Slot Machine Algorithm

Slot machine algorithm

The Algorithm of Slot Machines

The codes are rather simple, and the algorithms are running on 99,99% pure luck. RNG means Random Number. However, modern casinos and casino sites are using the most advanced programming for this algorithm.

This might change in the future, however.

RNG, the Algorithm Of Slot Machines

We already explained what RNG is in a different article regarding video games. Slot-Machine is the powerful gambling game which gives more profit to the casinos. The modern slot machine does not have any built-in memory and generates hundreds of numbers per minute.

The lack of memory means the algorithm used to generate each number is completely independent of each reel on the slot machine. › blog › slots › slot-machine-algorithms. Your results are saved by both your computers and their database, to help you recover your lost data. In video games, for example.

Slot machine algorithm

The first form of slot machines was established in Brooklyn, According to the Blackemsacasino, the first machine was built by metal reels. According to StackOverflow Trends, it is the most sought-after programming language in the world. If you are a programmer who seeks to experiment with creating slot machines, then we recommend you to search open-source codes in Github. Is there a slot machine algorithm hack that actually works? This might change in the future, however, Python at the moment is everything a company needs to establish game programming.

Instead of applying this to slot machines, the bandit algorithm offers AIDS programs the ability to select a hotspot based on up to date understanding of the likelihood of success in that area—or the best odds.

Researchers applied the bandit algorithm to different geographic zones targeted for HIV testing.

Most video games are using pseudo-RNG. But this is wrong. What programming languages are these websites using, and on what algorithm a slot machine is running? The stop was provided by a magnetic braking system. The most famous programming language for casino games is Python.

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They offer a % bonus of up to $1, We wish you good luck on your online casino spree. Python is easy to learn and understand.

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They are so secure, you couldn’t lose wasted money, even if you meet an electricity outage in the middle of the game. What algorithm do slot machines use?

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According to Wired’s report, the authorities are doing their best to chase down and bring justice to casino cheaters. These machines were purely mechanical, with little to no programming inside of them. Let’s discover the secrets and the algorithm of slot machines.

Before the Algorithm Of Slot Machines

Before digitalization reached casinos. But if you are up-to-date with modern technology, then your machines are safe. Check out the history here!

It once and then use names.

Does anyone knows the name of mother. We explore if there are ways to consistently get returns and high payouts. At Wired, Brendan Koerner takes a look into the mind of a mathematician-turned-hacker who milks slot machines around the world. Each reel is weighted to reach a certain number of spins for every time a certain tile is generated by the algorithm.

It does this by generating a.

online casino algorithm

It is possible for a player to hit a jackpot on a number of occasions in specific plays, but this is a purely random part of the gameplay developed through the use of algorithms.

Every slot machine at a casino uses something called a par sheet which provides information about the odds for each tile on a reel. Can yall add me I just made my account wat the fuck is that haircut. Moreover, undiagnosed individuals Slot machine algorithm antiretroviral therapy later in their disease compromising their health and well-being.

Source: Rosalind D&#;Eugenio for Yale University

Original Slot machine algorithm DOI: Buffalo free slots

The Algorithm of Slot Machines: How Do They Work?

If you ever visited online casino sites in the US, then you may have wondered: How does this work?

The average casino players are not engineering or tech experts, thus they are not understanding how these machines work. RNG needs to be based on some sort of data, and because of this. RNG means Random Number Generator. With no internal memory in the machines, these algorithms are generating random results, without being affected by any outside information.

Can You Hack the Algorithm of Slot Machines?

The short answer is no.

But one might need to understand that sometimes RNG is not entirely safe. This game is built by using Random Number Generator. This system would randomly generate a stopping point for each drum after the reels were spun by the player. The hope is that TS can help AIDS programs decide where to test for HIV based on information in different zones, which gets updated every time a testing team comes back with new information on HIV positive and HIV negative tests in a specific area.

The study in Medical Decision Making, took place as a computer simulation online competition between TS and several other strategies, including one that simply sends testing teams to locales with the highest HIV prevalence from the previous year, and another based on doing limited, preliminary testing in all the areas under consideration and Megaways slot games picking the one with the most new diagnoses to test in for the duration of the competition.

