Casino & Slots - Super4Bells Deluxe, super 4 casino game.

Super 4 casino game


The guys at stakelogic sure love making classic fruit slots. The latest in their line of old-school slots, super 4 bells deluxe is a video slot with 7 reels and endless possibilities to win big. The slot comes with a RTP of 95% and medium volatility. It offers a maximum possible win of 40,000 coins and a mystery jackpot fuelled by your own bets. Another great addition to the super 4 bells deluxe slot is the superbet. Activating it makes each next spin cost a bit more, but it’s definitely worth it. The superbet increases the RTP of the slot and also adds the exciting superbet mystery spins to the mix.


Casino & slots - super4bells deluxe



Super4bells deluxe


The guys at stakelogic sure love making classic fruit slots. The latest in their line of old-school slots, super 4 bells deluxe is a video slot with 7 reels and endless possibilities to win big. The slot comes with a RTP of 95% and medium volatility. It offers a maximum possible win of 40,000 coins and a mystery jackpot fuelled by your own bets.


Thanks to the old-school look and feel and the great winning potential, the super 4 bells deluxe slot will transport you back to the 70s in a las vegas casino.


How to play super 4 bells deluxe


It might look complicated on the surface but spinning the super 4 bells deluxe slot is actually pretty simple. Instead of setting your desired bet size, you get another slider which allows you to set the number of reels you want to play. The minimum is 4, and you can add the other reels into the mix one by one. Play at the max bet and the maximum number of reels and you get a chance to win top prizes.


Another great addition to the super 4 bells deluxe slot is the superbet. Activating it makes each next spin cost a bit more, but it’s definitely worth it. The superbet increases the RTP of the slot and also adds the exciting superbet mystery spins to the mix.


Super 4 bells deluxe bonus features


Besides the superbet, the super 4 bells deluxe online slot hides another great feature in the mystery progressive jackpot. A small part of each of your bets “fills” the jackpot which you can win if you’re lucky. A common feature in stakelogic games, the minimum jackpot you can win is €500, while the maximum is €5,000.


The chances to hit the progressive jackpot are bigger if you play at higher bets, so make sure to max them out.


Play the best fruit slots in unibet casino! Enjoy the retro vibe of super 4 bells deluxe!


Free super slots machine


Free mobile slots alternatives


Our flash powered slots unfortunately do not work on mobile devices. However, below we have a selection of of our exclusive HTML5 powered mobile friendly slots which you can play on phones and tablets. We're currently hard at work converting all our games into mobile friendly slots games and you can see our mobile slots page for all the latest!



Our valentines slot game is a 5 reel game with 9 paylines & a floating hearts free spins bonus feature.



Celebrate the year of the monkey with this great 9 payline slot with free spins and a bonus gamble feature!



Our winter wonderland game is a 5 reel, 20 payline slot game with two wilds and a gamble game.



Get 3 bingo bonus symbols on the reels to activate the speed bingo bonus game! This is a 30 ball version of bingo where you have to get 9 numbers daubed off your card before all 30 numbers are called.



Our exclusive cleopatra slots game features 2 scatter symbols, a wild symbol, free spins feature plus a pyramid bonus game.


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


Reels: 5.Paylines: 25
features: wild. Scatters. Free spins.
Bonus games: 3
starting credits: 3500.
Coin value: 2 credits.
Maximum bet: 125 coins


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


Overview: our free super slots machine is our second game to be sponsored by an online casino. As you would expect the game is packed full of features. It includes a video intro, 3 bonus games, and the chance to win free spins.


Symbols include the girl with the briefcase, taken from the bonus round of the reel deal game (a game based on the TV hit deal or no deal), cheerleaders from the immensely popular money shot slot and even some cleopatra symbols from the game cleopatra's pyramid!


Like all the best slots machines our super slots machine has a wild symbol which substitutes for other symbols to make winning combos. It also has no less than 5 scatter symbols. Giving you a really good chance of winning on every spin!


4 of the game's symbols are scatter bonus symbols. They are listed in the symbols guide section below. The only non-bonus activating scatter symbol is the image of the girl from the right prize slot game. Which is clearly a spoof of the TV show the price is right. When 2 or more of the right prize girl symbols appear in any position on the reels. You will win between 5 and 30 credits depending on how many of the symbols are showing on the reels.


