right[G\left]\right|\le 64$, as shown in Figure 4A. In most cases, goals, G, in $\left[G\right]$ can be split into several groups. Different groups contain different fans $\mathsf{\Phi }$ and represent different paths to win, while the goals within each group have different tile combinations for the same fans $\mathsf{\Phi }$.

4.3. Calculation Component $CC$ of Framework F

Calculation Component $CC$ of Framework F consists of Value Calculator C and Decision Selector $DS$. $CC$ contains three groups of tunable parameters ${\mathsf{\Theta }}_{fan}$, ${\mathsf{\Theta }}_{held}$, and ${\mathsf{\Theta }}_{tile}$ that control the behavior of Value Calculator C and Decision Selector $DS$. In all, these three groups of parameters, ${\mathsf{\Theta }}_{fan}$, ${\mathsf{\Theta }}_{held}$, and ${\mathsf{\Theta }}_{tile}$, are similar to parameters of neural networks; they are the key factors that control the behaviors of agents derived from framework F.

The Value Calculator C takes the results of the Goal Proposer P, $\left(\right[G],U)$ as input and estimates the value for each goal G. The detailed algorithm of C is shown in Algorithm 1. Simply put, C multiplies the probability of successfully collecting each missing tile of a proposed goal as its estimated value.

The value estimation in the Value Calculator C is governed by two parameter groups: ${\mathsf{\Theta }}_{fan}$ and ${\mathsf{\Theta }}_{held}$. The probability of acquiring a required tile t (t denotes a generic tile, and $t\in X$ indicates that tile t belongs to a set X) is decomposed into two components: drawing it from the wall or melding it from another player’s discard.

The probability of drawing tile t is modeled as follows:

$$P_{draw}\left(t\right)=U\left[t\right]/\Sigma \left(U\right)·Z·{\mathsf{\Theta }}_{held}$$

This formulation reflects the assumption that the likelihood of drawing t is proportional to the number of its remaining unshown copies $U\left[t\right]$ and inversely proportional to the total number of unshown tiles $\Sigma \left(U\right)$. Furthermore, the term $Z·{\mathsf{\Theta }}_{held}$ accounts for the effect of other players potentially holding the tile, where Z denotes a feature vector derived from local game state attributes, and ${\mathsf{\Theta }}_{held}$ serves as a set of linear weights:

$$Z:\{\Sigma \left(U\right),{\displaystyle \frac{1}{\Sigma \left(U\right)}},1-{\displaystyle \frac{1}{\Sigma \left(U\right)}},L,{\displaystyle \frac{1}{L}},1-{\displaystyle \frac{1}{L}},U[t-2]:U[t+2],bias\}$$

Algorithm 1 Value Estimation for A Single Goal

Input: Goal G: < missing tiles M:$<t$, Chow indicator $i_c$, Pung indicator $i_p$>, fan list $F>$, unshown dict U, game length L Parameter: ${\mathsf{\Theta }}_{fan}$, ${\mathsf{\Theta }}_{held}$ Output: Estimated value for goal G   1: Initialize value $v\leftarrow 100$   2: for all missing tile $m\in M$ do   3:      // Construct local tile feature $x_m$ from game length L,   4:      // and remaining adjacent tile count U.   5:      $x_m\leftarrow U,L$   6:      // Calculate probability of drawing m and others discarding m   7:      $p_{draw}\leftarrow U\left[m\right]/sum\left(U\right)\ast {\mathsf{\Theta }}_{held}\ast x_m$   8:      $p_{discard}\leftarrow U\left[m\right]/sum\left(U\right)$   9:      $source\leftarrow 0$ 10:      if $i_p$ then 11:         $source\leftarrow 3$ // one can pung from all others 12:      else if $i_c$ then 13:         $source\leftarrow 1$ // one can only chow from the one left 14:      end if 15:      $p_{meld}\leftarrow p_{discard}\ast source$ 16:      $v\leftarrow v\times (p_{draw}+p_{meld})$ 17: end for 18: Total fan weight $fw\leftarrow \sum {\mathsf{\Theta }}_{fan}\left[f\right]$ for fan $f\in F$ 19: $v\leftarrow v\times fw$ 20: return wr

Here, L denotes the current game length, and $U[t-2]:U[t+2]$ represents the unshown counts of tiles adjacent to t. Including a bias term, ${\mathsf{\Theta }}_{held}$ contains 12 learnable weights in total. In contrast, the probability of melding tile t from another player’s discard is modeled using a uniform distribution, $P_{meld}\left(t\right)=U\left[t\right]/\Sigma \left(U\right)$. We examine alternative probability models for $P_{draw}$ and $P_{meld}$ in Section 6.2, and we further discuss the rationale behind our modeling choices in Section 7.1.