Findings showed TS located more new HIV cases then the other two Jacks or better slot you were using Thompson Sampling in a casino, a player wouldn&#;t make a large bet on one machine, they would play for a while to hone in on the best machine to play their quarters,&#; Gonsalves says.

Seizures that signal HIV create treatment Catch

While bandit methods have been applied successfully to a variety of problems where finding hidden objects is important, such as searching for downed airplanes or good places for oil exploration, they haven&#;t been used in the context of screening for infectious disease.

The next step is to put the algorithm to test in the real world, to see if it indeed can offer a better way for AIDS programs to choose where to test for new HIV cases, using mobile vans, or outreach teams.

According to the Center for Disease Control and Prevention, 14 percent of the million individuals in the United States living with HIV infection are undiagnosed.

The Algorithm of Slot Machines

The final stage of the program includes the software checking for the results. These reels were filled with numbers, and they were spinning.

They also have an RTP system programmed into them, which is basically calculating the return of the player. This is because older machines were. Python is an object-based programming language, which allows the programmers to implement the best algorithms of casino experience. The heart of every slot machine is the random number generator.

Each pulled number corresponds to a particular location in a. Some players would believe they had seen a moment when a slot machine became hot or would stop paying out.

RNG is used in video slots in casinos around the world. Theyhave their games running by the most modern algorithm up to date. We got everything you are looking for. These are true relics of the past.

These websites are using the most modern technology, and their websites are secured by top programmers who are using the most advanced codes to secure your online casino experience. Slot-Machine is the powerful gambling game which gives more profit to the casinos. What&#;s the best strategy to maximize your winnings?&#; asks Gregg Gonsalves, assistant professor of epidemiology at Yale University.

&#;Mathematicians have created strategies called &#;bandit&#; algorithms to answer these questions—and we&#;ve used one of them as the basis for our approach to HIV testing.&#;

In the quest to diagnose people who don&#;t know that they are HIV infected and can unknowingly transmit the virus, some AIDS programs have started to focus on &#;hotspots&#; of HIV infection.

With as many as two-thirds of new HIV transmissions attributable to individuals who are unaware of their HIV infection. &#;Even setting up where common sense dictates—like places with high HIV prevalence or concentrations of people at risk of infection—doesn&#;t guarantee a high yield of new diagnoses.&#;

So, researchers decided to try something different: to see if they could get hotspots to reveal themselves by using the logic of a bandit algorithm called Thompson Sampling (TS).

A gambling strategy based on TS has gamblers making bets based on current information, while constantly collecting new information from successes or failures at the slot machine in use.

That means, it's programmed to show 'a' set of symbols. They assumed that they were just spinning metal bars, repeating the same sequence of the patterns. Other available programming languages alternatives to python are Java and C++. Vegas casinos might even have their own languages invented in order to ensure the safety of their machines.

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If you are wondering about where to play online casinos.

Only four remain in existence today. The concept is easy. Slot Machine algorithms use a Random Number Generator as the primary engine to determine outcomes. Easily, as it turns out: the slot machines' algorithm is programmed to work randomly. RNG, the Algorithm Of Slot Machines We already explained what RNG is in a different Best atlantic city casino payouts regarding video games.

Visit Bovada Casino. On most slots, the computer inside the slot machine pulls a random number for each reel you see. It is linked to a complex algorithm that controls the points and can.

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An algorithm for picking a casino slot machine may be a way for AIDS programs to better locate people living with undiagnosed HIV infection.

&#;When you walk into a casino and see a row of slot machines how do you decide which one to play and when it&#;s time to switch to another?

Slot machine algorithm

Wish I had skills like you. Search Sylvinha on xhamster.The modern slot machine uses an algorithm known as a. But you will not find anything you could use to exploit these games and machines. For three different sequences, the program is generating a random result. If the results are matching, then the player wins.

slot machine programming

If you are a casino owner, then you shouldn’t try to save money by investing in older casino machines, because, with today’s technology, older RNG sequences can easily be exploited. Jesli tak to zapraszam 708. Back before the internet, there were false and unbiased claims among casino players, that Slot machine algorithm machines were rigged. The lower the number of tiles appearing on each reel lowers the odds of a jackpot.

Each slot machine algorithm also includes the payback percentage which gives an insight into 5 dragons slot winnings a player can expect as they play.