Free spins: our super slots machine has a free spins feature. So if you get lucky you get to spin the reels without using any of your credits! Whenever you get 2 or more cleopatra symbols. The music will change and the reels will spin on their own. On the message bar, it will tell you how many free spins you have remaining. The number of free spins you win will depend on the number of cleopatra symbols that appear on the reels as listed below. It is important to note that you can win more free spins during the free spins feature itself!


2 cleopatras = 2 free spin
3 cleopatras = 5 free spins
4 cleopatras = 7 free spins
5 cleopatras = 10 free spins


Pick item bonus game:


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


Getting two or more mermaid symbols. Will cause the reels to fade to blue. Bubbles will also rise up the screen as you enter the mermaids world. The mermaid will then lead you to the hidden treasure chests. You will get a chance to select between 2 and 6 of the chests and will win the credits found within!


This 'pick an item' style game is our version of the bonus game you can play for real money in a slot called mermaids quest.


Wheel of chance bonus game:


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


If you get 3 or more symbols that feature a show girl and a wheel of chance (with the word scatter beneath). Then the wheel of chance bonus game will be activated.


Click spin and you win the credits shown on the segment that the wheel stops on.


That segment along with all other segments showing that number are then removed and replaced with the word BUST. You can then collect your winnings or select to spin again for a chance to win even more. But if you land on a BUST you will lose everything from that bonus round.


Pick item bonus game:


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


This game is a totally unique concept. Which as far as we know has never been done before. It is a virtual slot machine game. That is activated by getting one or more of the lady holding the 'virtual slot' board symbols in any position on the reels.


When the game is activated the girl walks across the reels and leads you into a virtual slots casino. Where you have to choose between two virtual slot machines.


Option 1 mini super slots machine: if you select this slot machine you will almost certainly win some credits from the bonus round. As you get 10 spins and it has a lot of winning combinations. Although the highest winning combination is 777 credits.


Option 2 the big jackpot super slots machine: if you select this option you stand a chance to win really big. But also have a really big chance of winning nothing at all. This is because you only get 3 spins. Also, the game has just one winning combination. But if you hit that winning combination you will win 7777 credits!


Free super slots machine


Free mobile slots alternatives


Our flash powered slots unfortunately do not work on mobile devices. However, below we have a selection of of our exclusive HTML5 powered mobile friendly slots which you can play on phones and tablets. We're currently hard at work converting all our games into mobile friendly slots games and you can see our mobile slots page for all the latest!



Our valentines slot game is a 5 reel game with 9 paylines & a floating hearts free spins bonus feature.



Celebrate the year of the monkey with this great 9 payline slot with free spins and a bonus gamble feature!



Our winter wonderland game is a 5 reel, 20 payline slot game with two wilds and a gamble game.



Get 3 bingo bonus symbols on the reels to activate the speed bingo bonus game! This is a 30 ball version of bingo where you have to get 9 numbers daubed off your card before all 30 numbers are called.



Our exclusive cleopatra slots game features 2 scatter symbols, a wild symbol, free spins feature plus a pyramid bonus game.


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


Reels: 5.Paylines: 25
features: wild. Scatters. Free spins.
Bonus games: 3
starting credits: 3500.
Coin value: 2 credits.
Maximum bet: 125 coins


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


Overview: our free super slots machine is our second game to be sponsored by an online casino. As you would expect the game is packed full of features. It includes a video intro, 3 bonus games, and the chance to win free spins.


Symbols include the girl with the briefcase, taken from the bonus round of the reel deal game (a game based on the TV hit deal or no deal), cheerleaders from the immensely popular money shot slot and even some cleopatra symbols from the game cleopatra's pyramid!


Like all the best slots machines our super slots machine has a wild symbol which substitutes for other symbols to make winning combos. It also has no less than 5 scatter symbols. Giving you a really good chance of winning on every spin!


4 of the game's symbols are scatter bonus symbols. They are listed in the symbols guide section below. The only non-bonus activating scatter symbol is the image of the girl from the right prize slot game. Which is clearly a spoof of the TV show the price is right. When 2 or more of the right prize girl symbols appear in any position on the reels. You will win between 5 and 30 credits depending on how many of the symbols are showing on the reels.


