Churn prediction of mobile and online casual games using play log data

Internet-connected devices, especially mobile devices such as smartphones, have become widely accessible in the past decade. Interaction with such devices has evolved into frequent and short-duration usage, and this phenomenon has resulted in a pervasive popularity of casual games in the game sector. On the other hand, development of casual games has become easier than ever as a result of the advancement of development tools. With the resulting fierce competition, now both acquisition and retention of users are the prime concerns in the field. In this study, we focus on churn prediction of mobile and online casual games. While churn prediction and analysis can provide important insights and action cues on retention, its application using play log data has been primitive or very limited in the casual game area. Most of the existing methods cannot be applied to casual games because casual game players tend to churn very quickly and they do not pay periodic subscription fees. Therefore, we focus on the new players and formally define churn using observation period (OP) and churn prediction period (CP). Using the definition, we develop a standard churn analysis process for casual games. We cover essential topics such as pre-processing of raw data, feature engineering including feature analysis, churn prediction modeling using traditional machine learning algorithms (logistic regression, gradient boosting, and random forests) and two deep learning algorithms (CNN and LSTM), and sensitivity analysis for OP and CP. Play log data of three different casual games are considered by analyzing a total of 193,443 unique player records and 10,874,958 play log records. While the analysis results provide useful insights, the overall results indicate that a small number of well-chosen features used as performance metrics might be sufficient for making important action decisions and that OP and CP should be properly chosen depending on the analysis goal.


Introduction
The global game market continues to grow, and it is expected to grow 9.6 percent per year between 2013 and 2018 with a stable revenue stream [1]. As the number of published games increase exponentially, game market is becoming too complicated to understand as a single sector. Therefore, researchers often divide the market into multiple sectors and analyze each There are a few aspects to consider when studying churn of casual games. For telecommunication or newspaper industries, the business is based on subscription. Therefore, a churner can be very clearly defined when the subscriber notifies termination of service. Some of the sophisticated games, such as MMORPG, are based on subscription as well. Casual games, however, are widely based on freemium models where players might not return to the game for a few months or even for good without notifying anyone or paying monthly charges. For such dormant players, it becomes impossible to have one single golden definition of churn, and an adequate definition needs to be adopted in accordance to the main analysis purpose-one might be interested in if a player will return in 10 days in one case, and 1 month in another case. In this study, a flexible churn definition using observation period (OP) and churn prediction period (CP) is provided to address this issue.
Another aspect to consider is the target group to analyze. While most of the existing churn analyses focus on the entire user base, another important approach is to consider the new users only. In most of the industries, churn rate is much higher for the newly acquired group as the users try out the service. Therefore, it becomes crucial to fully understand the new users and address their issues. For casual games, this effect is pronounced even more. For the three casual games that we analyze in this study, 70~90% of the players stop playing within 10 days from the first day of play. Apparently new player analysis is essential for monitoring and improving the casual games.
In this study, we focus on new players of non-subscription-based casual games, and establish a standard procedure of analysis. Three datasets are used, where two are mobile casual games and one is online casual game. We build an analysis model by observing a new player's play log data from the first OP days of play and predicting if the player will play again in the following CP days. Note that a player might not play for the CP days but then return at a time in a farther future. Such a player is still considered as a churner in this study, because otherwise it is impossible to define 'ground truth'. To explain this, assume that we make CP infinite and eliminate the 'returning at a farther future' problem. Then, no matter how long we wait, we cannot tell if a player is really a churner or not. The player is not paying subscription fee, and therefore there will be no special action such as a service termination notice. To avoid this problem, we need to compromise, set CP at a reasonable value, and make it possible to identify churners by looking into CP days of future. This turns out to be a practical compromise, because most of the players who do not return in CP days do not return at least until the end of data collection period that is way much later than CP days.
In the following, we summarize the related works, formally define churn of casual games, and explain the data. Then, feature engineering is performed over three games to understand the data details and the influence of common and game-specific features. Performance results follow, where prediction performance for five different prediction algorithms is compared and sensitivity to the different selections of OP and CP is investigated. AUC (area under the curve) of ROC (receiver operating characteristic) [17][18] through ten-fold cross-validation [19] is used as the performance measure. Overall, we derive interesting insights on mobile and online casual games through the churn prediction analysis.

