Lotto Games Research Articles

Strategically Revealing Intentions in General Lotto Games

Strategically Revealing Intentions in General Lotto Games

Reasons for Gambling in University Students, Loneliness? A study on sports science students

This study was conducted to investigate the reasons behind university students' gambling and especially to examine the relationship between loneliness and gambling. The population of the research consists of the students of the Faculty of Sports Sciences in Istanbul. The sample consisted of 1051 volunteer students of the Faculty of Sports Sciences selected by random method. The study data were obtained through Personal Information Form, Reasons for Gambling Scale and UCLA Loneliness Scale. The sample group of the study consisted of students from 5 private and 2 foundation universities with a Faculty of Sports Sciences who had played at least one of the online games, sports betting, horse racing, lottery, card/table games and numerical lotto games with money in the last 3 months. The data obtained were analyzed using SPSS 25.0 package programme and the significance level was set as 0.05. According to the findings obtained as a result of the study, it was determined that students studying at private universities need to gamble for the reason of earning money, while students studying at public universities have a high urge to have fun/excitement as a reason for gambling. In addition, it was determined that students who do not work need to gamble for the reason of earning money. As another result, it was determined that students who do not do sports as a licensed athlete feel themselves more lonely than licensed athletes. In line with the main purpose of the study, it was concluded that loneliness triggers the urge to gamble.

Is There a Gender Gap in the Birthday-Number Effect? The Case of Lotto Players and the Role of Sequential Choice.

The literature on lottery gambling shows that players do not select numbers randomly, a phenomenon which is called conscious selection. Mainly, players prefer "small" numbers (less than thirty), either because of the existence of small lucky numbers or because they are victims of the so-called birthday-number effect. Because lotto games are parimutuel, such preferences result in poor ticket choices in terms of achieving below average returns. Using data from Belgium, where approximately 10% of the population plays lotto games every week, this paper extends prior literature by documenting the existence of a gender gap in the birthday-number effect, with women displaying a stronger birthday-number effect than men, as well as the non-persistence of the birthday-number effect (and consecutively of the gender gap) when participants are asked to fill in a second lotto ticket immediately after their first one. The disappearance of the birthday-number effect in sequential choices appears to be driven by response speed, with participants being twice as fast to fill in the second ticket compared to the first one. Moreover, we find that participants who bet on their birthday numbers take significantly more time to complete their ticket. Contrary to prior research, we find that the strength of the birthday-number effect is positively related to deliberative number choices, not intuitive and automatic number choices. Our results are robust to controlling for potential confounding effects including those related to participants' age, education, self-esteem, and superstitious beliefs.

Extension Theorems for General Lotto Games With Applications to Network Security

The General Lotto game is a well-studied model where two opposing players strategically allocate a limited amount resources to multiple contests. In the classic setup, each contest represents an individual battlefield with an associated value, and the objective is to maximize the accumulated value by winning individual battlefields. In this paper, we consider scenarios beyond the classic setup, where (i) the notion of a battlefield is generalized to individual contests, (ii) success on a contest can depend on securing subsets of battlefields, and (iii) the winner of a battlefield can be based on alternate winning rules other than the classic winner-take-all rule. Our main results demonstrate that having an equilibrium solution to a single contest scenario can provide immediate equilibrium characterizations for two important generalizations: 1) the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">linear-count extension</i> , where performance is measured by the cumulative weight of the contests that are won. 2) The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">weakest-link extension</i> (best-shot), where one player must win <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">all</i> (at least one) of the constituent contests in order to earn any value. We demonstrate the applicability of these extensions to a general class of network path defense problems. In particular, our results can generate exact solutions to series-parallel networks, as well as provide bounds on equilibrium payoffs bounds for arbitrary networks. To conclude, we provide equilibrium solutions to a novel class of contests with non-linear favoritism winning rules.

DETERMINING THE PROBABILITIES OF THE OUTCOMES OF LOTTO GAME USING HYPERGEOMETRIC DISTRIBUTION

The probability density function (PDF) of the hypergeometric is used to model the probability of outcomes of lotto game given some selected predetermined scenarios (K) from (n = 5) samples at the instances of six sample scenarios x = 0, 1, 2, 3, 4, 5. This is exactly mimicking the Nigerian Premier Lotto game where interested players are expected to choose five random numbers from 1 to 90. That ‘A’ win implies that at least three of the randomly chosen 5 numbers are drawn from the national lotto draw often televised to the players. In this paper, different predetermined scenarios are defined and the probability is computed using the probability density function of the hypergeometric distribution. The data are results from 31625 games played on premier lotto in a span of 3 years. The data are for morning, afternoon, night, in Enugu center, regional and national premier lotto results during the period. The chi-square test of goodness of fit shows that the premier lotto is random, fair, and validates the results of the adoption of the PDF of hypergeometric distribution. Players of lotto games are advised to be aware of the slim chances of winning and play reasonably and sensibly.