The Decision Selector $DS$ collects results from the Value Calculator C and calculates the final action based on each goal’s estimated value. The detailed algorithm for S is shown in Algorithm 2. The goal of S is to efficiently select the tile to discard with the most negligible impact on the overall value. Heuristically, the required tiles of goals with higher values are more important than those with lower ones. Conversely, the redundant tiles of such goals are more worthless since their existence actually hinders the goals’ completion. Thus, each tile’s worthless degree can be computed by accumulating the value of goals that regard it as a redundant tile, and the tile with the highest worthless degree has the most negligible impact on the overall value. Decision Selector $DS$ accepts ${\mathsf{\Theta }}_{tile}$ as parameters, which are used similarly as ${\mathsf{\Theta }}_{fan}$ to break ties between tiles. For action predictions, such as Chow or Pung, F records values computed by C, assuming those actions are taken, and F selects the action with the highest value.

Algorithm 2 Discarding Tile Selection

Input: List of goals and their values L = [(Goal G, value v)], Hand tiles H Parameter: ${\mathsf{\Theta }}_{tile}$ Output: Tile to discard   1: Initialize tile values $d\leftarrow$ Dict {tile $t:0\}$   2: for all $(G,v)\in L$ do   3:      for all tile $t\in G$ do   4:         $d\left[t\right]\leftarrow d\left[t\right]+v$ // redundant tiles   5:      end for   6: end for   7: for all tile $t\in d$ do   8:      $d\left[t\right]\leftarrow d\left[t\right]\times {\mathsf{\Theta }}_{tile}\left[t\right]$   9: end for 10: return$arg{max}_{t\in H}d\left[t\right]$

4.4. Differentiable Network N of Mxplainer

The search-based Framework F is a parameterized search-based agent template, and its parameter $\mathsf{\Theta }$ needs to be tuned to approximate any target agents’ behaviors. Luckily, Calculator C and Decision Selector $DS$ only contain fixed-limit loops, with each iteration independent from others and if–else statements whose outcomes can be pre-computed in advance. Thus, C and S can be converted into an equivalent neural network N for parallel computation, and the parameters $\mathsf{\Theta }$ can be optimized through batched gradient descent. The rules for the conversion can be found in Appendix B.

$$\mathbb{I}=\left\{\begin{array}{cc}1\hfill & \mathrm{if}\mathrm{it}\mathrm{is}\mathrm{real}\mathrm{data}\hfill \\ 0\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(1)

To distinguish between padding and actual values, we define a value indicator as Equation (1) to facilitate parallel computations. Then, Algorithm 1 and Algorithm 2 can be easily re-written as Listing 1 and Listing 2. The inputs to the Listings are as follows:

• $F\in {\mathbb{R}}^{80}$, $U\in {\mathbb{N}}^{34}$, $H\in {\mathbb{N}}^{64\times 34}$, $X\in {\mathbb{R}}^{34\times 12}$: Vectorized F, U, H, and $x_m$ from Algorithm 1 and Algorithm 2.
• $MT:(\mathbb{I},M)\in {\mathbb{R}}^{34\times 2}$: Missing tiles M with indicators.
• $BM\in {\mathbb{N}}^{34\times 3}$: One-hot branching mask from $i_c$ and $i_p$.
• $V\in {\mathbb{R}}^{64\times 1}$: The computed value from Listing 1.
• w_held, w_fan, w_tile: ${\mathsf{\Theta }}_{held}$, ${\mathsf{\Theta }}_{fan}$, and ${\mathsf{\Theta }}_{tile}$.