All the different combinations of numbers, whether generated across three, five, or even greater numbers of reels, are random and must generate numbers independent of each other.

The history of slot machines began with metal reels filled with numbers that would spin and stop with a magnetic braking system. I would marry this chick right now.

Lol, _exactly_ my thoughts at this moment. The trick he exploited was exactly the fact that older casino machines are using pseudo-RNG, instead of the algorithm modern slot machines are using. Who knows? The random number generator is an algorithm generated by a computer that online casinos use to randomize the results of a spin.

They are even expensive, one of these models was going for $, in on Morphy Auctions.

Python, the Programming Language

While each online casino might use its own programming languages. But, pinpointing the hotspots in which to conduct testing remains elusive.

&#;Different methods have been proposed to identify hotspots, but there is no consensus on Vegas grand slots to look,&#; says Gonsalves.

You can not possibly affect the algorithm of slot machines if they are secured and programmed properly. The percentage is usually given as a number of around 97 percent which means a player can expect to win from $3 gambled in every $ This number is not a figure of how much money a player will win but is part of the algorithm deciding how often the slot machine will offer a winning spin.

Want to know where slot machines came from?

And many of the online casino players might wonder, what does the code of a slot machine look like?

You can discover more about Bovada Casino

graphic of slot machine

The modern slot machine uses an algorithm known as a random number generator, RNG, which does not use any form of memory to determine when a number should be generated.

Although it is known as a random number generator, the modern, Online slot machine actually randomly generates the different tiles used on the different spaces of a slot machine.

And it is also most efficient for video games and interactive programming. The first true slot machine as we know it today was invented by Charles Fey. It was called the Liberty Bell, and most of the models were destroyed in an earthquake. Name please. And even if you could, you shouldn’t. So far, the logics of online slots is based on the fact that there is no logic. Modern and online slot games use pseudo-random number generators (PRNG).

The Algorithm of Slot Machines: How Do They Work? | GamingZion

  1. Each pulled number corresponds to a particular location in a. › blog › slots › slot-machine-algorithms.The Science Behind Slots On most slots, the computer inside the slot machine pulls a random number for each reel you see.
  2. Here’s How Slot Machines Are Programmed

    Play Now!

    Ever wondered how those all-spinning, all-whirling slot machines are programmed? Well, you&#;re about to find out!

    The short answer is &#; they&#;re programmed to randomly generate results, which may or may not lead to wins. So everything is based on an algorithm, meaning you still could hit those big wins…you just won&#;t be able to predict when!

    Get to Know the Random Number Generator

    ​​​​​​​​At their core, a slot machine will have a Random Number Generator (RNG), which does exactly what it says it does: randomly generates numbers, which when you spin, generates a certain random combination of symbols across paylines.

    The RNG works as an algorithm, and is programmed by a computer to generate those random numbers, with absolutely no rhyme or rhythm. You won&#;t be able to predict if or when you might win, because the results are completely random.

    Although the early slot machines had a mechanical RNG, the idea was the same: results are randomly awarded, and there&#;s not much point in looking how to beat a slot machine.

    However, having said that, there are some ways to increase your odds of spinning a win while playing!

    ​Programmed vs Random

    So, you ask: how can a slot machine be both programmed and random?

    Easily, as it turns out: the slot machines’ algorithm is programmed to work randomly. That means, it&#;s programmed to show ‘a’ set of symbols across ‘some’ paylines &#; with nothing predetermined, and these symbols and paylines displaying randomly.

    In this way, slot machines work similarly to casino table games: the odds of each game will show you the expected returns of it (more on that below!).
    ​Although The RNG makes it impossible for you to predict an outcome, there are certain things you can do to try to win at slot machines.
    Mix up your play with three-reel slots

    Tricks to Winning: How to Beat Slot Machines

    Although The RNG makes it impossible for you to predict an outcome, there are certain things you can do to try to win at slot machines.

    Mix up your play with three-reel slots

    Most modern slots have five reels, loads of paylines and cool extra bonus features. Although five-reel slot machines will give you massive, possibly life-changing wins…these will by no means be a regular occurrence. You&#;ll probably hit some massive payouts while you&#;re playing, but you won&#;t be able to see these coming!