Related works
Early user churn prediction research has been conducted in a variety of commercial fields such as telecommunication, newspaper, bank, credit card, and insurance [20] [21] [22] [23]. In each field, churn prediction has evolved in accordance to the industry development.
As the game industry has matured, a number of user churn prediction studies have been conducted because the insights from such studies can have critical influences on the game revenue. Runge et al. (2014) performed a churn prediction research for high-value players in casual social games, and provided a framework for game churn analysis [24]. They predicted churn for the target group of top 10% of high paying users of two freemium mobile casual games using four algorithm types (neural network, logistic regression, decision tree, and support vector machine), and defined a churner to be a player with no play for 14 consecutive days. The model performance was evaluated using AUC of ROC, and the effectiveness of prediction model was gauged using A/B test. While [24] focused on high-value players who show long lifetimes, this work focuses on casual players who typically show very short lifetimes after the first play of a game. Hadiji et al. (2014) explained the definition of user churn prediction as two concepts and formulated the input data for the prediction as two methods as well [11]. They used decision tree, logistic regression, neural network, and naïve Bayes algorithm models, i.e., four models using freemium game data for each of four input data sets generated according to the two definitions of user churn and the two methods. F1-score was used to compare the models' performance, and the decision tree model performed best. Kawale et al. (2009) determined the factor that affects user churn in two ways, social influence among users and their personal engagement in MMORPGs [25]. The social influence factor was used to create a network graph using group-play records. The personal engagement factor was used to create a beta function using user session time records. Furthermore, they created a modified diffusion model based on an existing simple diffusion model for evaluating performance and described model-dependent processes that classify users who will or will not churn.
Another noticeable change in the research is the use of deep neural networks (DNN). DNN have improved remarkably on some traditional research problems, such as image classification and speech recognition [26][27] [28]. Wangperawong et al. (2016) applied deep CNNs and autoencoders to telecommunication churn analysis and showed that their approach outperforms decision tree modeling with 12 temporal features for each user [29].
Although the importance of user churn prediction of games has been acknowledged and research results including the aforementioned ones are available, our understanding on churn analysis of games is far from being complete or mature. Overall, the existing works seem to have mainly three limitations, and our study focuses on the three. First, most studies focus on rather blindly defining features for predicting user churn and do not provide in-depth analysis. Prediction performance significantly varies depending on how we define features, and it is difficult to make churn rate improvement without fully understanding the chosen features and their implications in the domain [30][31] [32]. Thus, we provide the details of defining and analyzing features in this study. Second, algorithms as well as features for a prediction model can have a substantial effect on building a prediction model, but there have been limitations to using algorithms in past studies [33]. Hence, we design prediction models using three representative algorithms together with two of the latest deep learning models, and compare the performances of those models. Third, existing studies set the observation period (OP) and churn prediction period (CP) arbitrarily without conducting additional studies for setting those periods. However, the definition of the churn is directly dependent on the two periods and the prediction results and performance can substantially depend on them. To overcome this limitation, we analyze their effects and provide useful insights.

