The Need for the Empirical Determination of Games of Chance and Skill

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– Malcolm Katrak*

I. Introduction

Recently, a Division Bench of the Bombay High Court sought a reply from the State authorities on the allegation that a game application called Ludo Supreme was engaged in gambling activities. Essentially, the Applicant’s (Mr. Keshav Muley) argument is that Ludo is a ‘game of chance’, and not a ‘game of skill’. The Supreme Court, in the past, in its decision in KR Lakshmanan (Dr.) v. State of Tamil Nadu (‘Lakshmanan’), has elaborated on the difference between games of chance and skill. A game of chance is determined entirely or in part by luck, whereas, although a game of skill may have an element of chance, success in the game depends predominantly on the player’s skill. If the game is one of chance, the penalty provisions of the Public Gambling Act, 1867, or its equivalent state legislations, would be attracted against people for keeping a ‘common gaming house’ where games of chance are played. To categorize whether the game is one of chance or skill, the court in Lakshmanan laid down the ‘dominant factor’ test, where the courts must determine whether the dominant element is skill or chance. 

The aim of this piece is two-fold. Firstly, and most importantly, the author posits an argument that there must be an objective measure to analyse whether the outcome of a game depends predominantly on chance or skill. To buttress this point, the author uses a study by Duersch et al to lay down the scientific test for measuring the ‘dominance of skill/ chance’ in a game. The author opines that the objective element could be undertaken by courts by appointing amicus curiae having special knowledge of law and economics, or by allowing expert witnesses to testify in matters related to the classification of games. Secondly, the piece also intends to briefly touch upon Professor Faisal Alvi’s research on playing strategies in a non-deterministic race game, such as Ludo. Essentially, a non-deterministic game involves some element of randomness, like rolling a die. This would imply that Ludo has elements of both chance and skill, making it a good study for the present post. Part II of the piece provides a brief analysis of the game of Ludo, including the strategies involved, and the subtle differences between the game of Ludo and the game application, i.e., ‘Ludo Supreme’. Part III delves into the ‘dominant factor’ test laid down by the Supreme Court in the case of Lakshmanan. This Part, specifically, covers the game of poker, primarily to showcase the importance of carrying out mathematical research in analyzing ‘dominance’. Part IV embarks on an analysis of the research conducted by Duersch et al on the process of analyzing ‘dominance’. Part V touches, rather briefly, on the research carried out by Professor Faisal Alvi on the game of Ludo. Through Part VI, the author concludes with remarks about the game of Ludo, and the need to have a uniform objective standard of measuring ‘dominance of skill/ chance’ in a game.

II. Ludo (Supreme) – Strategies and Differences 

In a game of Ludo, two to four players “race” their tokens from start to finish according to the rolls of a dice. The areas (red, blue, green, and yellow), as displayed in Figure 1, where the tokens are situated, indicate the ‘coloured areas’ of each player. Adjacent to the coloured area, is the ‘home column’. As indicated in Figure 1, the home column of Player 4 is the green column, adjacent to the green coloured area. Essentially, the goal of the players is to deposit all four tokens inside the coloured area into the home column, and, eventually, into the home area, which is situated right at the centre of the board. A normal game of Ludo requires the player to get a ‘six’ on the roll of a die to move one token out of the coloured area. Thereafter, the number obtained through the roll of die will determine the number of steps the token moves on the board. 

Figure 1: Ludo Board: Top view of Ludo Game Board with Dice

Whilst a normal game of Ludo, as mentioned above, requires a ‘six’ on the die to get a token out of the coloured area, the gaming application in contention in the case before the Bombay High Court, i.e., Ludo Supreme, waives this requirement for all players. Therefore, as seen in Figure 2 below, all four tokens of each player would be on the first tile, instead of inside the coloured area. This difference is important as the players do not have to wait for the ‘six’ on the roll of the die, which would be dependent on chance. Thus, after a few moves, the players can use several strategies to improve their position comparable to the others. Beyond the waiver of the requirement of throwing ‘six’ on the die, the Applicant in the case pointed out that Ludo Supreme has a ‘prize pool’, as indicated in Figure 2 below. In the prize pool, the game accumulates some portion of monies as wagers for a given draw from the players. Eventually, the winner takes the whole prize pool, or the same is proportionally divided depending on the position of the players. 