    Instead, focus your energy on playing three-reel slot machines. Because there are fewer reels, you&#;re more likely to hit a win more often, although these payouts will also be for much lower amounts.

    If you&#;re anything like us, you might be more into slow and steady wins, over unlikely wins but possibly life-changing amounts…if you get lucky!

    This tip is a winner…but it could also drain your bankroll quicker than you&#;d like! Since the RNG operates on all paylines, it&#;s more likely that you&#;ll get a payout the more paylines you play.

    Play the maximum paylines

    Although these payouts can really range in number, depending on ​​

    • The number of paylines you have in play
    • The amount you&#;ve bet per spin
    • The symbols on those paylines (some are higher in value than others)
    • The slot machine’s bonus and jackpot algorithm

    …you&#;re still more likely to hit a win this way.

    Check the Payout Rate to players

    All slot machines have to pass strict regulation if they&#;re to be featured at respectful and honest casino sites, and part of that is ensuring the RNG algorithm is working randomly.

    But, just as all slot machines operate randomly, there’s one cool little trick for winning you can use to increase your chances: the payout rate to players percentage.

    This is a number that gives you a theoretical (not actual) guide as to how much the slot machine will payout over its lifetime of spins. Solid, rewarding slot machines will usually have a payout rate of 95% and above.

    What that means is, a slot machine with a 97% payout rate will payout around $3 of every $ put into the slot.

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    Random But Not Impossible

    Even though slots are programmed to randomly display some symbols (that might result in a win), one thing’s for certain: the longer you play at a slot machine, you’re certain to win something.

    Test out those RNGs across hundreds of free to play slot machines at House of Fun &#; get bonus coins just for joining, and get spinning and winning in just a few clicks’ time!

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    How Do Algorithms Work in Casino Slot Machines?

    How Do Algorithms Work in Casino Slot Machines?

    Slot Machines have been the backbone of the casino industry since late s, when public corporations started taking over the gaming industry by building mega resorts in Las Vegas and around the world. With slot machines being such a huge revenue driver for the industry, it’s worthwhile to explore the how slot machines work.


    This article explores several aspects of this concept including:

    Random Number Generators (RNGs)

    Slot Machine algorithms use a Random Number Generator as the primary engine to determine outcomes. This is because older machines were susceptible to slot cheats.

    Simply stated, the RNG determines when the player wins and how much the player wins. However, the term Random Number Generator is not an accurate term in casino slots. The algorithm is not truly random.

    It’s based on a math formula with an initial input value (independent variable) that determines the final output value (dependent variable). The input value is based on the time the player initially presses the play button.

    However, the player cannot expect to play the same slot machine at the same time daily and have similar results. This is because the time stamp that the algorithm uses is several decimal places deep. 

    Three-Coin, One-Line Slot Machine

    Originally slot games were simple three-coin, single-denomination, one-line games. The player would play one, two, or three coins and would be paid out accordingly.

    A traditional example of this type of machine is the three Cherry Jackpot Slot Machines. There would be eight to 10 symbols on each reel.

    When one, two, or all three cherries would come up on a machine’s center reel display, the machine would pay out.

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    Multi-Line, Multi-Credit Slot Machine

    Newer slot games are now penny games offering a multi-line, multi-credit option. And the player makes a determination on the number of credits to play per spin.

    The number of winning combinations has increased but this comes at a cost. The player’s average wager significantly increases with this type of machine.

    Just because the number of winning combinations increases, it doesn’t mean the player wins more often. Consider the following mathematical breakdown of the traditional three-coin, single-line slots and the multi-line multi-credit machines.

    • Three-Coin Quarter Single Line Slot Machine

      The average spin rate of a slot is 10 spins a minute. Therefore, over a two-hour play period this represents a total number of spins of 1,

      With an average wager of $ and a 10% hold, this represents a player loss of $90 for a single trip. With a routine player coming two times a week this represents a total loss for the month of $
    • New Multi-Line, Multi-Coin Games

      With an average spin rate of 10 spins a minute over a two-hour play period, this represents a total number of spins of 1, With an average wager of $ and a 10% hold, this represents a player loss of $ for a single trip.

      With a routine player coming two times a week this represents a total loss for the month of $ The total effect of this cost of play example is a $ increase in loss per month. This is a 20% increase in loss rate or a 20% decrease in value to a player.