Listing 1. Paralleled Algorithm 1 in PyTorch 2.3.1

1 def calc_winrate(F, MT, BM, X, U, w_held, w_fan):   2    v = 100   3    p_uniform = MT[:, 1] ∗ U/torch.sum(U)   4    p_draw = p_uniform ∗ X ∗ w_held   5    p_discard = p_uniform   6    # encode chi, peng, no-op coeff   7    cp_cf = torch.tensor([3, 1, 0])   8    # compute tile-wise cp_coeff   9    cp_cf = cp_cf ∗ BM 10    cp_cf = torch.sum(cp_cf, dim = 1) 11    p_meld = p_discard ∗ cp_cf 12    p_tile = p_darw + p_meld 13    # use indicator to set paddings 0 14    masked_tile = MT[:, 0] ∗ p_tile 15    # convert 0’s to 1 for product op 16    masked_tile += 1-MT[:, 0] 17    v ∗= torch.prod(masked_tile, dim = 0) 18    # calculate preference for fan 19    p_fan = F ∗ w_fan 20    return v ∗ p_fan

Listing 2. Paralleled Algorithm 2 in PyTorch

1 def sel_tile(H, V, w_tile): 2    tile_v = H ∗ V 3    tile_v = torch.sum(tile_v, dim = 0) 4    tile_pref = tile_v ∗ w_tile 5    return torch.argmax(tile_pref)

The Resulting Network N and the Training Objective

The sizes and meanings of the network N’s outputs and three groups of parameters are reported in

Table 1. Sizes and meanings of neural network N’s components.

Entry	Size	Meaning
Overall Output	39	Combined output size
Output (Action)	5	5 Actions:
		Pass, 3 types of Chow , Pung
Param ${\mathsf{\Theta }}_{fan}$	80	Preference for all 80 fans
Params ${\mathsf{\Theta }}_{held}$	12	Linear features weights w/bias
Param ${\mathsf{\Theta }}_{tile}$	34	Preference for all 34 tiles

. Action Kong is not explicitly encoded in the action space. Instead, it is logically implied and automatically executed by the Mxplainer agent under the following conditions:

• Converting a Melded Pung: The agent has an existing, exposed Pung of tile t and tries to discard the fourth t. The agent then executes Kong automatically.
• Forming a Concealed Kong: The agent has three identical tiles t concealed in its hand. Kong is triggered when it draws the fourth t and tries to discard it.
• Forming a Kong: The agent has three identical tiles t concealed in its hand. Kong is triggered automatically, when another player plays tile t, and the agent tries to Pung and discard t at the same time.

In the framework’s decision process, declaring Kong in these scenarios is always the optimal action, as it increases the hand’s value without altering the strategic plan. This design formally decomposes the policy into a piecewise-linear component for high-level actions and a domain-logic component for specialized decisions like discards and Kongs. The resulting composition can be viewed as building a complex policy from simpler, interpretable sub-policies, a concept with rigorous footing in optimization theory [30,31,32].

The learning objectives depend on the form of target agents $\mathsf{\Psi }$ and the problem context. Since we are modeling the selection of actions as classification problems, we use cross-entropy (CE) loss between the output of N and the label Y. The label can be soft or hard depending on whether the target agent gives probability distributions. Since we cannot access action distributions from Botzone’s game log, we use actions as hard ground-truth labels for all target agents. Additionally, an L2-regularization term of ${({\mathsf{\Theta }}_{fan}-abs\left({\mathsf{\Theta }}_{fan}\right))}^2$ is added to penalize negative values of fan preferences to make the heuristic parameters more reasonable.

We employ supervised learning for this imitation task as it provides a direct and stable optimization objective to achieve high behavioral fidelity, which is a prerequisite for generating faithful explanations.

After training, the learned parameters $\mathsf{\Theta }$ can be directly filled back into $CC$. Since $CC$ is equivalent to N, $SC\left|CC\right(\mathsf{\Theta })$ inherits the characteristics of $SC\left|N\right(\mathsf{\Theta })$, approximating the target agent $\mathsf{\Psi }$. By analyzing the parameterized agent $SC\left|CC\right(\mathsf{\Theta })$, we can study the parameters to learn the comparative characteristics between agents and gain insights into the deduction process of $\mathsf{\Psi }$ through the step-by-step algorithms of Framework $SC|CC$. Since only data pairs are required from the target agents, we can use Mxplainer on both target AI agents and human players.