Equilibrium characterizations of multi-resource Lotto games

The allocation of heterogeneous resources plays an increasingly important role in the completion of system objectives and tasks. In this paper, we focus on deriving optimal strategies for the allocation of heterogeneous resources in a well-known adversarial model known as the General Lotto game. In standard formulations, outcomes are determined solely by the players’ allocation strategies of a single type of resource across multiple contests. In particular, a player wins a contest if it sends more resources than the opponent. Here, we propose a multi-resource extension where the winner of a contest is now determined not only by the amount of resources allocated, but also by the composition of resource types that are allocated. We completely characterize the equilibrium payoffs and strategies for two distinct formulations. The first consists of a weakest-link/best-shot winning rule, and the second considers a winning rule based on a linear combination of the allocated resources. We then provide equilibrium investment strategies in scenarios where the resource types are costly to purchase, and players each have a limited monetary budget.

Strategically revealing capabilities in General Lotto games

Can revealing one's competitive capabilities to an opponent offer strategic benefits? In this paper, we address this question in the context of General Lotto games, a class of two-player competitive resource allocation models. We consider an asymmetric information setting where the opponent is uncertain about the resource budget of the other player, and holds a prior belief on its value. We assume the other player, called the signaler, is able to send a noisy signal about its budget to the opponent. With its updated belief, the opponent then must decide to invest in costly resources that it will deploy against the signaler's resource budget in a General Lotto game. We derive the subgame perfect equilibrium to this extensive-form game. In particular, we identify necessary and sufficient conditions for which a signaling policy improves the signaler's resulting performance in comparison to the scenario where it does not send any signal. Moreover, we provide the optimal signaling policy when these conditions are met. Notably we find that for some scenarios, the signaler can effectively double its performance.

Designing Didactic Lotto Games As A Means Of Teaching Primary School Children

Designing Didactic Lotto Games As A Means Of Teaching Primary School Children

Asymmetric Battlefield Uncertainty in General Lotto Games

Asymmetric Battlefield Uncertainty in General Lotto Games

SETTING THE ODDS OF WINNING THE JACKPOT: ON THE ECONOMICS OF (RE) DESIGNING LOTTERY GAMES

In many jurisdictions, domestic lotto games have experienced a decline in sales revenue due to the introduction of new products and the absence of appealing jackpots. To reverse this trend, operators worldwide have conducted major reforms to the design of games. In this paper, we focus on Spain's largest domestic lottery game, which was redesigned in 2012 by significantly reduced the odds of winning the jackpot to produce more frequent and larger rollovers. Findings show overall negative results of such reform, as players seem to no longer react to large jackpots, and the declining trend in sales has even worsened. (JEL D12, H27, L83)

The optimal structure of lotto games

Operators of state-owned lottery games generally attempt to set the parameters of the game(s) to maximize revenue to the state. This paper discusses the state of the literature on how to set the parameters of a lotto game so as to accomplish this objective.

THE EFFECTS OF LOTTO GAME CHANGES AND LARGE JACKPOTS ON INCOME ELASTICITIES AND SALES

Using daily lottery data from Washington State by zip code from January 2011 through mid‐March 2016, we estimate that Powerball income elasticities range from −0.16 to 0.16 as the Powerball jackpot increases from its minimum to $1.5 billion, while Mega Millions income elasticities range from −0.08 to 0.03 as the Mega Millions jackpot increases from its minimum to $640 million. Controlling for jackpot size, each of three major game changes during this time period has a significant effect on own‐game and cross‐game sales. Despite these significant game changes, however, these lotto games are a highly regressive source of revenue for Washington State. (JEL H22, H71, L83)

Uniqueness of optimal strategies in Captain Lotto games

We consider the class of two-person zero-sum allocation games known as Captain Lotto games (Hart in Int J Game Theory 45:37–61, 2016). These are Colonel Blotto type games in which the players have capacity constraints. We consider the game with non-strict constraints, and with strict constraints. We show in most cases that when optimal strategies exist, they are necessarily unique. When they don’t exist, we characterize the pointwise limit of the cumulative distribution functions of \(\varepsilon \)-optimal strategies.