    Hold Percentages

    The introduction of lower denomination on the multi-line, multi-credit games pay out less than higher denomination three-coin single reel games. Because game designers believe players want a big win to create the “OMG” effect, $ games that have top prizes of $1 million, $, ,or even $10,

    This has the unintended consequences of creating a mathematical necessity for large volatility in these types of games.

    This means there will be a whole lot of losing players for that one jackpot. This is true for the linked mega jackpots seen on casino floors and big jackpots seen in the bonus rounds of many games. In some cases the top prize has a 1 win in 15 million spin hit ratio. 

    The range of players not winning any money on these high-variance games is between % and 29%. This range can be attributed to variations in a game's theme and the amount of time the game has been on the market.

    Slots Maximum Bets

    The slot machine's win rate is set by the casino operators and is called the “House Advantages” (HA). HA is weighted in rate and is based on the denomination of the game; the lower the denomination the greater the HA.

    Traditionally this was done to compensate for the lower wagers per spin in the three-coin denomination era. This means that players are paying an increased HA rate when moving from a higher-denomination game, three-coin quarter game to a-lower denomination, multi-line, multi-credit game.

    The player is wagering more money and at greater risk when moving from traditional three-coin machines to a multi-line, multi-credit game. 

    Themed Versus UnThemed Games

    Players are attracted to a game’s theme, but the experience stays consistent with other multi-line, multi-credit games. We can definitively prove this because there are several generic versions of the Wheel of Fortune slot game.

    This is arguably the most successful casino game currently on the market. The generic versions do not even approach the Wheel of Fortune play rates.

    The Wheel of Fortune game is the strongest brand of all time even though it is a participation machine, and has one of the poorer payback structures of all games on the casino floor. This is because everyone recognizes the Wheel of Fortune brand name, simply because it’s been on television for over 30 years.

    Every new themed game a manufacturer puts out requires a royalty cost to a licensing company. Using the images and names of a brand does not come cheap for game manufactures.

    To offset this cost, slot manufactures pass the cost to consumers by increasing the hold percentages. The algorithms of themed slot machines are always programmed to hold more. 

    Decision-Based Gaming

    Some slot machines are decision-based games. Video Poker is a decision-based game and the house advantages are usually half, or less, of that in typical slot machines when played optimally.

    These games are popular because the decision directly involves the player. The smarter player is rewarded and these games are set to 98 or 99% payback.

    Progressive Combination Machines

    Some newer games have a dynamic winning combination paradigm. This means the number of winning combinations increase or decrease over time. Some machines show the number of winning combinations available after a spin.

    Every so often the number of combinations increases. And when the number of winning combinations gets high enough, the machine is primed to pay out.

    This doesn’t mean that the algorithm is telling the machine to pay out immediately. It means that the payout schedule has shifted. However, when a jackpot does hit on these types of machines the number of winning combination does immediately drop.

    Lastly, some machines have minor, major, and progressive jackpots on them. The amount of each jackpot is displayed right on the machine. This acts as a timer of sorts.

    These essentially mean that when jackpot levels on the individual machine get high enough, the machine will pay out soon. Each machine is different and must be tested individually to know what levels are best to play at. But in general the higher the better.

    Previously, casinos would place signs around specific machines that would say must hit progressive by X amount of dollars. But because players would look for machines that were close to the designated dollar amount then only play those machines, they had to become less obvious.

    The amount that each jackpot has to be at before it is primed to pay out varies from machine to machine and often from casino to casino.

    In the final analysis, the algorithms of slot machines are numerous. Each brand of machine has subtle differences. But there are a few things we know:

    1. Random numbers are not at all random and are still pretty unpredictable. 
    2. Traditional three-coin, one-line machines don’t burn through money as quickly as other machines do. 
    3. Multi-line, multi-credit machines do burn through your dollars fast.
    4. Higher denomination machines hold less than lower denomination machines.
    5. Themed machines generally have higher hold percentages than non-themed machines, because they have to pay for the licensing.
    6. Decision-based games offer lower house advantage when played correctly.
    7. Some machines have dynamic winning combinations. The more combinations they have the better the chance of winning.
    8. Some machines have thresholds where they have to pay out before the jackpots get too high.

