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- See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/295173180 Slot Machines RTP Optimization with Genetic Algorithms Conference Paper · February 2015 DOI: 10.1007/978-3-319-15585-2_6 CITATIONS 10 READS 4,891 3 authors, including: Some of the authors of this publication are also working on these related projects: ESGI 131 - Bilbao, Spain View project ESGI 132 - Sofia, Bulgaria View project Todor Balabanov Bulgarian Academy of Sciences 168 PUBLICATIONS 172 CITATIONS SEE PROFILE Iliyan Zankinski Bulgarian Academy of Sciences 42 PUBLICATIONS 119 CITATIONS SEE PROFILE All content following this page was uploaded by Todor Balabanov on 23 September 2016. The user has requested enhancement of the downloaded file.
- Slot Machines RTP Optimization with Genetic Algorithms Todor Balabanov11 , Iliyan Zankinski1 and Bozhidar Shumanov1 Institute of Information and Communication Technologies, Bulgarian Academy of Science, acad. G. Bonchev St., Block 2, 1113 Sofia, Bulgaria, todorb@iinf.bas.bg, http://www.iict.bas.bg/ Abstract. Slot machine RTP optimization problem is usually solved by hand adjustment of the symbols placed on the game reels. By controlling symbols distribution it is possible to achieve desired return to player percent (RTP), but also some other parameters can be adjusted (for example free spins frequency or bonus game frequency). In this paper, RTP optimization automation is proposed based on genetic algorithms. Keywords: slot machines, RTP, genetic algorithms, optimization 1 Introduction Slot machines are electronic gambling devices that offer variety of games. They are found mainly at casinos and some bars. Slot machines are relatively inexpen- sive to run compared to roulette, blackjack or poker, that is why they become very popular and very profitable form of gambling. The game consists of three or five reels which spin when button is pushed. The game pays off according patterns of symbols visualized on the screen after spin stop. The main scope in this paper is about symbols distribution on the machine reels.On each reel there are ordered symbols (usually represented with numbers in math models). The order in which symbols are presented on the reel is discrete probability distribu- tion. According symbols distribution, different wining combinations can appear on the game screen. Mathematicians who develop slot machine reels have the task to select such discrete probability distribution which will produce certain RTP. The value of RTP (return to player) is calculated by division of money won over money lost multiplied by one hundred. The RTP value is very important for slot machine vendors, because this is the main gambling game parameter which is under government regulation. The RTP value has mathematical meaning as expected value. The other interesting parameter of the slot machine games is volatility, but this parameter is not discussed in this study, because it is less of- ten taken into account during government regulations. The proposed approach for symbols discrete distribution optimization can be very handy for mathemati- cians who are working on new slot gambling games.
- 2 Slot Machine Reels In this section brief review of the basic concepts of the slot machine will be given and game reels in particular. Slot machines are based on the concept of spin reels. In the beginning slot reels were mechanical and the spin of the reels were done by manual pull of the game handle. Nowadays most of the slot machines are computerized and game reels are virtual only and stops are selected by RNG (for more info [1]). In most games five independent reels are presented, but also there are variations with three or more than five reels. After the push button is hit reels starts spin and one by one each reel stops. The win of the player is calculated according combinations of symbols presented on the screen. Each game has its own pay table, which is visible for the player usually on the separate screen. Some symbols are presented on the reels more often than others. Less frequent symbols form wining combinations less often and because of that the win for the player is bigger. Main characteristic of each slot machine is RTP%. This parameter is calcu- lated by the ratio between won and lost money, multiplied by one hundred. The RTP can be from 80% in Las Vegas up to 98% in some EU member states. Fruit machines in the United Kingdom, for example, are required by law to pay out a minimum percentage within a short period of time.[2] Usually the RTP is above 90%. In order the desired RTP to be achieved mathematicians and game design- ers are working in collaboration to populate game reels with proper symbols in proper discrete distribution (for more info [3]). 3 Genetic Alghorithms Genetic algorithms (GAs) are search heuristic inspired by the process of natural selection.[4][5] GAs are routinely used to generate points (candidate solutions) into solutions space. By application of techniques for inheritance (crossover), mutation and selection generated points can get closer to the optimums. GAs are classified also as population based algorithms, because each point into solution space represents individual inside GAs population. Each individual has a set of properties which are subject of mutation and modification (usually crossover). Traditional representation of the properties is binary as sequence of 0s and 1s, but other encodings are also available (binary tree for example). Optimization usually starts from random generated population of individu- als, but this is also subject of implementation. The optimization process is itera- tive and the population in each iteration is called generation. For each individual of the generation fitness value is calculated. Fitness value usually represents the objective function which is subject of optimization. The most fit individuals into the population are selected (according selection rule) and recombined (crossover and/or mutation) to form a new generation. This new generation is used in the next iteration of the algorithm. Algorithm termination is usually achieved by reaching maximum number of generations or by reaching desired level of the fitness value.