5. Experiments

We conducted a series of experiments to evaluate the effectiveness of Mxplainer in generating interpretable models and analyze their explainability. Three different target agents are used in these experiments. The first agent ${\psi }_1$ is a search-based MCR agent with manually specified characteristics as a baseline. Specifically, this agent only considers the fan of Seven Pairs to choose, and all its actions are designed to reach this target as efficiently as possible. When multiple tiles are equally good to discard, a fixed order is predefined to break the equality. The second agent ${\psi }_2$ is the strongest MCR AI from an online game AI platform, Botzone [33]. The third agent ${\psi }_3$ is a human MCR player from an online Mahjong platform, MahjongSoft.

Around 8000 and 50,000 games of self-play data are generated for the two AI agents. Around 34,000 games of publicly available data are collected from the game website for the single human player over more than 3 years. The datasets for each agent were split into training, validation, and test sets on a per-game basis to prevent data leakage and ensure a robust evaluation. Through supervised learning on these datasets, three sets of parameters ${\theta }_{1,2,3}$ are learned and filled back in the search-based framework F as-is, creating interpretable white-box agents ${\widehat{\psi }}_{1,2,3}$ with similar behavior to the target agents ${\psi }_{1,2,3}$. The weights for each agent are selected with the highest validation accuracy from three runs. To make weights comparable across different agents, reported weights are normalized with $100\times (\mathsf{\Theta }-{\mathsf{\Theta }}_{min})/\Sigma (\mathsf{\Theta }-{\mathsf{\Theta }}_{min})$.

Since it is common in MCR where multiple redundant tiles can be discarded in any order, it is difficult to achieve high top-1 accuracy on the validation sets, especially for ${\psi }_2$ and ${\psi }_3$, which have no preference on the order of tiles to discard. As a reference of the similarity, ${\widehat{\psi }}_{1,2,3}$ achieves the top-three accuracy of 97.15%, 93.47%, 90.12% on the data of ${\psi }_{1,2,3}$ (All the accuracy figures presented in this paper only take into account states $\ge 2$ valid actions, which account for less than 30% of all states. The overall accuracy can be roughly calculated as $70+0.3\times acc$, where $acc$ represents the reported accuracy).

5.1. Correlation Between Behaviors and Parameters

In the search-based framework F, the parameters, $\mathsf{\Theta }$, are designed to be strategy-related features that should take different values for different target agents. Here, we analyze the correlation between the learned parameters and target agents’ behavior to prove that Mxplainer can extract high-level characteristics of agents and explain their behavior.

5.1.1. Preference of Fans to Choose

${\mathsf{\Theta }}_{fan}$ stands for the relative preference of agents to win by choosing each fan. For the baseline target ${\psi }_1$, which only chooses the fan of Seven Pairs, the top values of ${\theta }_{1,fan}$ learned are shown in

Table 2. (A). Defined order for tiles and their learned weights. (B). Sorted weights in the learned parameters ${\theta }_{1,fan}$ and their corresponding fans. Learned weights for ${\theta }_{2,fan}$ are added for comparison. (C). The major fans of ${\psi }_2$ and ${\psi }_3$ with a difference of at least 1% in historical frequency, which is calculated from their game history data.

A	Tile Name	Defined Order	${\theta }_{1,tile}$
	White Dragon	1	1.41
	Green Dragon	2	1.13
	Red Dragon	3	1.07
B	Fan Name	${\theta }_{1,fan}$	${\theta }_{2,fan}$
	Seven Pairs	56.19	3.59
	Pure Terminal Chows	7.42	1.99
	Four Pure Shift Pungs	4.10	0.42
C	Fan Name	Frequency Diff	Param Diff
		${\psi }_2-{\psi }_3$ (%)	${\theta }_{2,fan}-{\theta }_{3,fan}$
	Pure Straight	1.30	0.45
	Mixed Straight	1.94	0.65
	Mixed Triple Chow	2.09	0.63
	Half Flush	1.04	0.27
	Mixed Shifted Chows	5.08	0.31
	All Types	2.60	0.27
	Melded Hand	−8.25	−1.24
	Fully Concealed Hand	1.83	−0.55