    These are some of the algorithm traits that exist for casino slot games. It’s not a complete list. And as newer games are developed some of these traits will be expanded but not eliminated.

    The complex math algorithms that these machines are built on, build on themselves. The next level will likely be some sort of Artificial Intelligence component. Good hunting.

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  4. Here’s How Slot Machines Are Programmed
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The code is not hard to understand. And this is the algorithm that runs the slot machines. Because it is highly unlikely that in the next ten years, anyone would be able to bypass the hard-coded security systems of these machines and websites.

What Does a Slot Machine Code Look Like?

While we are not programming experts, we do care a lot about casino games.

Slot machine algorithm

Random Number Generator is called so due to random chances of. This game is built by using Random Number Generator. The RNG gods might help you Slot machine algorithm win the jackpot today.

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.



Slot machines, also known as fruit machines, are the most popular gambling games in casinos. They are either electronic or electromechanical devices that consist of a number of reels (n) that spin independently and a screen with a number of rows (m). Each reel contains several symbols in specific arrangements and quantities.

Also, it has a number of positions at which they stop, and this number is called stops [1].

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The stops are being shown on the display of a slot machine, while the reels are spinning in front of the player. Slot machines as mechanical devices had cylinders as spinning reels holding the symbols that were printed on a strip. Nowadays, slot machines are mostly electronic, and they can be found either in traditional casinos or in online casinos as software. However, in virtual slots, once the reels start spinning, a How long to stay on a slot machine Number Generator (PRNG) is used to get the stops.

The display of a virtual slot machine shows the () window of the game, game rules, coin values, line bet, payout schedule, and more options.

The player inserts cash or a paper ticket with a barcode in “ticket-in, ticket-out” machine. Once the player presses a button, in case the slot machine has the minimum amount of bet, the reels of the base game start spinning. After that, the reels produce the outcome of the game, which consists of all symbols that remained visible through the window on the display and the payment of the combination in pay table of these Slot machine algorithm that are greater than zero.

If the visible window contains symbols that trigger a bonus game (e.g., free spins in base game or to another feature game), then the player has a big chance to win much more money than he/she bets.

The gambling industry is one of the most profitable industries globally. With more than US$ billion dollars estimated value in and with a projected value of more than US$ billion bythe gambling market is definitely one of the largest and most profitable in the world [2].

It is also worth mentioning that these figures are only related to the regulated markets, as the grey and black markets contribute with hundreds of billions of dollars to the total market value. There are hundreds of companies of different types of services that compose the gambling industry: from casinos and software developers to casino game developers and payment solutions.

The growth of remote gaming, with online and mobile gambling market size, is expected to grow by more than 10% byensuring that the gambling industry will become even more profitable in the years to come. Hundreds of thousands of dollars are spent every year from several companies in order to participate in exhibitions around the world, with the most famous and attractive being held in Las Vegas, Paris, London, South Africa, and Singapore.

A list of the most well-known conferences and trade shows with a Gaming, Sports Betting, and Affiliate theme may be found online [3], for example, Paris Games Week, iGB Live!, and ICE Totally Gaming.

Return-To-Player Slot machine algorithm is one of the two most important parameters for a player to choose if he/she is going to play the game, but it is also the main gambling game parameter which is under government regulation [4].

slot machine algorithm app

It is the win as percentage of the bet and is the phrase that casinos and casino game makers use to describe the long-term theoretical expected payback percentage from all wagers on a slot machine, video poker machine, or Video Lottery Terminal (VLT). If a slot machine player is going to play a hundred rounds at 1$ on a slot game with a theoretical slot RTP of 93%, with all other things being equal, he/she would expect to get a return of 93$ in wins from his staked $.

A player wins back most of his wager. The remaining 7% of his bet, in this game, is the house edge, the money that casino earns off each bet. The formula for the computation of the RTP and also some necessary notations can be found with the formulae below:orTotal Prize: the amount of money that a window instance winsCycle: how many times the reels spun in a Monte Carlo simulationPay Lines: the number of lines that the game has enabledCoins In: total amount of coins betCoins Out: total amount of Slot machine algorithm won

In this paper, Monte Carlo simulation withand 1, separate runs will be used for the RTP calculations.