- In order one to run GAs he/she should provide: 1. Genetic representation of the solution space (solution domain); 2 appropriate fitness function to evaluate the solution domain. Once these two conditions are met GAs can proceed with population initialization and iterative population improvement by repetitive ap- plication of selection, crossover, mutation and individuals evaluation. 4 Proposed Model In the proposed model every individual consists of slot machine symbols (as numbers) distributed on the reels. Each symbol in the reels is represented by single integer number in such way that symbol and its position on the reel are significant. Solution domain is finite and discrete. Each position in each reel should be single integer number from the list of possible game symbols. Population initialization is usually done by random generation, but the pro- posed model in this paper use initial reels configuration to initialize population. Initialization is done by addition of random noise to the initial reels configura- tion ([6] for more details). Population size is subject of experimental estimation and may vary from several individuals to hundreds or thousands. Into selection process individuals are selected according fitness based value. Some selection methods prefer the best individuals, but other methods prefer only random subset of the population. The fitness function is problem depen- dent and is defined over the genetic representation as measure of the quality of the represented solution. In the proposed model, as fitness function, absolute difference between desired RTP and obtained RTP is used. For obtained RTP Monte-Carlo simulation is used in order to estimate how slot machine will be- have in 100 000 or 1 000 000 separate runs. The rule of elitism is also applied in order the best individual to survive between generations. For crossover operation pair of parent individuals are selected (individuals, part of the selected population subset). Single point cut is used in order to recom- bine attributes of the first and second parent in order to create child individual. It is subject of additional research is it better to use more than two individuals as parents. After crossover mutation is applied over the child by random selection of symbol, which is changed with randomly selected symbol. As termination criteria maximum number of generations is used and also manual observation/termination of the process was implemented. Final solution, found by GA, is an integer vector. This vector is directly used as slot machine symbols distribution. For example if there is a slot game with 5 reels (visible on the screen as 5 columns and 3 rows) and on each reel there are 63 symbols, the final solution of GA would be integer vector of 5x63 values ([6] for more details). 5 Experiments and Results Experiments were done with non-commercial slot machine (5 reels with 3 sym- bols visible on the screen for each of the reels) with particular pay table and combination lines. The game has paytable shown in (Tab.1) which is valid for
- Fig. 1. GA convergence for different target RTPs. On the axes: x - number of genera- tions, y - ABS(TargetRTP - ObtainedRTP).