Churn definition
We focus on the new players of casual games (no subscription). To study churn, we predict if a new player will stop playing after a certain number of days since the first day of play. As addressed in the introduction, this definition of churn is quite different from the case of targeting 'the entire user base' where the question is if an existing user, regardless of the length of inservice period, will still pay in the following month. To formally define a churner for casual games, we first introduce a few notations. For a player u, let s i and t abs i represent the score and timestamp, respectively, of the player's i th play. Because we focus on new players only, it is convenient to define t rel i , relative time with respect to the player's first play time. For the simplicity of the notation, we use t i to represent t rel i in the rest of the paper.
As an example, if the timestamp of a player's first play is 1,469,623,182 and the timestamp of the third play is 1,469,633,182, then t 3 is 10,000 seconds. Note that t 1 = 0 by definition, and it is emphasized in the above equation.
We define a churner in terms of observation period (OP) and churn prediction period (CP). An OP is a period for observing a user's plays, and the play log data are used to create features and predict churn for the following CP days. A CP is a period for determining whether a user actually churned or not. Using the two periods, a churner is defined as a user playing the game for the first time when t 1 = 0 and possibly more in the first OP days, and not playing the game at all in the following CP days. The definition is for each individual player, and the player's own clock since the first play time is used for defining OP and CP. Fig 1 shows a time-diagram example. Together with the 8 plays that the user has played, observation period of 2 days (OP = 2) and churn prediction period of 2 days (CP = 2) are highlighted in the diagram. In reality, larger OP and CP values are preferred, but small values are shown here to simplify the diagram. As explained in the introduction, the play activity after the OP+CP does not affect if the user is a churner or not. Unlike subscription-based services, this is necessary for freemium casual games because we cannot wait forever for deciding if a user is a churner or not. A decision needs to be made within a reasonable time frame to allow a meaningful analysis and action for the new users. Despite of the limitation, this definition turns out to be quite reasonable and practical, because most of the churners indeed do not return to the game forever when CP is larger than just several days. This is due to the nature of casual games where the players are not serious.
In Fig 2, two examples of churners and two examples of active users are shown. User 1 has three play records in OP but no play record in CP, and therefore User 1 is a churner. User 2 has active play records after OP+CP days, but it is also a churner according to our definition. Again, this type of player is seldom found in reality compared to the type of User 1. In contrast, if a user has play records in the CP, the user is called an active user. User 3 has three play records in the OP and two records in the CP, and User 4 has 2 play records in OP and 1 play record in CP.
For the freemium games, the choice of OP and CP needs to be made prudently depending on the goal of churn analysis. If a quick and targeted action is needed within the first 3 days of a player's first play, obviously OP needs to be set at 3 days or below. On the other hand, if a popularity metric for a newly released game is needed, OP can be set to a larger number such that the prediction accuracy can be enhanced. For CP, one could choose a small value to predict the short term behaviors or choose a large value to predict the long term behaviors. In the rest of this paper, we fix OP to 5 days and CP to 10 days and perform feature engineering and algorithm performance analysis. The studies were completed for many different OP and CP choices as well, but the main insights remain the same and hence we fix the values and avoid over-complications. Instead, we provide explicit analysis results on the impact of OP and CP choices in the 'Performance for different choices of OP and CP' section.

Data
The three casual games chosen for churn prediction are Dodge the Mud, a casual racing game with an undisclosed title (per data owner's request), and TagPro. Dodge the Mud is a casual action game on Android. In the game, a player dodges mud coming down from the sky by touching buttons on the phone screen or tilting the phone; the player receives scores, which are proportional to the number of muds the player dodges. Game #2 is a casual racing game on Android and iOS. A player rides a vehicle over challenging terrain with a specified time limit. Then, the player receives game money, which can be used to upgrade the vehicle. Lastly, TagPro is a casual CTF (capture-the-flag) game on a web browser. It is a team game in which a player seizes the other team's flag and brings it back to his or her own team. The player then receives individual play scores and team points, which can be earned only when the player's team wins a game. Table 1 summarizes the three games, with data descriptions of each game.
The raw play log records of Game #1 were available in MySQL database. The raw data of Game #2 was provided in text files with the contents in a JSON (JavaScript Object Notation) format. For Game #3, a public API for downloading play log data was available, and JSON files were obtained through the API. From the raw datasets, redundant, irrelevant, and not-soinformative data fields were filtered out after a careful examination and pre-processing. The resulting data fields that are used in this research are summarized in Tables 2-4. Among the three games, Game #2 is the only game where items can be purchased. As will be discussed in the feature engineering section, purchase.price is used for game-specific feature extractions. For Game #3, the play.duration and win are used for game-specific feature extractions. The last attribute, points, is different from score because the accumulated value of points is used to decide rankings, and subsequently the list of players to list in the leaderboard. While the highrankers can be motivated to continue playing, this attribute was not considered in this research because typically only 100 players are listed in the leaderboard.

