Betting Games Research Articles

The phenomenon of electronic betting games: socioeconomic and health impacts - an integrative literature review

Introduction: The phenomenon of bets referred to as electronic gambling in Brazil, following precarious regulation of the activity through a federal normative act has impacted the economic, social, and health realities of the Brazilian population. Objective: This study aims to identify the factors associated with gambling in the context of the scientific literature between 2014 and 2024, as well as its implications for the economy and public health. Method: An integrative literature review was conducted, based on research using databases accessible through Scielo, PubMed, Scopus, and BVS search engines. Results: Articles addressing the economic and public health impacts of gambling, particularly addiction and its social consequences, were analyzed. The study includes an examination of the effects of gambling on vulnerable communities and offers policy recommendations. Conclusion: The findings indicate that while gambling generates revenue, it exacerbates inequalities and creates new challenges for public health systems.

On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games as a Demonstration Case

The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear feedback, the use of nonlinear control is conspicuously absent. This is epitomized by the large subset of this literature dealing with Kelly Betting. With this as the high-level motivation, we study the potential for use of nonlinear control in this framework. To this end, we consider a “demonstration case” which is one of the simplest scenarios encountered in this line of research: repeated flips of a biased coin with probability of heads p, and even-money payoff on each flip. First, we formulate a new robust nonlinear control problem which we believe is both simple to understand and apropos for dealing with concerns about distributional robustness; i.e., instead of assuming that p is perfectly known as in the case of the classical Kelly formulation, we begin with a bounding set P0,1 for this probability. Then, we provide a theorem, our main result, which gives a closed-form description of the optimal robust nonlinear controller and a corollary which establishes that it robustly outperforms linear controllers such as those found in the literature. A second, less significant, contribution of this paper bears upon the computability of our solution. For an n-flip game, whereas an admissible controller has 2n-1 parameters, at the optimum only O(n2) of them turn out to be distinct. Finally, it is noted that the initial assumptions on payoffs and the use of the uniform distribution on p are made mainly for simplicity of the exposition and compliance with length requirements for a Letter. Accordingly, the paper also includes a new section with a discussion indicating how these assumptions can be relaxed.

A Generalization of the Classical Kelly Betting Formula to the Case of Temporal Correlation

For sequential betting games, Kelly's theory, aimed at maximization of the logarithmic growth of one's account value, involves optimization of the so-called betting fraction K. In this letter, we extend the classical formulation to allow for temporal correlation among bets. To demonstrate the potential of this new paradigm, for simplicity of exposition, we mainly address the case of a coin-flipping game with even-money payoff. To this end, we solve a problem with memory depth m. By this, we mean that the outcomes of coin flips are no longer assumed to be i.i.d. random variables. Instead, the probability of heads on flip k depends on previous flips k - 1, k - 2, ..., k - m. For the simplest case of n flips, with m = 1, we obtain a closed form solution K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> for the optimal betting fraction. This generalizes the classical result for the memoryless case. That is, instead of fraction K* = 2p - 1 which pervades the literature for a coin with probability of heads p ≥ 1/2, our new fraction K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> depends on both n and the parameters associated with the temporal correlation. Generalizations of these results for m > 1 and numerical simulations are also included. Finally, we indicate how the theory extends to time-varying feedback and alternative payoff distributions.

LİSE ve ÜNİVERSİTE ÖĞRENCİLERİNİN SPOR MEDYASINI İZLEME VE BAHİS OYUNU OYNAMA ALIŞKANLIKLARI

Bu arastirmanin amaci, lise ve universitelerde ogrenim goren ogrencilerin spor medyasini izleme ve bahis oyunu oynama aliskanliklarinin belirlenmesidir. Bu kapsamda ogrencilerin medyayi izleme duzeyleri ve bahis oyunu oynayip oynamadiklari da sorgulanmistir. Bolu ve Sakarya’da genel lise, Anadolu lisesi ve meslek liselerinde ogrenim goren 554 ogrenci ile Abant Izzet Baysal Universitesi ve Sakarya Universitesi’nde ogrenim goren 521 ogrenci arastirmanin orneklemini olusturmustur. Ankete katilan lise ogrencilerinin % 42’si hic bahis oyunu oynamadigini bildirirken, % 38’i ara sira, % 11’i ise duzenli olarak oynadigini bildirmistir. Bu sonuc, 18 yasindan kucuklerin bahis oyunu oynamasinin yasak oldugu Turkiye icin uzerinde dusunulmesi gereken bir durumdur. Universite ogrencilerin % 80.4’u spor medyasini takip etmektedir. Spor medyasini takip eden ogrenciler, en cok televizyondaki spor haberlerini ile spor programlarini takip etmektedir. Katilimcilarin % 33’u ara sira, % 9.2’si de duzenli olarak bahis oyunu oynamaktadirlar. Bahis oyunlarini yogun olarak erkek ogrenciler oynamaktadir. Aileleri dar gelirli universite ve lise ogrencileri, para kazanmak amaciyla bahis oyunu oynamaktadir.

Exact Learning Algorithms, Betting Games, and Circuit Lower Bounds

This article extends and improves the work of Fortnow and Klivans [2009], who showed that if a circuit class C has an efficient learning algorithm in Angluin’s model of exact learning via equivalence and membership queries [Angluin 1988], then we have the lower bound EXP NP not C. We use entirely different techniques involving betting games [Buhrman et al. 2001] to remove the NP oracle and improve the lower bound to EXP not C. This shows that it is even more difficult to design a learning algorithm for C than the results of Fortnow and Klivans [2009] indicated. We also investigate the connection between betting games and natural proofs, and as a corollary the existence of strong pseudorandom generators. Our results also yield further evidence that the class of Boolean circuits has no efficient exact learning algorithm. This is because our separation is strong in that it yields a natural proof [Razborov and Rudich 1997] against the class. From this we conclude that an exact learning algorithm for Boolean circuits would imply that strong pseudorandom generators do not exist, which contradicts widely believed conjectures from cryptography. As a corollary we obtain that if strong pseudorandom generators exist, then there is no exact learning algorithm for Boolean circuits.