B. We also include ${\theta }_{2,fan}$ values for comparisons, demonstrating the differences in learned weights between specialized Seven Pairs agent and other agents. It can be seen that the weight for Seven Pairs is much higher than those of other fans, showing the strong preference of ${\widehat{\psi }}_1$ to this fan. The fans with the second and third largest weights are patterns similar to Seven Pairs, indicating that ${\widehat{\psi }}_1$ also tends to approach them during the gameplay based on its learned action choices, though it eventually ends with Seven Pairs for 100% of the games. For targets ${\psi }_2$ and ${\psi }_3$ with unknown preferences of fans, we count the frequency of occurrences of each major fan in their winning hands as an implication of their preferences and compare these two agents on both the frequency and the learned weights of each fan. Table 2C shows all the major fans with a difference of 1% in frequency. Except for the last row, the data shows a significant positive correlation between the preference of target agents $\psi$ and the learned ${\theta }_{fan}$.

5.1.2. Preference of Tiles to Discard

${\mathsf{\Theta }}_{tile}$ stands for the relative preference of discarding each tile, especially when multiple redundant tiles are valued similarly. Since ${\psi }_2$ and ${\psi }_3$ show no apparent preference in discarding tiles, we focus on the analysis of ${\psi }_1$, which is constructed with a fixed tile preference. We find the learned weights almost form a monotonic sequence with only 3 exceptions out of 34 tiles, showing strong correlation between the learned parameters and the tile preferences of the target agent. Table 2A shows the first a few entries of ${\theta }_{1,tile}$.

5.2. Manipulation of Behaviors by Parameters

Previous experiments have shown that greater frequencies of fans within the game’s historical record lead to elevated preferences. In this experiment, we illustrate that through the artificial augmentation of fan preferences, the modified agents, in contrast, display elevated frequencies of the corresponding fans. We make adjustments to the parameters ${\theta }_{2,fan}$ within ${\widehat{\psi }}_2$ by multiplying the weight assigned to the All Types fan by a factor of 10 (The factor of 10 is an arbitrary but significant multiplier chosen to induce a strong and clearly observable shift in the agent’s behavior, thereby demonstrating that the learned parameters in ${\mathsf{\Theta }}_{fan}$ are actionable and directly influence strategic preferences.). This gives rise to the generation of a new agent, ${\psi }_2^{\prime }$, which is expected to exhibit a stronger inclination towards selecting this fan.

We collect roughly around 8000 self-play game data samples from ${\psi }_2$ and ${\psi }_2^{\prime }$. Subsequently, we determine the frequency with which each fan shows up in their winning hands. The data indicates that among all the fans, only the All Types fan undergoes a frequency variation that surpasses 1%. Its frequency has risen from 2.59% to 5.76%, signifying an increment of 3.17%. In contrast, the frequencies of all other major fans have experienced changes of less than 1%. Given that Mahjong is a game characterized by a high level of randomness in both the tile-dealing and tile-drawing processes, adjusting the parameters related to fan preferences can only bring about a reasonable alteration in the actual behavior patterns of the target agents. In conjunction with the findings of previous experiments, we can draw the conclusion that the parameters within Mxplainer are, in fact, significantly correlated with the behaviors of agents. Moreover, through the analysis of these parameters, we are capable of discerning the agents’ preferences and high-level behavioral characteristics.

5.3. Interpretation of Deduction Process

In this subsection, we analyze the deduction process of the search-based framework F on an example game state by tracing the intermediate results of ${\widehat{\psi }}_2$ to demonstrate the local explainability of Mxplainer agents in decision-making.

The selected game state S is at the beginning of a game with no tiles discarded yet, and the player needs to choose one to discard, as shown in

Table 3. (A). An example game state at the beginning of the game where no tiles have been discarded by other players. (B). Some proposed goals for state s by ${\widehat{\psi }}_2$ and the estimated win probabilities. “H&K” is an abbreviation for Honors and Knitted due to space constraints.