Figure 2: Ludo Supreme (starting position of the tokens)[1]

If Ludo Supreme is found to be a game of chance, the indication of a prize pool would expressly showcase a wager on the game. Furthermore, a prize pool in an online game of chance would make the application a ‘common gaming house’ under the Maharashtra Prevention of Gambling Act, 1887. Therefore, if the courts deem Ludo Supreme to be a game of chance, the Respondent would be liable under the aforesaid Act.  

The Applicant’s argument as far as the game of skill/ chance is concerned, is that a roll of the die gives anyone an opportunity to win the game, without any prior understanding of the rules. Thus, the contention is that the outcome of the game is dependent entirely, or in part, on mere lot or luck. To analyze whether Ludo is one of chance or skill, it becomes imperative to inquire if there are any strategies involved. Ludo has been categorized as a non-deterministic race game, essentially entailing some element of chance, due to the randomness of the role of the die. It is also a race game, wherein the goal is to bring the tokens into the safety zone, often referred to as the ‘home column’. In general, race games can be games of either chance or skill. For instance, a game of snakes and ladders can be considered a game of chance, since the participants have no control over the roll of the die and, thereby, the outcome of the move. On the other hand, a game of backgammon, which can also be classified as a race game, entails using strategies such as, inter alia, blocking, priming, and duplication. 

In respect of the game of Ludo, Professor Faisal Alvi argues that there are at least five strategies involved. The following strategies could be used by the players: (i) Random Strategy: A player chooses to play a token at random. In this case, the player sees no advantage in moving a particular piece and, therefore, moves his tokens at random; (ii) Aggressive Strategy: The player, through this move, uses his token to eliminate the token of another player. An aggressive strategy has an impact on the other player, as his token goes back to the special area; (iii) Defensive Strategy: Through this, the player’s intent is to secure his token, essentially moving it out of the knocking range of one to six tiles. For instance, if the player rolls ‘five’ on the die, he could use his first token to move aggressively against an opponent’s token. However, in this strategy, the player would prefer to secure his second token, which is five blocks away from safety. Thus, in a defensive strategy, the player would use the roll of five to secure his second token, instead of attacking with the first one; (iv) Mixed Strategy: This is the general play structure, wherein the player may use different strategies depending upon his position in the game. He may use a hybrid of aggressive and defensive strategies; (v) Fast Strategy: In this case, the player’s only aim is to deposit his token in the home column as soon as possible. Therefore, if he gets an opportunity to remove another token after getting a ‘six’ on his roll, he would rather use the ‘six’ to race his first token into the home column.

Evidently, several strategies are involved in the game of Ludo for the participant. Unfortunately, the lack of analysis, specifically due to lack of available data, makes it difficult to show the time taken to grasp the fundamentals of the game and to reach a performance level. However, Professor Faisal Alvi’s study comes closest to analyzing the complexity of Ludo. He uses the expected value of die rolls and average token movement over many games, to conclude that the mixed strategy is far superior, when compared to the other basic strategies. He also finds that a defensive strategy can be assigned a higher weight than an aggressive strategy. This shows, at the very least, that even though there is an element of chance based on the roll of the die, the success could depend upon the training, attention, and experience of the player.