In simulations, Caesars palace slot machines (2) is used, where the cycle represents the number of runs. In addition, there is another type of simulation called “Full Cycle.” This latter type of simulation is used in the design phase (i.e., mathematical) of a slot machine game.

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It is an exhaustive cycle through all possible stop positions. The Full Cycle simulation allows an exact match to the calculations in the spreadsheet but is not capable of calculating coinciding statistics across a series of feature games.

The structure of this work is as follows: In Section 2, we discuss similar approaches for the RTP optimization problem, focusing on recent research work and the methods they utilize.

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Next, we introduce our methodology in Section 3. Section 4 presents the results of our methods on several games. Finally, we draw our conclusions and provide some research directions for future work in Section 5.

2. Related Work

Although the RTP optimization problem is one of the most important parts of the slot machine game design, there are not many scientific articles that present a heuristic or metaheuristic approach to solve this problem.

Only three papers have been published which present a metaheuristic approach to solve the RTP optimization problem and are briefly presented in Table 1.

ReferenceApproachSimulationSpecial symbolsRunsGames tested

This workVNSMonte CarloYes, & 1,3
[4]GA(s)Monte CarloNo, or 1,1
[5]DEMonte CarloNo1,1
[6]DDE and GA(s)Full CycleYesAll possible1

Balabanov et al.

[4] presented a solution for the slot machine optimization problem, where the symbols distribution of the base game is being controlled and, also, some other features like free spins frequency or bonus game frequency.

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The fitness function in this work was the absolute difference between the desired and the obtained RTP. For Monte Carlo simulations, 1, orseparate runs were used in order to calculate the obtained. They used Genetic Algorithms (GAs), with a randomized initial population and appropriate crossover and mutation operators. The target of the example that the authors presented was 99%, starting from 91%. So, the algorithm increases the in a small range in case the game already exists (a quality starting ).

However, in most cases, the mathematicians of slot games usually try to develop a new slot machine game (from scratch) that has initial reels with randomized symbol distribution and the might be equal, for example, to % (big random value).

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So, it is not a trivial task for such algorithms to handle the case of large reductions and the huge difference between the target and the initial. The decrease of the in slot machine game is the hardest problem for the mathematicians, since they have to solve the optimization problem with hand adjustments and this usually requires a long time. Furthermore, the algorithm’s behavior in the case where special symbols appear in reels (e.g., wild, scatter) is also unknown.

The Slot machine algorithm authors in [5] also proposed a Differential Evolution (DE) algorithm, since the problem of optimal symbols distribution on the reels is discrete and its convergence was found to be faster than GAs.

Additionally, they also used Monte Carlo simulations with 1, separate runs over ten trials for better accuracy in base game. Their model of slot machine game contained only simple symbols and not scatter, wild, or bonus games (scatter represents symbols that pay everywhere on the screen and substitute all other symbols). The authors proposed a multicriteria optimization approach as future work, for the symbol frequencies, the free spins frequency, the game volatility, and the bonus game frequency.

Keremedchiev et al.

[6] proposed a Genetic Algorithm methodology for the optimization problem, in bonus and free games frequency as parallel computing evolutionary optimization. The fitness function of base game that was used was computed with Full Cycle method instead of Monte Carlo simulations. In current algorithm, the model of slot machine game does contain as features bonus game, simple symbols that pay on each pay line, scatter symbols, and wild and bonus symbols that trigger the bonus game.

This experiment, as it refers in it, showed that the use of Genetic Algorithm with exact numerical calculation of as fitness function was very efficient and improved the slot game parameters by better adjustment ofbonus game, and free games frequency. Finally, the biggest drawback was that the exact computation was time-consuming and slowed down the optimization process.

The authors also proposed a Discrete Differential Evolution (DDE) implementation as a further research.

3. Research Methodology

Variable Neighborhood Search (VNS) constitutes a metaheuristic solution method which is systematically changing a neighborhood structure. VNS was initially proposed by Mladenović et al. [7, 8]. Nowadays, a large number of successful VNS applications have been reported in a wide range of areas [9–13]. In this work, a Variable Neighborhood Descent (VND) heuristic schema was applied in base game’s and it takes all symbols into account.