A		Other Information			Current Hand
		None
B	ID	Major Fan	Probs	Redundant Tiles R	Final Target
	25	Lesser H&K Tiles 1	1.000	D7, C9, B6, B8, B9
	0	Knitted Straight 1	0.125	C9, B9, NW, RD, WD
	11	Pure Straight	0.018	D2, C3, C6, NW, RD, WD
	50	Seven Pairs 1	0.017	B6, B8, B9, NW, RD, WD

¹ A fan that does not follow the pattern of four melds and a pair.

A. The target black-box agent ${\psi }_2$, selects the tile B9 as the optimal choice to discard for unknown reasons. However, analyses of the execution of the white-box agent ${\widehat{\psi }}_2$ explain the choice.

The Search Component $SC$ proposed 64 possible goals for s, and Table 3B shows a few goals representative of different major fans. With fitted ${\theta }_2$, Algorithm 1 produces an estimated value for each goal G, as listed under the “Value” column of Table 3B. We observe that though B9 is required in goals such as Pure Straight, it is not required for many goals with higher estimated values, such as Knitted Straight.

Following Algorithm 2, we accumulate the values for tiles in Redundant Tiles R. The higher value of a tile indicates a higher value if the tile is discarded, and B9 turns out to have a higher value than other tiles by a large margin, which is consistent with the observed decision of ${\psi }_2$.

This section merely demonstrates an analysis of action selection within the context of a simple Mahjong state. However, such analyses can be readily extended to other complex states. The Search Component $SC$ consistently takes in information and puts forward the top 64 reachable goals, ranked according to distances. The Calculation Component $CC$ calculates the value for each goal using the learned parameters. Finally, an action is chosen based on these values.

Without Mxplainer, people can only observe the actions of black-box MahJong agents, but they cannot understand how the decisions are made. Our experiments show that Mxplainer’s fitted parameters can well approximate and mimic target agents’ behaviors. By examining the fitted parameters and Mxplainer’s calculation processes, experts are able to interpret the considerations of black-box agents leading to their actions.

6. Ablation and Comparative Study

6.1. Number of Searched Goals

To assess potential bias from the 64-goal cap, we performed a sensitivity analysis on goal recall for the target agent ${\psi }_2$. Given that the probability of success decreases exponentially with Shanten Distance D (approximately by a factor of $1/34$ per unit increase), we specifically measured the recall rate for goals with the minimum D in each state.

A survey of approximately 10,000 game logs revealed that the average number of such minimum-D goals was 13.28. The coverage rate for these goals and the corresponding search time are summarized in

Table 4. Recall rate and time cost for goals with different caps.

Cap (K)	Coverage Rate@K	Time (s)
16	79.31%	0.097
32	87.85%	0.098
64	96.82%	0.109
128	99.79%	0.128

.

We further evaluated the predictive accuracy of the approximated agent $\widehat{{\psi }_2}$ under different goal caps (16, 32, 64, and 128). The results, illustrated in Figure 5, show that both Top-1 and Top-3 accuracy improve substantially when the cap is increased from 16 to 64. However, increasing the cap further to 128 yields only marginal gains, indicating diminishing returns beyond 64 goals.

6.2. Distribution Modeling

To rigorously evaluate the impact of probability model specification, we conducted an ablation study comparing different configurations for modeling $p_{draw}$ and $p_{discard}$.

The results are summarized in

Table 5. Ablation study on probability models for tile acquisition.

${\mathit{p}}_{\mathit{draw}}$	${\mathit{p}}_{\mathit{discard}}$	Top-1 Acc	Top-3 Acc	Parameter Size
Uniform	Uniform	66.26	90.65	114
Network	Uniform	71.49	93.47	126
Uniform	Network	67.35	91.16	126
Network	Network	71.49	93.44	138

. Here, “Network” denotes a learnable module that uses local game features Z to estimate the acquisition probability, whereas “Uniform” assumes a simple uniform distribution over unshown tiles. The configuration highlighted in bold was selected for our final framework, as it achieved the highest overall accuracy without a substantial increase in parameter count. This suggests that accurately modeling the draw probability from the wall is more critical for policy imitation than refining the discard model under the current framework.