Free spins: our super slots machine has a free spins feature. So if you get lucky you get to spin the reels without using any of your credits! Whenever you get 2 or more cleopatra symbols. The music will change and the reels will spin on their own. On the message bar, it will tell you how many free spins you have remaining. The number of free spins you win will depend on the number of cleopatra symbols that appear on the reels as listed below. It is important to note that you can win more free spins during the free spins feature itself!


2 cleopatras = 2 free spin
3 cleopatras = 5 free spins
4 cleopatras = 7 free spins
5 cleopatras = 10 free spins


Pick item bonus game:


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


Getting two or more mermaid symbols. Will cause the reels to fade to blue. Bubbles will also rise up the screen as you enter the mermaids world. The mermaid will then lead you to the hidden treasure chests. You will get a chance to select between 2 and 6 of the chests and will win the credits found within!


This 'pick an item' style game is our version of the bonus game you can play for real money in a slot called mermaids quest.


Wheel of chance bonus game:


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


If you get 3 or more symbols that feature a show girl and a wheel of chance (with the word scatter beneath). Then the wheel of chance bonus game will be activated.


Click spin and you win the credits shown on the segment that the wheel stops on.


That segment along with all other segments showing that number are then removed and replaced with the word BUST. You can then collect your winnings or select to spin again for a chance to win even more. But if you land on a BUST you will lose everything from that bonus round.


Pick item bonus game:


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


This game is a totally unique concept. Which as far as we know has never been done before. It is a virtual slot machine game. That is activated by getting one or more of the lady holding the 'virtual slot' board symbols in any position on the reels.


When the game is activated the girl walks across the reels and leads you into a virtual slots casino. Where you have to choose between two virtual slot machines.


Option 1 mini super slots machine: if you select this slot machine you will almost certainly win some credits from the bonus round. As you get 10 spins and it has a lot of winning combinations. Although the highest winning combination is 777 credits.


Option 2 the big jackpot super slots machine: if you select this option you stand a chance to win really big. But also have a really big chance of winning nothing at all. This is because you only get 3 spins. Also, the game has just one winning combination. But if you hit that winning combination you will win 7777 credits!


The best PS4 casino games


It might feel a little strange to hear about casino games on the PS4. After all, they’re not exactly the type of game which will push a state-of-the-art console to its limits, nor are they a sub-genre which you necessarily associate with innovation.


There are a surprisingly large number of options out there, which bring very different takes on the classic casino games that so many know and love. Let’s take a look at some of the very best casino games that are currently available on the playstation 4.


The four kings casino and slots


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


This is undoubtedly one of the most popular casino games on the console (it has a whopping 11K ratings on the official playstation store), and it’s certainly one of the best too.


There’s a robust customization system in place for your avatar, who you can continue to augment with some snazzy looking items with the money that you win in-game. As for the actual casino portion, you’ll find essentially every major game you could hope for: texas hold’em, blackjack, roulette, and so on.


It’s actually pretty rare to find a title that offers such great variety in its casino games; most tend to focus in on a specific game. If you’re the type of player who likes to rotate between different types of casino game, then the four kings casino and slots should be the perfect choice for you. The sociable MMO elements which are also included are simply the icing on top of a delicious casino cake!


Pure hold’em


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


Texas hold’em is undoubtedly one of the most popular casino games going, and has been for a very long time. If you want to focus solely on this classic poker variant, albeit with some lovely, modern graphical flair, then pure hold’em is an excellent choice.


The multiplayer support on offer is excellent, and includes the opportunity to square off with up to seven other players of your choosing; or, of course, you can simply hop into a game with some shifty-looking strangers. The choice is yours!


The great thing about pure hold’em is that it is laser-focused on the one casino game which it offers, and it executes it absolutely brilliantly.


Prominence poker


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


This is another title which – as you can probably guess from the title – is squarely focused on poker. It takes a completely different approach to the subject than the aforementioned pure hold’em, however, and is arguably far more ambitious.


This ambition is primarily realized in a single player story mode. Poker games take place in a series of “sleazy location” (in the developers’ words), like shadowy offices and disused laundromats. You square off against unsavory types as your custom-created character moves up through the ranks of players, with the aim of eventually defeating the “the mayor”.


If that’s not your scene, then there are still the usual multiplayer modes that you’d expect from a casino game, which deliver a more standard poker experience. In truth, though, the appeal of prominence poker comes from its willingness to take chances, and its attempts to imbue your poker games with some kind of narrative and purpose. It’s almost certainly the most original casino game on the PS4, and arguably the most fun too.