Participation and Spending Attitudes in the Mauritian Lotto Market

The Mauritian Lotto was first introduced on the 7th of November 2009 by lotto tech. The first jackpot was Rs 12 million. To play the game, choose 6 numbers from 1-40. Drawings are held once a week on Saturdays. The odds of winning Mauritius Lotto are one in 3,838,380. For a pick-6 lotto game, the Mauritius Lotto 6/40 lottery game has relatively excellent odds when compared to other pick-6 lotto games around the world. The present study tries to attempt to understand the attitude of Mauritians' towards the lotto game and the impact of socio-economic, psychological and demographic variables on addiction towards these game. For this purpose, a double–hurdle frame work was used, having conducted a drop-off survey of households with a paper and pencil, comprising of 3 distinct sections, namely, personal profile of the respondents, demographic characteristics and personality traits comprising 30 questions of open-ended, close-ended, partial open-ended and psychometric scales questions. 1027 respondents' involvement and the spendthrift nature are analysed. This study brings in the light to the influence of personality trait heterogeneities, coupled with socio-economic and risk-taking behaviours are controlled in the model. Recommendations on future areas of innovation in personality research and policy implications on social perspective ladder, such as alcohol beverages and cigarettes and indulgence in other forms of gambling have serious consequences on both the lotto participation and expenditure decisions. Retailers and corner shops can come up with marketing strategies which will help them to capitalize on cross-buying behaviours. Suppliers' coffers will see new height in terms of revenue at the detriment of public health in terms of cross-addictions. State intervention via consumer laws will have to be made more stringent while sufficient rules and regulations need to be implemented to protect the growing generation from such potential health risks associated with gambling.

On Suboptimal Solution of Antagonistic Matrix Games

The paper examines resource allocation games such as Colonel Blotto and Colonel Lotto games with the goal to develop tractable method for building suboptimal solution in mixed strategies of these games without solving the relevant optimization problem. The foundation of proposed method lies in the specific combinatorial properties of the partition games. It turned out that as far as distribution of resource along battlefield is concerned that pure strategies participating in e-optimal solution possessed specific structure. Numerical experiments showed that these specific structural peculiarities can be easily reproduced utilizing previously found combinatorial properties of partition. As a result, we get e-optimal solution of partition games and support set mixed strategies can be computed in polynomial time.

Allocation games with caps: from Captain Lotto to all-pay auctions

A Lotto game is a two-person zero-sum game where each player chooses a distribution on nonnegative real numbers with given expectation, so as to maximize the probability that his realized choice is higher than his opponent’s. These games arise in various competitive allocation setups (e.g., contests, research and development races, political campaigns, Colonel Blotto games). A Captain Lotto game is a Lotto game with caps, which are upper bounds on the numbers that may be chosen. First, we solve the Captain Lotto games. Second, we show how to reduce all-pay auctions to simpler games—expenditure games—using the solution of the corresponding Lotto games. As a particular application we solve all-pay auctions with unequal caps, which may yield a significant increase in the seller’s revenue (or, the players’ efforts).

Gamblers’ Love for Variety and Substitution among Lotto Games

This paper considers the whether offering multiple lotto games within a state by joining a multi-state lottery increases total ticket sales compared to offering a single state game. The question is considered from two different perspectives, which both lead to the conclusion that states do tend to benefit from increased ticket sales overall by joining a multi-state lottery association. There is, however, a noted difference in the magnitude of that effect depending on the size of the average jackpots of the previously existing state games.

EVALUATING THE EFFECTS OF GAME DESIGN ON LOTTO SALES: A CASE STUDY FROM SPAIN

In February, 2005 the Spanish National Lottery Agency (LAE) made several modifications to the design of one of its lotto games. The entry fee was not changed but the familiar 6/49 format was replaced by 5/54 + 1/10. This considerably lengthened the odds against winning a share of the grand prize. However, extra lower tiers of prizes were added and a guaranteed jackpot of €5m introduced. The change in rules provides an unusual opportunity to study the effect on sales of features of lotto games other than entry fee and pay-back rate. The changes in design appear in this case to have allowed the operator to achieve higher and more stable sales. Reasons for this are explored through estimation of demand models. Results indicate that gains to the operator had been achieved by better satisfying players’ preference for skewness in the distribution of returns.

Non-symmetric discrete General Lotto games

We study a non-symmetric variant of General Lotto games introduced in Hart (Int J Game Theory 36:441–460, 2008). We provide a complete characterization of optimal strategies for both players in non-symmetric discrete General Lotto games, where one of the players has an advantage over the other. By this we complete the characterization given in Hart (Int J Game Theory 36:441–460, 2008), where the strategies for symmetric case were fully characterized and some of the optimal strategies for the non-symmetric case were obtained. We find a group of completely new atomic strategies, which are used as building components for the optimal strategies. Our results are applicable to discrete variants of all-pay auctions.

Football pools and lotteries: substitute roads to riches?

Football pools offer an older alternative to lotto games for gamblers seeking high prizes with low stakes. The article models football pools demand in Spain over nearly 40 years. The introduction of lotto games to the market led to substantial cannibalization of the pools but, subsequently, there is no evidence that the products were substitutes when the relative value for money fluctuated. Entry fee is shown to be a determinant of demand independent of the expected loss per euro, implying that long-odds games should not be analysed as if buyers were acquiring a purely financial asset.