Feature engineering
For traditional machine learning algorithms to work well, an appropriate feature engineering needs to be performed. When done properly, feature engineering not only improves the algorithm performance but also enables discovery of important insights. In this section, intuitively meaningful features are extracted first, and their importance is evaluated by analyzing single feature ranking and by identifying the best feature combinations.

Feature extraction
Feature extraction from the play log data is required to predict whether a user will churn, because not all of the original attributes are directly usable or helpful in prediction. Features influence the prediction capability of a model. In addition, features are useful for understanding prediction results better. In this study, we extracted ten common features for the three games and two game-specific features for Game #2 and #3.
As explained in the Data section, the three games have the same attributes, which are unique ID, score, and time in the play log data. From the attributes, we generated ten common features focusing on the user's play pattern and game scores. Three features, playCount, active-Duration, and consecutivePlayRatio, are extracted from a user's play pattern. The feature play-Count (n) is the total number of plays of u in the OP. The feature activeDuration is the time difference between the last play and the first play in the OP, which is the same as the relative time of the last play t n in the OP. We use c i to denote the time difference between two adjacent plays for consecutivePlayRatio. That is, For example, if the second play time of u is 1,469,632,182, and the third is 1,469,633,682, then c 2 is 1,500 seconds. The other features are score-related features extracted from basic statistics of a user's play scores and their transformations. The feature bestScore (μ) is the best score earned during the OP. That is, The feature meanScore (" s) is the average score during the OP. That is, Table 5 shows the common features of the three games. Game-specific features are extracted from the data fields that are related to genre or characteristics of the game. For instance, since Game #2 is a racing game, vehicle can be upgraded in a store and the purchase related information is reflected in the play log data. Similarly, since Game #3 is a team-play game where a team can win or lose, counts of winning and losing can be derived from play log data. In addition, Game #3 provides play duration information for each game, which is not available for Game #1 and #2.
To introduce game-specific features, we adopt a few extra notations. For Game #2, we use p j to represent the price paid for the j th vehicle, where j = 1, 2, . . ., L. We let t pur j represent the relative time of the j th purchase. For Game #3, whether the player wins the i th play or not is encoded in binary. That is, We let d i represent the playing duration of the i th play (ending time-starting time of each play). Table 6 shows game-specific features for Games #2 and #3.

Single feature ranking
Among the features that were extracted, some are more important than the others in terms of their contributions to churn prediction. To understand which features are the most important ones for each game, we perform a single feature ranking analysis by adopting the variable ranking strategies described in Guyon(2003) [32]. First, we evaluate rankings in five different ways by examining five different scores-absolute value of Pearson correlation coefficient between a feature and churn, three classification performance values (AUC) of the three traditional machine algorithms using only a single feature as the input, and the feature importance that is calculated by gradient boosting library. Then, the overall ranking is determined by comparing the average ranking of the five results.
Among the five, two of them are shown in  Index of the best score normalized by play count 1 n argmax i s i , where t i < t op bestSubMeanCount Difference between best score and mean score normalized by play count ðmÀ " sÞ n bestSubMeanRatio Ratio between the best score minus mean score and the mean score ðmÀ " sÞ " s consecutivePlayRatio Ratio between the count of consecutive plays, where c i is less than C, and the total number of adjacent plays (C: a game specific duration threshold to distinguish whether two adjacent plays are consecutive plays or not)(  occurs for Game #3 when the feature is activeDuration. On the other hand, meanScore turns out to be the worst feature. Similar results can be found in (b) in terms of ranking. Overall single feature rankings, by averaging the five, are shown in Table 7. For all three games, active-Duration and playCount are ranked as the top two important features. This implies that playtime related metrics matter much more than play-score related metrics for casual games. For Game #2, purchase related features, that are game-specific features available only for Game #2, rank as the next two important features. For Game #1, bestScore ranks at the third position. For Game #3, however, worstScore ranks at the third position. While the best score is an important metric for Game #1 that is the simplest among the three games, the worst score is an important metric for Game #3 that is a team-play game.