6.3. Parameter Size and Methods of Behavior Cloning

In an effort to boost the explainability of Mxplainer, we have minimized the parameter size of the Small Network N. Nevertheless, this design might compromise its expressiveness and decrease the accuracy of the approximated agents. Consequently, we aim to further investigate the impact of the parameter size of the Small Network N on the approximation of the Target Agent $\mathsf{\Psi }$. Specifically, we augment the parameter size and train networks $\widehat{{\psi }_2^{\prime }}$ and $\widehat{{\psi }_2^{″}}$ to approximate the identical Target Agent ${\psi }_2$. We do not elaborate on the modifications to the network structures herein. The parameter sizes and their respective top-3 accuracies are presented in

Table 6. (A). Comparison between parameter size and resulting accuracies. (B). Comparison between different methods and accuracies.

A	Network	Param	${\theta }_{fan}$	${\theta }_{held}$	${\theta }_{tile}$	Top-3 Acc%
	$\widehat{{\psi }_2}$	126	80	12	34	93.47
	$\widehat{{\psi }_2^{\prime }}$	2804	2720	50	34	93.77
	$\widehat{{\psi }_2^{″}}$	3280	2800	435	45	94.57
B	Method	Param		Acc%		Top-3 Acc%
	Mxplainer	126		71.49		93.47
	Decision Tree	N/A		28.91		34.82
	Behavior Clone	34M		75.31		95.69

A.

We observe that by increasing the parameter size, Mxplainer can approximate the Target Agent $\mathsf{\Psi }$ with greater accuracy. Nevertheless, the drawback lies in the fact that the larger the number of parameters in the Small Network N, the more challenging it becomes to explain the actions and the meaning of the parameters to users. Although the approximated agents cannot replicate the exact actions of the original black-box agents, they can account for their actions in most scenarios, as demonstrated by previous experiments.

We also conduct a comparison of the effects of different methods. Specifically, we construct a random forest consisting of 100 decision trees and employ a pure neural network to learn the behavior policy of ${\psi }_2$ through behavior cloning. The results are presented in Table 6B. Although decision trees are inherently self-explanatory, their low accuracies render them unsuitable for Mahjong, which involves numerous OOD states. The accuracy of Mxplainer is not notably lower than that of traditional neural networks with sufficient expressivity, but it has the advantage of being able to explain the reasoning underlying the actions.

7. Discussion

A primary limitation of Mxplainer is that its fidelity is inherently bounded by the expressiveness of the hand-crafted search framework F. Strategies that operate outside the paradigm of goal-search and linear parameterization may not be fully captured.

7.1. Choice of Probability Distributions for Tiles

A key design choice in the Mxplainer framework is the use of different probability models for drawing a tile from the wall ($p_{draw}$) and for an opponent discarding a tile ($p_{discard}$). We model $p_{draw}$ with a learnable neural component that incorporates local game features, while $p_{discard}$ is modeled using a uniform distribution over the unshown tiles.

This choice reflects a deliberate trade-off between expressiveness and interpretability. Modeling $p_{draw}$ with a learnable network is both feasible and critical. The wall is a passive, stochastic element; its state can be reasonably approximated by tracking unshown tiles. A model that learns to weight features like total unshown tiles, game length, and availability of adjacent tiles (Z) can effectively capture the nuanced likelihood of drawing a specific tile, providing a significant accuracy boost over a uniform assumption, as shown in our ablation study (Section 6.2).

In contrast, we employ a uniform distribution for $p_{discard}$. This assumption is a significant simplification, as it likely introduces a systematic bias by overstating the melding probability for tiles that opponents would strategically withhold. In theory, this could inflate the learned value of goals that rely on melding such tiles.

However, our ablation study (Section 6.2) demonstrates that the core conclusions of Mxplainer, specifically, its high imitation accuracy and the strategic insights derived from $\mathsf{\Theta }$, are remarkably robust to this simplification. The minimal performance gap between uniform and learned discard models suggests that the framework successfully absorbs much of this potential bias into the other calibrated parameters (e.g., ${\mathsf{\Theta }}_{fan}$) while maintaining a highly interpretable structure. Therefore, while a more sophisticated opponent model is a worthwhile goal for future work, the uniform assumption is not a prerequisite for Mxplainer’s current ability to deliver faithful and explainable agent imitations. We prioritized this simpler, interpretable model to maintain a clear causal chain of reasoning, accepting a theoretically sub-optimal but empirically adequate approximation for the purpose of high-fidelity policy imitation.