III. The Lakshmanan Rekha: Can the Line be Tweaked?

In Lakshmanan’s case, the Supreme Court had occasion to decide whether horse racing amounted to ‘gaming’ under the Madras City Police Act, 1888, and the Madras Gaming Act, 1930. The court, rightly, determined that games may be games of chance, or skill, or skill and chance combined. According to the court, a game of chance is one where the element of chance predominates over the element of skill, and a game of skill is one in which the element of skill predominates over the element of chance. Essentially, the courts must use the ‘dominant factor test’ to see whether the element of skill or chance dominates over the other. The Supreme Court, whilst deciding Lakshmanan, relied on its previous decision in State of Andhra Pradesh v. K. Satyanarayana (‘Satyanarayana’)wherein it had differentiated the game of rummy and three card games, such as flush and brag, to conclude that rummy was ‘predominantly’ a game of skill. This begs the question of how one should measure the ‘predominance of chance/skill in a game’. 

The court in Lakshmanan enumerated that the test for a game of skill could include analyzing the requirement of knowledge, strength, dexterity, reaction time, speed, mental/physical feats, developed or learnt through practice, experience, or study. This would imply that the court would, in all cases, determine the probability of the outcome of the game through a proper probability and statistical analysis. However, in almost all cases, the judges have used their discretion, albeit relying on previous judicial decisions, to conclude whether the game is one of chance or skill. Research studies, controlled mathematical experiments, and scientific studies of these games have very rarely been taken into cognizance by the courts in India. Poker is one example in which the courts in India have refused to rely upon extensive studies carried out by research scholars. The courts have often used bare descriptions of the rules of the game to conclude that a game, such as poker, is one of chance. Without reliance on extensive investigations or the conducting of scientific studies, the Lakshmanan standard of analyzing knowledge, strength, and other factors of a player would hold no weight. Lack of statistical analysis is easier in the case of a pure skill-based game, i.e., chess. However, in a game such as poker, it becomes extremely difficult. 

Oftentimes, it is easy to characterize certain games as games of skill. Chess, a combinatorial game, is one example of this. In a combinatorial game, it is extremely difficult to determine how a game should develop from a given position, considering that there are innumerable combinations of moves. Therefore, in almost all jurisdictions, chess has been rightly categorized as a game of skill.[2] Meanwhile, the lack of clarity on the ‘dominant factor test’ can be witnessed in poker cases, not just in India, but around the world. For instance, in India, there has been uncertainty surrounding the legality of the game of poker for decades, especially considering that most of the High Courts’ decisions could be applied to their own factual scenarios, rather than having a precedential/ general applicability. The Indian Poker Association cases decided by the Karnataka and Calcutta High Courts tend to favour an interpretation of poker variants being a game of skill, although neither of them affirms this position categorically. The Karnataka High Court, in the case of Indian Poker Association v. State of Karnataka, held that if a game of poker is played as a game of skill, a license is not required and, therefore, the party would be well within its right to conduct such games. Similarly, the Circuit Bench of the Calcutta High Court, in its decision in Indian Poker Association v. State of West Bengal, observed that since poker was not explicitly included within gambling activities under the state’s Gambling Act, there would not be any liability. 

Meanwhile, the Gujarat and Bombay High Courts have categorized poker and its variants as games of chance. The Gujarat High Court, in the case of Dominance Games Pvt. Ltd. v. State of Gujarat, compared to the other High Courts, has delved into the nature of poker and its variants, eventually relying on the Supreme Court’s decision in Satyanarayana and M.J. Sivani v. State of Karnataka (‘M.J. Sivani’) to conclude that poker is a game of chance. More importantly, the Petitioner’s counsel had, in this case, relied on several academic articles which had concluded that poker is a game of skill. The court, unfortunately, refused to give much importance to these articles, stating that articles must be considered in the background of the facts. Lastly, the Bombay High Court, in the case of Nasir Salim Patel v. State of Maharashtra, referred to the game played by the Petitioner as one related to “game of card”, eventually concluding that it depended primarily on chance. 

The Supreme Court through its decision in M.J. Sivani has held that poker is a game of chance when played on electronic machines, which are adjusted in such a way that no player can win any game. In that sense, M.J. Sivani can be easily distinguished from the facts of any other case. This shows the need to devise a standard method for measuring the skill and chance components of games.