So there you have it: three of the best casino games on the PS4, with each being an excellent way to enjoy a slice of virtual gambling action. All are worthy choices, but if you have another suggestion then please don’t hesitate to let us know!


Сыграть в the four kings casino and slots


Об этой игре


The four kings casino and slots социальной MMO, что позволяет погрузиться в моделируемый симулятор казино . Вы начнете с создания персонализированного 3D аватара, который представляет вас в онлайн-мире. По результатам игры вы будете вознаграждены более экстравагантной и престижной одеждой для дальнейшей настройки вашего вида. Как только вы входите в казино, вы сможете принять участие в самых популярных играх казино, таких как texas hold'em покер, слоты, блэкджек, рулетка, видео покер и многое другое. Four kings casino and slots живой, дышащий мир, который постоянно развивается с новыми событиями, одеждой и играми.


В four kings casino and slots вы можете играть в своем собственном темпе. Вы можете общаться и играть на низких ставках, или вы можете работать над вашем путем в VIP зону и играть по-крупному. Игроки с самым высоким рейтингом в конце каждого сезона в казино награждаются эксклюзивными внутри-игровыми наградами сезон последние 3 месяца № 1 ранг игрок получит картину размещенную в зале славы.


Получите королевский статус в four kings casino and slots.


Системные требования



    минимальные:

    • ОС: windows 10

    • Процессор: intel core i3

    • Оперативная память: 4 GB ОЗУ

    • Видеокарта: intel HD graphics 4000

    • Directx: версии 10

    • Сеть: широкополосное подключение к интернету

    • Место на диске: 2 GB

    • Звуковая карта: directx compatible sound card

    • Дополнительно: A 64-bit OS may be needed depending on your available RAM.





    Рекомендованные:

    • ОС: windows 10

    • Процессор: intel core i5

    • Оперативная память: 8 GB ОЗУ

    • Видеокарта: NVIDIA geforce GT 630 or radeon HD 7950, or equivalent rated

    • Directx: версии 10

    • Сеть: широкополосное подключение к интернету

    • Место на диске: 2 GB

    • Звуковая карта: directx compatible sound card





    минимальные:

    • ОС: snow leopard 10.6.8, or later

    • Процессор: intel core 2 duo processor

    • Оперативная память: 4 GB ОЗУ

    • Видеокарта: intel HD graphics 3000

    • Сеть: широкополосное подключение к интернету

    • Место на диске: 2 GB





    рекомендованные:

    • ОС: OS X mavericks 10.9

    • Процессор: 2.5 ghz dual-core intel core i5

    • Оперативная память: 8 GB ОЗУ

    • Видеокарта: intel HD graphics 4000

    • Сеть: широкополосное подключение к интернету

    • Место на диске: 2 GB




The four kings casino and slots is a trademark of digital leisure inc. Game design and programming © 2019 digital leisure inc.


Super 4 casino game


Casino & Slots - Super4Bells Deluxe, super 4 casino game.


GET 400% up to €1000 casino bonus + 50 free spins . Use bonus code: 9GD65L


18+ NEW CUSTOMERS ONLY. MIN WAGERING REQUIREMENT. General T&C's apply


software: blueprint slots free, microgaming slots, nextgen slots
deposit methods: visa, mastercard, ecopayz, bitcoin, maestro, skrill, neteller
withdrawal methods: visa, wire/bank, ecopayz, bitcoin, skrill, neteller
currencies: EUR, GBP, USD
best for: UK
year est: 2019
licence: curacao

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.

Slot games mathematics


Note: this article is based on microgaming slots - however the same logic applies to the full range of slot software makers. With this in mind I have put together a range of informative articles and slot playing guides that will help you select the perfect online slot game to play. These articles cover several different topics, which are based on several different aspects of each slot mentioned in them which have an effect on your overall winning chances.


Online slots math - understanding the numbers can help you choose the best slot games


Understanding the maths surrounding slot games


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
There are a whole host of factors that slot players can take into account when they are selecting a slot game to play online. Many players often choose to play slots on which they have had some recent large winning sessions, or could be attracted to a slot purely based on the theme of that slot or possibly the bonus games attached to one individual slot game.


However, with many slot players becoming much more educated in regards to the way these types of gaming machines have been designed, and by getting a much better understanding of the mathematics surrounding the way they have been structured and designed, even a novice slot player can make a much more informed decision on which slot to play.