Furthermore, the imitation accuracy of Mxplainer approaches that of a large, black-box neural network trained via behavior cloning (see Table 6B). This near-state-of-the-art performance, achieved with only 126 interpretable parameters compared to 34 million, underscores the efficiency of our parameterized search framework. It validates that the high fidelity of the approximation is not sacrificed for explainability but rather achieved through a structured, interpretable model.

7.2. Compare Characteristics of Agents with Mxplainer

With Mxplainer, we can compare the differences between agents. By comparing the fitted parameters in parallel with other agents, we can analyze the characteristics of different agents. For example, we can easily observe that the black-box AI agent ${\psi }_2$ has a much higher weight on Thirteen Orphans, Seven Pairs, and Lesser H&K Tiles. In contrast, the human player ${\psi }_3$ has a significant inclination of making Melded Hand, and these observations are indeed backed by their historical wins in Supplemental Material Table S2. Note that while Mxplainer successfully profiles an individual’s strategy, its ability to capture population-level human playstyles requires future study with a broader dataset.

7.3. Limitations

While Mxplainer provides faithful and interpretable approximations, its fidelity is inherently bounded by the expressiveness of the manually constructed search-based framework F. Strategies that operate on principles fundamentally beyond the template’s goal-search logic and linear parameterization—for instance, those relying on complex, non-linear state evaluations or long-term deceptive plays not captured by our goal-oriented model—may not be fully captured. This is a deliberate trade-off we make to prioritize interpretability, as the components of F are designed to be comprehensible to domain experts.

7.4. Extend Mxplainer to Other Settings and Future Direction

Our proposed approach has a unique advantage in quantifying and tuning weights for custom-defined task-related features in areas where interpretability and performance are crucial. While Mxplainer is specifically designed for Mahjong, we hypothesize that its unique approach and XAI techniques may be applicable to other applications. In fact, we experimentally applied our proposed framework to two examples: Mountain Car from Gym [26] and Blackjack [34]. Both examples, which can be found in Appendix A, confirmed the effectiveness of our proposed method. However, the scope of application of our method still requires further study.

Another compelling future direction is to extend Mxplainer into a multimodal framework. By incorporating auxiliary data streams—such as eye-tracking to measure attention, heart rate variability to assess cognitive load or stress, and mouse-movement dynamics—we could move beyond modeling a static strategic policy. This would allow us to create a context-aware model that explains how a player’s decisions are modulated by their real-time psychological and physiological state. Such an expansion could bridge the gap between pure game-theoretic strategy and the rich, situated reality of human decision-making.

8. Conclusions

In this work, we introduced Mxplainer, a novel framework that bridges the gap between the high performance of black-box agents and the critical need for interpretability in complex domains like Mahjong. Unlike existing imitation learning or post hoc explanation methods that often trade accuracy for transparency or struggle with high-dimensional state spaces, Mxplainer’s unique approach constructs a parameterized, search-based agent whose components are directly convertible into an equivalent, trainable neural network. This core design allows it to accurately approximate sophisticated agents while retaining a human-understandable deduction process and strategically meaningful parameters.

Our experiments demonstrate that Mxplainer successfully extracts and quantifies agent characteristics, such as fan and tile preferences, and provides local explanations for individual decisions. The framework’s ability to manipulate agent behavior by tuning these parameters further validates that the learned values capture genuine strategic inclinations.

Nevertheless, Mxplainer has limitations. Its approximation power is inherently constrained by the expressiveness of the hand-crafted search framework, and the current use of uniform distributions for tile-drawing and discarding probabilities is a simplifying assumption that could be refined. Future work will focus on enhancing the model’s expressiveness without sacrificing interpretability, exploring more sophisticated probability models, and, most importantly, generalizing the explanation template to a wider range of applications beyond Mahjong. We believe that the paradigm of converting a domain-specific, parameterized classical agent into a trainable network offers a promising path forward for building performant, transparent, and trustworthy AI systems.