IV. Factoring in the Predominant Factor 

Duersch et al begin their paper with two substantial questions: (i) how can one measure whether the outcome of a game depends predominantly on chance?, and (ii) if one were to agree that ‘predominantly’ means more than 50%, the question is, “50% of what?” Their paper aims at providing a clear 50% benchmark for the predominance of chance. They use the Elo rating system, which is a method for calculating the relative skill levels of players and applying the same to the players in their dataset. Essentially, a player’s Elo rating is represented by a number which may change on the outcome of the rated games played. Therefore, after every rated game, the winning player takes points from the losing one. Simply put, if Player A, a higher-rated player, wins against Player B, a lower-rated player, then only a few rating points will be taken from the lower-rated player. On the other hand, if Player B beats Player A, many rating points will be transferred. Through Elo ratings, it is easier to match players with similar abilities together. Consequently, the difference in the ratings of two players has a direct correspondence with the winning probabilities when the two players are matched against each other. 

Duersch et al propose an explicit 50% benchmark for skill and luck differentiation. They create an artificial game that is exactly half chance and half skill. The game of chess is used as a parameter for pure skill. An artificial game, created by the authors, randomly replaces 50% of the matches in the chess data by coin flips. They contend that through this, they mix a pure skill game with 100% chance game (coin flip), essentially constructing a ‘50% chess game’. Using this 50% chess benchmark, they find that games such as poker and backgammon are below the 50% chess threshold, thereby entailing that the games are chance based. Of course, this is not to say that there is no skill involved. However, if the word ‘predominant’ is taken as more than 50% of skill, several games, including rummy, which has been declared by Supreme Court vide its decision in Satyanarayana as a game of skill, may not pass this threshold. This shows that the ‘predominant test’ laid down in Lakshmanan cannot be analyzed by a subjective outlook of the judges. The judges must consider the mathematical evidence/ statistical studies carried out by research scholars. It is nevertheless necessary to point out here that, oftentimes, academic studies may reach different conclusions. In those cases, the courts could look at appointing an amicus curiae to provide the necessary evidence or to carry out research, specifically pertaining to the variant of the game in question. Further, considering that gambling laws attract penal provisions, the courts could allow expert witnesses to testify. 

Jörg Bewersdorff’s seminal book, ‘Luck, Logic, and White Lies: The Mathematics of Games’ analyses the most famous games and investigates mathematically the chance, combinatorial, and strategic elements of these games. He mentions the German Federal Administrative Court’s decision of 1984, where it realized the “need to determine the character of the game using scientific methods”. The court stated that it is imperative that the predominance of skill or chance be analyzed using scientific methods. It also mentioned that during an empirical analysis based on a series of test games, not all players had to use their skill to win a test game. In 2012, the United States District Court of New York, in the case of United States of America v. Lawrence Dicristina, allowed expert testimony by economists and statisticians to conclude that poker is ‘predominantly’ a game of skill. The specific conclusions of the expert witness were summarized by the court as follows:

(1) [P]oker involves a large number of complex decisions, which allow players of varying skill to differentiate themselves…; (2) many people play poker for a living and consistently win money over time…; (3) players who obtain superior results with other starting hands tend to obtain superior results with any given hand, indicating that the players’ abilities, not the cards, are responsible for the results…; (4) the published studies are all consistent with [these] conclusions”.

Not only did the court conclude using expert evidence, but also clarified the meaning of the word ‘predominate’. According to the court, “to predominate, skill must account for a greater percentage of the outcome than chance, i.e., more than fifty percent”. This is the approach that most of the courts should take into account while analysing whether games are those of chance or skill. 