Feature combinations
While single feature analysis provides useful insights on the common traits and the individual characteristics of the three casual games, ultimately multiple features need to be used for the  best performance of churn prediction. When multiple features are used, a feature may contain redundant information or noise-dominated information, and therefore feature selection needs to be applied. Saeys (2007) provides a succinct summary where feature selection methods are categorized into filter, wrapper, and embedded searches [31]. While a variety of techniques are available, we choose the most brute-force method of checking performance of all possible feature combinations and identifying the best. This full search is possible because we have only 10~12 features to consider for each game. To simplify the analysis, only gradient boosting algorithm is used for the evaluations.
The results are shown in Table 8. For Game #1, nine out of ten features are used for the best performance. The missing one is worstScore, and possibly the worst score is random and conveys no information because many players freely stop playing when interrupted in real-life. For Game #2, four features are used and a game-specific feature, bestPurchase, is included. For Game #3, six features are used and a game-specific feature, winRatio, is included. For Game #3, it can be also observed that worstScore is not included in the best combination, even though it ranked number three in single feature ranking. One can infer that the feature's churn-related information is mostly redundant when other features are present.
Overall, activeDuration and playCount, which are the first-and second-ranked features in single-feature ranking, are included in all three games' combinations (underlined in Table 8). Furthermore, some of the low-ranking features can be found in the combination list, too. Overall, the combination list provides interesting results, but the value of additional features is questionable. In Fig 4, AUC performance as the number of utilized features is shown for all three games. The leftmost point of curve corresponds to the best single-feature performance. It can be seen that the performance improves when the number of features is increased from one to 2~3. Beyond that point, having more features have very marginal effect and the curves look almost flat. Although the best combination results in Table 8 are achieved for 4~9 features, the curves in Fig 4 indicate that casual games are very simple and analysis beyond single-feature ranking might not be very helpful. For the technical completeness, however, the combination lists shown in Table 8 are used for the performance evaluations in the rest of this paper.

Performance results
Churn prediction performance can be affected by the choice of machine learning algorithm and the choice of OP and CP in the churn definition. In this section, we investigate the effects of algorithm choice and OP/CP choice on the AUC performance.

Performance for different algorithms
We use three traditional algorithms and two deep learning algorithms to investigate performance sensitivity to different machine learning algorithms. To be specific, logistic regression, gradient boosting, and random forests, which are widely used for binary classification problems, are used as the traditional algorithms. A CNN model [34] and a LSTM model [35] are tuned and evaluated as deep learning algorithms. Logistic regression is a linear model for providing the posterior probabilities of multiple classes [36] [37]. In contrast, gradient boosting is an ensemble algorithm that increases its performance through randomized subsampling of training data [38]. Random forests is also an ensemble algorithm, and performance is improved by independently generating sampled trees and combining some of the tree predictors [39]. For the implementations of the three algorithms, we used R package's xgboost, glm, and cforest, respectively [40][41] [42].
For research problems such as image classification and natural language processing, deep learning has achieved remarkably enhanced performance in the past decade [29]. One main advantage of deep learning is that it avoids hand-crafting of features (i.e. feature engineering), which is typically required for traditional machine learning algorithms to work well. For image classification, for instance, previously human-coded programs had to be used to detect edges and textures. But, now CNN can automatically extract the edges and textures without human interventions [27]. Here, performance results of deep learning algorithms are provided to investigate if the churn prediction problem of casual games can significantly benefit from automatic feature extractions. Two popular deep learning algorithms are evaluated. For CNN, we use two convolutional layers with successive pooling layers followed by two fully connected layers. We tuned the hyper-parameters such as numbers of filters, filter sizes, and pooling sizes using a grid search. For LSTM, we tuned the number of neurons and input dimensions using a grid search. The deep learning algorithms were implemented using TensorFlow 1.0 library.
For the three traditional algorithms, the carefully designed features from the feature engineering section are used as the inputs. For deep learning algorithms, however, we do not use the extracted features. Instead, the raw data of three games are minimally processed such that the data's time patterns potentially can be utilized by the deep learning algorithms. To be precise, play log data is transformed into a one-dimensional vector that can be used as the input to the deep learning algorithms. For the transformation, a time framing was adopted as shown in Fig 5. In the figure, the value for each 10-minute time frame is calculated as the sum of all available play scores whose play end-time falls into the time frame. The aggregation of the scores in each time frame causes a slight reduction in information resolution, but the effect should be minimal because the size of a time frame is only 10 minutes. Table 9 summarizes the performance results of the five algorithms. A rigorous evaluation was performed by first setting aside 20% of the data as test data, and using the other 80% for 10-fold cross-validation. We allocated an independent test data set, as opposed to reusing validation data as test data, because training plus validation data was used for tuning hyperparameters of traditional machine learning algorithms and deep learning algorithms, and because the evaluation accuracy can be compromised unless an independent test data set is used for the final performance calculation. LSTM performed the best for Game #1, gradient boosting for Game #2, and both of logistic regression and gradient boosting for Game #3. While the winner varied over the three games, the performance advantage of the best performing algorithm was not very large compared to any other algorithm. This indicates that the data of the three casual games might not have a strong structure or pattern to take advantage of, and therefore simply running a reasonably well chosen machine learning algorithm might  Churn prediction of casual games suffice for churn prediction. Also, it can be observed that the performance of deep learning algorithms is comparable to the performance of traditional algorithms. In fact, deep learning algorithms performed slightly worse for Game #2 and Game #3. This indicates that the play patterns in time dimension is not very helpful for predicting churn, and simply utilizing active-Duration and playCount can be sufficient.
Only AUC results are shown in Table 9. The best accuracy values can be found by tuning the thresholds, and for gradient boosting they turn out to be 0.93, 0.86, and 0.85 for Game #1, #2, and #3, respectively. The values are high, but the high accuracy is simply because of many players quickly becoming churners for casual games. In general, AUC is a better evaluation metric, because it does not depend on a threshold [43].