On Loss Aversion, Level-1 Reasoning, and Betting

Previous research suggests that human reaction to risky opportunities reflects two biases: and level of that leads to overconfidence. Rejection of attractive gambles is explained by loss aversion, while counterproductive risk seeking is attributed to limited level of reasoning. The current research highlights a shortcoming of this popular (but often implicit) contradicting biases assertion. Studies of negative-sum betting games reveal high rate of counterproductive betting even when limited level of reasoning and loss aversion imply no betting. The results reflect two reasons for the high betting rate: initial tendency to participate and slow learning. Under certain conditions, the observed betting rate was higher than the rate predicted under random choice even after 250 trials with immediate feedback. These results can be captured with a model that assumes a tendency to select strategies that have led to good outcomes in a small set of similar past experiences, and allows for an initial framing effect.

Revisiting games of incomplete information with analogy-based expectations

This paper studies the effects of analogy-based expectations in static two-player games of incomplete information. Players are assumed to be boundedly rational in the way they forecast their opponent's state-contingent strategy: they bundle states into analogy classes and play best-responses to their opponent's average strategy in those analogy classes. We provide general properties of analogy-based expectation equilibria and apply the model to a variety of well known games. We characterize conditions on the analogy partitions for successful coordination in coordination games under incomplete information [Rubinstein, A., 1989. The electronic mail game: Strategic behavior under ‘almost common knowledge’. Amer. Econ. Rev. 79, 385–391], we show how analogy grouping of the receiver may facilitate information transmission in Crawford and Sobel's cheap talk games [Crawford, V.P., Sobel, J., 1982. Strategic information transmission. Econometrica 50, 1431–1451], and we show how analogy grouping may give rise to betting in zero-sum betting games such as those studied to illustrate the no trade theorem.

Parimutuel betting under asymmetric information

This paper examines simple parimutuel betting games under asymmetric information, with particular attention to differences between markets in which bets are submitted simultaneously versus sequentially. In the simultaneous parimutuel betting market, all (symmetric and asymmetric) Bayesian–Nash equilibria are generically characterized as a function of the number of bettors and the quality of their private information. There always exists a separating equilibrium, in which all bettors follow their private signals. This equilibrium is unique if the number of bettors is sufficiently large. In the sequential framework, earlier bets have information externalities, because they may reveal private information of bettors. They also have payoff externalities, because they affect the betting odds. One effect of these externalities is that the separating equilibrium disappears if the number of betting periods is sufficiently large.

Gambling behavior in two-outcome multistage betting games

In a favorable multistage gambling process, a biased coin with the probability of “heads” p > 1 2 is tossed repeatedly. Before each toss, a gambler is required to bet a fraction of his capital on “heads”. His problem is to choose a betting policy that is optimal with respect to some criterion. A model yielding a proportional stationary Markov betting policy is presented and generalized. The sensitivity of the model to departures from optimality is investigated. Fifty-one subjects participated individually in a multistage gambling experiment. While most subjects performed efficiently in terms of the model, the model was not strictly supported, since both the current amount of capital and the pattern of previous outcomes affected subjects' betting decisions.

Gambling behavior in multiple-choice betting games

In a multistage gambling process, a gambler is required to apportion his capital over the available alternatives, and is paid according to the outcome of the game. His problem is to choose a betting policy that is optimal with respect to some criterion. Examinations of logarithmic and power utility functions yield proportional stationary Markov betting policies which are generalized to cases where the vector of probabilities of outcomes is unknown. The sensitivity of the model to departures from optimality is investigated. Twenty-nine subjects participated individually in a multiple-choice multistage gambling experiment. While neither the logarithmic nor the power model was strictly supported, the former was favored by the data. Both the current amount of capital and the pattern of previous outcomes, irrelevant factors in both models, were found to affect subjects' betting decisions.

Minimization of risk and maximization of expected utility in multistage betting games

Consider the following multistage betting game (MBG) with m alternatives, each of which obtains with probability p i ( p i > 0,Σ m i=1 p i =1, i=1, 2, …, m). Case 1 of the MBG, which is discussed in this paper, requires that on each stage of the game the player allocate all of his capital, denoted by x, x > 0, over the m alternatives, betting the amount y i on alternative i ( y i ≧ =0, Σ m i=1 y i = x). If alternative i obtains on a given stage, the player's new capital for the next stage is y i r i , where r i is the return for alternative i, r i > 0. The game is played for N stages, assuming that p i and r i are stationary. It resembles certain sequencial investment processes that have been studied by economists, and generalizes static, two-outcome, gambling experiments conducted by psychologists. Two models for MBG are proposed, both of which have been studied by economists and psychologists in the areas of portfolio selection and decision making behavior under risk, respectively. The first is a minimization of risk model, assuming that the player fixes an expected value and then attempts to minimize the variance of the gamble. The second is an expectation model, assuming maximization of expected utility. Proportional betting policies are presented for both models, assuming in the latter case linear, logarithmic, or power utility functions. Results obtained from five subjects in a computer-controlled MBG experiment show systematic effects of capital size on betting decisions, which are incompatible with any proportional betting policy.