With this in mind I have put together a range of informative articles and slot playing guides that will help you select the perfect online slot game to play. These articles cover several different topics, which are based on several different aspects of each slot mentioned in them which have an effect on your overall winning chances.


Note: this article is based on microgaming slots - however the same logic applies to the full range of slot software makers.


While microgaming slots are not currently available at US friendly casinos, there are still a lot of excellent games that are. I recommend the bovada casino (part of the bodog family), where you will find slots from realtime gaming, rival gaming and betsoft side-by-side. Bovada also have some really cool player promos, check out www.Bovada.Lv for yourself!


32 red casino is fully licensed UK based casino that has a large (and growing) following. This operator uses the powerful microgaming software suite, and for me are the best of any casino when it comes to looking after their loyal players. You can grab $/£32 for every $/£20 you deposit – check out www.32red.Com for yourself to see the latest offers and enjoy those microgaming slots!


Should you enjoy playing slot games online at casinos powered by microgaming software, then these articles and slot playing guides are going to introduce you to a range of slots that have been designed to payout more than other slots, award their jackpots regularly and also trigger their respective bonus games more frequently.


We have also got a section dedicated to alerting you to the worst online slot games, by worst I mean those that have the lowest payout percentages or have been designed in such a way you are least likely to win a jackpot when playing them or slots that rarely trigger their bonus feature rounds!


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.


Return to player payout percentages


One of the most confusing aspects of playing online slot games for many players is in regards to payouts percentages and slot game RTP's. Each slot game you will come across online will have been designed to return to players a proportion of the stakes wagered upon that game. Knowing what these figures are enables you to spot a slot which is going to give you higher winning payouts over the long term.


We have also put together guides that will show you how easy it is to work out your actual payout percentages of any slot session you play online, and this will enable you to keep quite detailed playing logs of just how well or how bad you are doing!


Bonus game feature rounds


Whether you like playing slots that can award you with sets of free spins, pick to win bonus games or even the popular spin the wheel type of bonus features, one article that we feel will be of interest to you is my how frequently are slot game bonus rounds triggered slot playing guide.


In it we list several microgaming slot games and take a look at how many scatter or bonus symbols are on each reel, and then work out what the actual chances are of you being awarded the bonus games offered on each of those slots.


You will be surprised at how many spins on average are actually required between bonus games being triggered. However, once you do find this information out, you can then play the slots which should award their respective bonus feature rounds more regularly, if of course bonus games are what excites you the most when playing online slots!


Frequency of slot jackpots being won


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
You will never know just when you are going to spin in the jackpot paying combination when playing any slot game, which is why they are so exciting to play. However, much like the way in which bonus games are triggered, once you dissect the reels of any slot machine, and work out how many symbols are found on each reel and how many of those symbols are jackpot symbols, you can then work out your chances of actually winning the jackpot.


To enlighten you on what are the odds of winning a slot jackpot are, we have a range of slot games found in the gaming suite of microgaming software powered casinos listed, and have done all of the workings out for you, and as such present to you the odds of you spinning in the jackpot paying combination on all of those slots we have highlighted.


If you have not checked out the huge jackpots at microgaming slots recently, then you are in for a surprise! You'll regularly find the biggest ones at $2,000,000+ and plenty in the $100,000+ range are being won every week. Check out www.32red.Com for the latest totals!


Best paying online slot games


Each slot games found online will have been designed in such a way that players will get a certain percentage of their stakes returned to them as winnings. Each slot will have its own unique RTP which is the return to player payout percentage of that respective game.


The best slots to play are obviously those which through their design are set to give you more of your stakes back as payouts, and there are some huge differences in regards to just how much some slot games payback.


You will of course be seeking information on just which slots return more to players, and to help you in your quest to find the better paying slots we have the top paying slots currently found in all casinos utilizing microgaming’s suite of slot games.


Slot games best left alone


Even though slot games are completely random, if you do regularly play them online, then by opting to play only those slots offering you the best paybacks, you are ultimately going to have longer playing sessions. Plus a much better chance of winning than you would by playing slots which have been designed to return less to players via their respective RTP’s.


So to complement the above playing guide which showcases to you the best slots to play we have also compiled a guide of microgaming’s worst paying slot games. This guide will enlighten you fully on the slots you should never be tempted to play online, as those listed upon it have the lowest long term expected payout percentages, and as such offer very poor value and low winning opportunities, more so when you play slots online quite regularly!