Performance for different choices of OP and CP
All analysis results so far are based on OP = 5 days and CP = 10 days. While the choice of algorithm does not affect AUC much, the choice of OP and CP can have a substantial impact. To investigate the sensitivity, we have evaluated AUC for OP between 1 and 30 days and CP between 1 and 30 days. For Game #2, an exception was made and OP was evaluated only up to 15 days because the data collection period was relatively shorter (3.5 months) and buffer periods were set in the beginning and ending part of the data collection periods to prevent boundary effects. A total of 900 combinations (450 for Game #2) were evaluated for the three casual games, where the overall best performing gradient boosting algorithm was used with ten-fold cross-validation.
The results are shown in Fig 6, where three dimensional plots along with two dimensional plots are shown for Game #1, #2, and #3. In the case of OP, increasing OP has a strongly positive effect on the prediction performance. By having a longer observation period, more data for playing pattern and playing frequency can be obtained. Furthermore, churn players typically start showing less frequent play history as time goes by, and it becomes easier to distinguish typical churners if we wait longer. Choosing a large OP, however, has a few downsides as well. First, a large OP means a longer waiting time before churn can be predicted. If OP = 30 days, for instance, it means we can predict churn rate of the players who have started playing at least 30 days ago, and 30 days can be an unacceptably long time when a newly released casual games need to be quickly evaluated. Secondly, if we wait long enough, there might be almost no chance to contact the 'likely-to-churn' players and take preventive actions. For mobile games, preventive actions should be taken at least before the app is removed from the device.
In the case of CP, the effect is reversed and decreasing CP has a positive effect on prediction performance. By having a shorter churn prediction period, the prediction algorithm can focus on the short-term behaviors without worrying about long-term churning or returning. The effect is easily noticeable for CP between 1 and 5 days. The influence, however, becomes weaker or even unnoticeable after 5 days. As explained before, this implies that even CP = 5 days or larger might be sufficient to model most players' long-term behaviors as well as shortterm behaviors for casual games. Overall, there are tradeoffs for choosing OP and CP, and they are considered further in the discussion section.