V. Can Ludo Reign Supreme?

Before the High Court proceedings, the Applicant had approached the local Metropolitan Court against the makers of Ludo Supreme, Cashgrail Pvt. Ltd. The Metropolitan Court was quick to dismiss the complaint on the grounds that “it was a game of skill and not a game of chance”. As mentioned above, Professor Faisal Alvi’s research analyzing strategies of basic moves applicable in Ludo, seems to indicate a combinatorial game with several possibilities after the token is out of the special area. Additionally, Alhajri et al used Reinforcement Learning (‘RL’), a popular machine learning technique, in which the agent created by the authors has self-learning ability. The agent learned the game through a trial-and-error process, in an environment that is not controlled. Thereafter, the authors created an expert player, who knew the strategies applied in the game of Ludo. The strategies were those identified by Professor Faisal Alvi in his research. Eventually, the agent created through RL was pitted against the expert player. The authors found that the agents were able to exhibit better game play against the expert players. 

The research conducted by Professor Faisal Alvi and Alhajri et al indicate that several strategies are involved in the game of Ludo. Nevertheless, there is a randomness element in any game involving the roll of a die. Therefore, more statistical evidence is required to show that the game of Ludo predominantly is a game of skill, i.e., that it crosses the 50% threshold. 

Taking the case of Ludo Supreme, as mentioned previously, a player does not have to roll ‘six’ on the die to release his token from the coloured area. This is important, as all four tokens of the player start outside the player’s coloured area on the first tile. Therefore, the release move that a player requires a ‘six’ is waived off, which, in turn, allows the player to select any of the strategies mentioned above without the initial die roll, which is often directed by the algorithm. Taking the Lakshmanan standard, it would be easy to conclude, on the face of it, that Ludo, especially Ludo Supreme, is a game of skill. Nevertheless, considering the uncertainty involved, it is necessary to carry out mathematical/ scientific studies for this specific game. The question that one could ask is whether the randomness element is reduced if the requirement of ‘six’ is waived off compared to a normal game of Ludo. 

VI. Conclusion

The Supreme Court has categorized several games as games of skill. In doing so, it has allowed certain contracts to be fulfilled by taking them out of the purview of a wager under section 30 of the Indian Contract Act.[3] However, courts must, especially while examining games which involve chance and skill, consider mathematical evidence to determine ‘substantial degree’ or ‘preponderance of skill’. This, as mentioned previously, could be done by appointing an amicus curiae having specialized knowledge in law, statistics, and economics. Courts may also consider the possibility of calling expert witnesses to testify, if contradictory studies are present on the classification of games having elements of skill and chance. 

Even though the piece concentrates on the game of Ludo, it transcends that boundary to lay down how mathematical evaluation can take place. It is pertinent to note that all the studies relied on by the author have been conducted by researchers outside India. For this reason, it is imperative that research into the variants of Ludo, poker, and online gaming take place in the Indian context. This would allow the courts to use this research in specific scenarios, applying it to particular cases in India. For instance, research on Pachisi and Parcheesi, two variants of Ludo, may have different strategies and randomness elements when compared with the game of Ludo as played in India. Researchers may then be called as expert witnesses to provide evidence on the predominance of skill/ chance element in a game. Only an empirical evaluation, which is not influenced by subjective standards, can determine whether a game is one of chance or skill. 

* Malcolm Katrak is a Lecturer at the Jindal Global Law School (JGLS). His primary research interests are Law and Economics, and the Law of Contracts.  


[1] Screenshot from the gaming application ‘Ludo Supreme’ taken by the author. The same is available on file with the author.

[2] State v. Gupton (30 N.C. 271; 8 Iredell, 271), arguably, one of the first cases dealing with the skill-chance differentiation, regarded chess as a game of skill. See also, People ex Rel. Ellison v. Lavin (179 N.Y. 164), which, in 1904, relied on Gupton to elaborate that chess is a game of skill; M/s Gaussian Network Pvt. Ltd. v. Ms. Monica Lakhanpal (N.C.T Suit No. 32/ 2012), in which the Delhi District Court opined that the games of rummy, chess, billiards, and bridge are games of skill. It relied on the analysis of Lakshmanan’s case to come to this conclusion.

[3] Section 30 of the Indian Contract Act, 1872, declares wagering agreements void, and prohibits suits for recovering anything won on a wager. 

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