Slot games mathematics


Configurations
there is a wide variety of the slot machines with regard to parametric design and rules. The configuration of a slot machine is specified by the configuration of its display and the configuration of its reels.
The display of a slot machine shows the outcomes of the reels in groups of spots (spot refers to a unit part of a reel holding one symbol, visible through its window; a spot on the display corresponds to a stop of the reel; a window can show one or more spots) having a certain shape and arrangement. The configuration of the display can be defined and modeled mathematically through a cartesian grid of integers, where the gridʼs points stand for the reel spots/stops and a (pay)line is a finite set of minimum 3 points that can be connected through a path linking successively neighboring points of that set. The length of a line is the cardinality of that set. Most of the slot machines have the display arranged as a rectangular grid. Lines can be of any shape and complexity and have all kinds of geometrical and topological properties. There are horizontal, vertical, oblique, or broken lines; symmetric, transversal lines; triangular, trapezoidal, zigzag, stair, or double-stair lines.
The distribution and arrangement of the symbols on each reel is also part of the configuration of a slot machine. On virtual slot machines and slot games in new slot sites, the physical configuration is replaced by parametric constraints upon the RNG (random number generator).
For the probability calculus in slots, only a part of the parameters and properties of the entire configuration of a slot machine do count [. ]. Read more on configurations


Winning combinations, slots events
any winning rule on a payline is expressed through a combination of symbols (for instance, the specific combination

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
) or a type of combinations of symbols (for instance, any bar-symbol twice or any triple of symbols) and any outcome is a specific combination of stops on that line. Therefore, the combination of stops should be naturally taken as an elementary event of the probability field. We have
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
possible combinations of stops in case A and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
possible combinations of symbols on a payline of length n across n reels. In case B, we have the same
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
number of possible combinations of symbols and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
possible combinations of stops for that payline of length n.


With regard to the complexity of the events in respect to the ease of the probability computations, we have:


Simple events. These are the events related to one line, which are types of combinations of stops expressed through specific numbers of identical symbols (instances). For example,

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
on a payline of length 3 is a simple event, defined as "two seven and one orange symbols".


Complex events of type 1. These are unions of simple events related to one line. For instance, the event any triple on a payline of length 3 of a fruit machine is a complex event of type 1, as being the union of the simple events

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
,
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
,
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
, and so on (consider all the symbols of that machine). Any double or two cherries or two oranges or at least one cherry are also complex events of type 1.


Complex events of type 2. These are events that are types of combinations of stops expressed through specific numbers of identical symbols, related to several lines. For instance,

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
on paylines 1, 3, or 5 is a complex event of type 2 expressed through "two seven and one plum symbols". The event
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
on at least one payline is also a complex event of type 2.


Complex events of type 3. These are unions of events that are types of combinations of stops expressed through specific numbers of identical symbols (like the complex events of type 2), related to several lines. For instance, any triple on paylines 1 or 2 is a complex event of type 3. At least one cherry on at least one payline is also a complex event of type 3.


General formulas of the probability of the winning events related to one payline


For an event E related to a line of length n, the general formula of the probability of E is:


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
In case A and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
in case B, (1)


Where F(E) is the number of combinations of stops favorable for the event E to occur.


For an event E expressed through the number of instances of each symbol on a payline in case A, formula (1) is equivalent to:


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
(2)


Where

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
is the number of instances of
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
, and so on,
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
is the number of instances of
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
(
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
).


Formula (2) can be directly applied for winning events defined through the distribution of all symbols on the payline, in case A. These are simple events. For more complex events, we must apply the general formula (1), which reverts to counting the number of favorable combinations of stops F(E), or, for particular situations, apply formula (2) several times and add the results.
In case B, the number of variables is larger and therefore most of the explicit formulas from case B are too overloaded. We take here one particular type of events for which we present its probability formula in terms of basic probabilities, namely the events expressed through a number of instances of one symbol. If E is the event exactly m instances of S (

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
), then:


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
(3)


Where

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
are the basic probabilities (the probability of symbol S occurring on reel number j, respectively k).