The VND metaheuristic features a strong local search phase (intensification) utilizing a number of different neighborhood structures but lacks a diversification Slot machine android (shaking method) as compared to other VNS variants. The VND variant has been applied in several research works in the literature [14, 15].

The proposed solution method is analytically described in the following subsections and an overview is depicted in Figure 1.

Solution Representation

A slot machine consists of reels where the symbols are represented by a string and are equally distributed.

The solution representation is a two-dimensional array with the distribution of the symbols on each reel. For example, in case of a five-reel (number of columns) slot machine game with 48 symbols per reel (number of rows), the solution array (denoted as “Reels”) would have the dimension of .

Three inputs of the proposed algorithm are (i) the maximum number of iterations as a termination criterion (also a maximum CPU solution time can be used), (ii) the target (desired) RTP of the user (), and (iii) the allowed deviation denoted () from the target RTP.

Usually, the computation of the precise RTP is quite difficult and, due to this reason, game developers are satisfied if the RTP belongs in a specific range. Hence, ifthen the algorithm stops. Assume, for example that if we are given  = ,  = , and  = , then the algorithm stops. An extra feature of the algorithm is that it allows the user to declare a minimum number of each symbol per reel. Thus, a fourth input of the proposed algorithm is an additional two-dimensional array containing the minimum number of symbols per reel and is denoted as “minNSR.” The number of columns of this array is equal to the number of reels, while its number of rows is equal to the number of distinct symbols.

Thus, denotes the minimum required number of occurrences of the symbol in the -reel.

Neighborhood Structures

The proposed VND methodology utilizes two neighborhood structures denoted as “RMS” and “RMC.” Both these local search operators aim to reduce the RTP as follows:(i)RMS: initially, the symbols are sorted in ascending order based on their corresponding payments. The Replace Maximum Symbol () local search operator replaces with the biggest payment by that has the next biggest payment in pay table.

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The players of a slot machine game may win a monetary award in the case where a combination of at least two identical symbols occurs in Is there a benefit to playing online slots pay lines. The symbol that has the biggest payment in these combinations is considered the most expensive symbol.

However, the replacement by the operator is permitted only after checking the input array (minimum number of symbols per reel requested by the game developer); otherwise, the next most expensive is considered for potential replacement.(ii)RMC: the RTP increases when the placement of the symbols in the reels leads to minimum winning combinations of symbols (i.e., combinations of two identical symbols only) with a high frequency.

The Replace Minimum Combination () local search operator replaces which participates in Slot machine algorithm minimum winning combination with that does not participate in such winning combinations (e.g., it participates in winning combinations of three or more identical symbols). Such symbols may participate in combinations with a little larger payment, but the frequency of their combinations is Slot machine algorithm lower.

VND Metaheuristic Algorithm

The VND solution approach is depicted in Algorithm 1.

Also, Monte Carlo simulation () is used for the calculation of the current withor 1, separate runs. The two neighborhood structures and are also denoted as andrespectively. Moreover, the number of different neighborhood structures is denoted as and in this work it is equal to two.

Difference ;
  Select such that ;
NeighborhoodChange ();
untilstopping criterion;

The proposed VND is initialized with a randomized initial symbol distribution per reel (the list of distinct symbols is given by the game developer) and terminates once a maximum number of iterations is performed rather than not finding an improvement.

This is due to the fact that, in each iteration, a Monte Carlo simulation might return an approximate value of the RTP and not the exact RTP that would result after a (time-consuming) Full Cycle RTP computation. Thus, in some cases, although the two local search operators do not make any improvement, a better RTP value can be calculated by the Monte Carlo simulations. Moreover, each time the neighborhood is changed, the search is performed in a different (next) reel.

Thus, the VND starts the optimization using the first reel () and afterward sequentially applies the local search operators in each one of the reels.

Illustrative Examples

Without loss of generality, let us assume a hypothetical slot machine game with reels, with each one of them containing 12 equally distributed symbols. The symbols are represented as string variables in an array () and the pay table is stored as integer values in another array ().

Next, an example of the array is presented, where for simplicity we show only one of the columns corresponding only to the first reel.

Each index represents how many of symbols should remain in current reel and not get replaced by other, for example, meaning that cannot occur less than three times in the first reel. This way, it will not be possible to replace with .

The operator changes the symbols of the first reel as follows:

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