Slot Machine RTP Optimization Using Variable Neighborhood Search

This work presents a Variable Neighborhood Search (VNS) approach for solving the Return-To-Player (RTP) optimization problem. A large number of software companies in the gaming industry seek to solve the RTP optimization problem in order to develop modern virtual casino gambling machines. These slot machines have a number of reels (e.g., three or more) that spin once a button is pushed. Each slot machine is required to have an RTP in a particular range according to the legislation of each country. By using a VNS framework that guides two local search operators, we show how to control the distribution of the symbols in the reels in order to achieve the desired RTP. In this study, optimization refers only to base game, the core of slot machine games, and not in bonus games, since a bonus game is triggered once two, three, or more specific symbols occur in the gaming monitor. Although other researchers have tried to solve the RTP problem in the past, this is the first time that a VNS methodology is proposed for this problem in the literature with good computational results.

Abstrakt-generelle Duldungen im europäisierten Glücksspielstrafrecht

Gaede examines the little-discussed question of whether administrative acquiescence precludes the accusation of unlawful gambling against the background of EU law. He shows that the transitional regime established until the full enforceability of the State Treaty on Gambling in 2021 limits criminal liability. In detail, he explains why a total internet ban on virtual slot machine games is no longer in conformity with EU law. He clarifies that general tolerations can also exclude § 284 StGB if they are in accordance with the legal discretion of the authorities. Gaede discusses the legal situation before and after 1.7.2021. The author is co-editor of the series and professor in particular of German and European economic criminal law.

The maximum rewards at the minimum price: Reinforcement rates and payback percentages in multi-line slot machines

Past research has shown that gamblers frequently use the mini-max strategy in multi-line slot machines, whereby the player places the minimum bet on the maximum number of lines. Through a detailed analysis and explanation of the design of multi-line slot machine games, we show that when using the mini-max strategy, the payback percentage remains unchanged, yet the reinforcement rate is significantly increased. This increase in reinforcement rate is mainly due to spins in which the amount won is less than the amount wagered, which we call losses disguised as wins. We have verified these conclusions by playing an actual slot machine game for 10,000 spins and recording the results. We believe that the high reinforcement rate that results from playing multiple lines on games of this type contributes to their potential addictiveness. We provide three theories for why players use the mini-max strategy and suggest further areas of research.

A New Cost Allocation Approach on One Machine Sequencing Games

One machine sequencing situation is introduced and cooperative games theory is used to allocate cost savings when agents cooperate and gain some cost savings. One machine games is proved to be balanced and have a nonempty core. A new cost allocation, the proportion gain allocation approach, is proposed and proved to give a core allocation for one sequencing games. The results in examples show that the proportion gain allocation approach are fair and reasonable for one machine games.

PAR Sheets, probabilities, and slot machine play: Implications for problem and non-problem gambling

Through the Freedom of Information and Protection of Privacy Act, we obtained design documents, called PAR Sheets, for slot machine games that are in use in Ontario, Canada. From our analysis of these PAR Sheets and observations from playing and watching others play these games, we report on the design of the structural characteristics of Ontario slots and their implications for problem gambling. We discuss characteristics such as speed of play, stop buttons, bonus modes, hand-pays, nudges, near misses, how some wins are in fact losses, and how two identical looking slot machines can have very different payback percentages. We then discuss how these characteristics can lead to multi-level reinforcement schedules (different reinforcement schedules for frequent and infrequent gamblers playing the same game) and how they may provide an illusion of control and contribute in other ways to irrational thinking, all of which are known risk factors for problem gambling.