Discussions
The behaviors of game players cannot be the same as the behaviors of the telecom or newspaper subscribers. Moreover, behaviors of casual game players can be even more different because of the light and temporal nature of playing casual games. People play for fun and easily quit without worrying about a contract or a subscription fee. By deep diving into the play log Churn prediction of casual games data of three casual games, we revealed the key insights that characterize casual games. The results are discussed further in this section.
The first result concerns single-feature analysis and feature combinations. We analyzed each single feature to determine its contribution to churn prediction performance. We defined 14 features, created five rankings, and then summarized the overall ranking by normalizing and averaging the five rankings. For all three games, activeDuration and playCount features took first and second positions. Not surprisingly, this indicates that a shorter playing time and a lower play count are more relevant to churning. On the other hand, meanScore feature took the lowest rank for all three games. One possible explanation is that casual game players often become distracted and quit in the middle of the play and therefore meanScore does not carry much of a meaning. Another possible explanation is that individual's skills and attitudes are vastly diverse that meanScore is difficult to utilize for characterizing individual players. Interestingly, bestScore and worstScore ranked 3 rd for Game #1 and Game #3, respectively. Game #1 happens to be the simplest game of the three, and Game #3 happens to be a team-play game where players might be keen to team members' assessments. Game-specific features, such as purchaseCount and winRatio, ranked 3 rd and 5 th , respectively for Game #2 and Game #3. They reflect the essential factors of each game's design, but ended up being less relevant than active-Duration and playCount. As for the feature combination analysis, the most important insight is that only 2~3 high-ranking features are needed for churn prediction. Technically, the best performance is obtained by using 4~9 features, but the performance improvement is negligible after using 2~3 features. We believe this is due to lack of complexity and diversity in the way casual game players behave. Casual games are quite different from other traditional games, and probably there are only a small number of factors that drive a player's behavior and the resulting churn. In this case, it is very important to choose effective features for monitoring users and making action decisions, but only a handful of well-crafted and validated features may be used safely for fully understanding user behavior.
The second result concerns the comparison of prediction performance of the five algorithms. LSTM and gradient boosting algorithms had the best prediction performance for the three games, but the performance advantage over the worst performance was small (AUC difference of 0.042 or less). As for the two deep learning algorithms, both of CNN and LSTM performed about same or slightly worse than the three traditional machine learning algorithms. This indicates that the deep learning's inherent capability to build and use features automatically by utilizing time-dimension patterns was not very helpful. Even though not included in this paper, additional studies including frame size tuning of both CNN and LSTM were conducted, but there was no significant improvement. The play log data of casual games is relatively simple, and our results indicate that indeed the prediction performance has little dependency on the choice of machine learning algorithm.
The last result concerns the definition of churn by choosing OP and CP. For churn analysis of non-subscription services, the performance can drastically change depending on how churn is defined. Therefore, it is essential to understand the tradeoffs and to specify the details. For the three casual games that we have analyzed, AUC performance can widely vary from below 0.7 to above 0.9 depending on the choice of OP and CP. Increasing observation period and decreasing churn prediction period can be helpful for enhancing performance value, but there are tradeoffs with how long one needs to wait before churn rate can be predicted and if the performance value well represents the business aspects that one is interested in. For casual games, a few to several days seem to be appropriate for both OP and CP, and we have used 5 and 10 days for most of our analyses.
A limitation of this research lies in the datasets of the three games. Casual games are becoming less simple as time goes by, and social functions (such as chatting, friend list, and team plays) and other new functions are being adopted. We have examined features relevant to item purchase (Game #2) and team winning (Game #3) in this study, but they are not sufficient for understanding future casual games, and further studies are needed.

Conclusions
In this work, we analyzed three casual games by performing churn predictions. Through the analysis, we demonstrated how play log data can be used to conduct a fundamental set of churn analyses. Churn was carefully defined for casual games, and a standard process for analysis was established. The definition and process are directly applicable not only to casual games, but also to any new user analysis of non-subscription-based services. Overall, the main findings in this study are due to the simple nature of casual games. If the findings generally hold true for most of casual games, choosing an appropriate churn definition and identifying a few core features can be the most important parts of understanding and preventing churn.