- 5 wining lines shown in (Tab.2). All wining combinations are paid from left to Table 1. Slot machine paytable. Each column represents wins of one particular symbol (9 possible symbols in this game). Sixth row shows the win of the symbols when there is a combination of 5 symbols, fifth row shows wins for combination of 4 symbols and so on. right. The lowest win is 2 for combination of 2 symbols (last column, row 3 of Tab.1). The highest win is 750 for combination of 5 symbols (first column, last row of Tab.1). The model of presented slot machine has 9 symbols which can form wining combinations on the screen. Slot game pay table is presented by this way in order to use row indexes as number of symbols on the particular wining line. For example, if on the screen there is a wining line which consists of 4 symbols of symbol type 3 it means that the win from this combination is 25 (3th column, 5th row). Table 2. Slot machine win combinations. First row shows that symbols should be presented on the middle row of the game screen (top row has index 0, middle row has index 1 and bottom row has index 2). Second win line is presented on the second row (all symbols should be positioned in the top row of the game screen) and so on for third, forth and fifth line. All experiments were done with elitism rule, population size of 17, maximum number of generations 213, and one million separate simulation game runs in ten separate sessions as fitness value estimation. Crossover probability is about 90%. Mutation probability is 100% and only one value in the chromosome is
- changed. More information about GA parameters can be found in[6]. As initial reels distribution handmade reels with 90.88% RTP were used. It is visible that GA convergence is pretty fast and around 51 generations optimal goal was achieved (Fig. 1 - Target RTP 90%). Because of the discrete nature of the process optimisation is done on separate steps visible in generations 6, 8, 15, 19, 31 and 51. In the second experiment target RTP of 91% is very close to initial RTP and convergence was with small steps around 15th generation and 67th generation (Fig. 1 - Target RTP 91%). Third experiment has target RTP of 92% and it is obvious how optimization process flows (Fig. 1 - Target RTP 92%). Few steps were done in generations 7, 15, 41, 55, 63 and 71. In some of the cases (Fig. 1 - Target RTP 93-99%) it is interesting to point initial difference from the target percent as it is in 97% target RTP optimization (initial difference of more than 5) and 99% target RTP optimization (initial difference of almost 8). The initial difference for 98% experiment is much smaller, because in each experiment initial difference was calculated after first generation. 6 Conclusions All experiments show that using GA can be very effective and can improve slot games development by better adjustment of RTP, but not only. As it was shown (Fig.1) in half of the experiments convergence was very fast and in the other half slower. These results are related to the probabilistic nature of GA. The main disadvantage of GA based optimization is the time of fitness value calculation. In the slot reels optimization problem fitness value is calculated by relatively slow game simulations. The biggest advantage of GA based optimization is the possibility to opti- mize more than single parameter. In this study RTP was optimized, but as multi criteria optimization, symbol frequencies, free spins frequency, bonus game fre- quency, and game volatility can be optimized. Acknowledgements This research is supported by AComIn ”Advanced Computing for Innovation”,grant 316087, funding by FP7 Capacity Programme, Research Potential of Conver- gence Regions (2012-2016), the European Social Fund and Republic of Bulgaria, Operational Programme Development of Human Resources 20072013, Grant BG051PO001-3.3.06-0048 from 04.10.2012. References [1] Brysbaert, M.: Algorithms for randomness in the behavioral sciences: A tutorial Behavior Research Methods, Instruments, and Computers vol.22 issue 1, pp.45-60, (1991)
- [2] Parke, J., Griffiths, M.: The psychology of the fruit machine: The role of structural characteristics (revisited), Paper presented at the annual conference of The British Psychological Society, Surrey, England (2001) [3] Osesa, N.: Bitz and Pizzas Optimal stopping strategy for a slot machine bonus game, OR Insight, 22, pp.3144, (2009) [4] Eiben, A. E: Genetic algorithms with multi-parent recombination. PPSN III: Pro- ceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature: 7887. ISBN 3-540-58484-6, (1994) [5] Ting, Chuan-Kang: On the Mean Convergence Time of Multi-parent Genetic Algo- rithms Without Selection. Advances in Artificial Life: 403412. ISBN 978-3-540-28848- 0, (2005) [6] Balabanov, T: Slot Genetic Algorithm, http://drive.google.com /file/d/0Bz5a6NKy7qNiYi1jS01ZVnFOV1U View publication stats View publication stats

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