Probability calculus tools for events related to several lines
for events related to several lines, other properties of probability are used (for instance, the inclusion-exclusion principle), along with formulas (1) and (2) and some approximation methods necessary for the ease of computations. When estimating the probability of an event related to several lines, some topological properties of that group of lines do count; for instance, the independence of the lines:


We call two lines independent if they do not contain stops of the same reel. This means that the outcome on one line does not depend on the outcome of the other and vice versa. Two lines that are not independent will be called non-independent.


For two non-independent lines, the outcome of one is influenced (partially or totally) by the outcome of the other. This definition can be extended to several lines (m), as follows: we call m lines independent if every pair of lines from them are independent. From probabilistic point of view, any two or more events each related to a line from a group of independent lines are independent, in the sense of the definition of independence of events from probability theory.


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.


Independent and non-independent lines in a 3 x 3-display of a 9-reel slot machine


In the previous figure, lines

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
are independent, while
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
, as well as
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
are non-independent (for the last two pairs, the lines have a stop in common).


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.


Non-independent lines in a 4 x 5-display of a 5-reel slot machine


In the previous figure, lines

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
,
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
,
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
, and therefore
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
,
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
, and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
, are non-independent, since within each of the mentioned groups we have stops of the same reel on different lines. In such configuration, there is no group of independent lines, regardless the shape or other properties of the lines.


An immediate consequence of the definition of independent lines is that if two lines intersect each other (that is, they share common stops), they are non-independent, so any group of lines containing them will be non-independent. Another consequence is that if two lines are independent, they do not intersect each other.
If two lines do not intersect each other, they are not necessarily independent. For instance, take lines

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
in the last figure. On the contrary, lines
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
not intersecting each other in the last but one figure are independent.


The non-independent lines (intersecting or non-intersecting) for which there are non-shared stops belonging to the same reels (like lines

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
and
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
in the last figure) are called linked lines. For events related to linked lines, the probability estimations are only possible if we know the arrangements of the symbols on the reels, not only their distributions.


All probabilities were worked out under the following assumptions:
- the reels spin independently;
- a payline does not contain two stops of the same reel (it crosses over the reels without overlapping them); this reverts to the fact that any m events, each one related to one stop of the payline, are independent of each other;
- each reel contains p symbols; this is actually a convention: if a symbol does not appear on a reel, we could simply take its distribution on that reel as being zero.


Given parameters
of course, any practical application can be fulfilled only if we know in advance the parameters of the given slot machine, that is, the numbers of stops of the reels and the symbol distributions on the reels. All the probability formulas and tables of values are ultimately useless without this information.
In the book the mathematics of slots: configurations, combinations, probabilities you will find explained some methods of estimating these parameters based on empirical data collected through statistical observation and physical measurements. Of course, taking into account the incomputable error ranges of such approximations, any credible information regarding these parameters should prevail over these methods of estimating them.
The mathematics department of infarom will launch soon the project probability sheet for any slot game, dealing with collecting statistical data from slot players, using the data to estimate the parameters of the slot machine, refining the estimations with the newly collected data and computing the probabilities and other statistical indicators attached to the payout schedule of the slot machine, in order to provide the so-called PAR sheet of any slot game on the market. Contact us with subject "slots data project" if you want to be part of our future project.


Practical applications and numerical probabilities


This section is dedicated to practical results, in which the general formulas are particularized in order to provide results for the most common categories of slot games and winning events. The practical results are presented as both specific formulas, ready for inputting the parameters of the slot game, and computed numerical results, where the specific formulas allow the generation of two-dimensional tables of values. The collection of results hold for winning combinations with no wild symbols (jokers) and is partial. You can find the complete collection of practical results in the book the mathematics of slots: configurations, combinations, probabilities, for 3-reel, 5-reel, 9-reel, and 16-reel slot machines.


3-reel slot machines
the 3-reel slot machines could have the following common configurations of the display: 1 x 3, 2 x 3, 3 x 3. The standard length of a payline is 3. The common winning events on a payline are:


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– A specific symbol three times
(for example, (
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
))


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– any symbol three times (triple)


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– A specific symbol exactly twice
(for example, (
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
any))


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– any symbol exactly twice (double)


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– A specific symbol exactly once
(for example, (
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
any any))


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– any combination of two specific symbols
(for example, (mix
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
&
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
) , that is (
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
) or (
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
))


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– any combination of at least one of three specific symbols
(for example, (any bar any bar any bar ), with three bar symbols like
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
,
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
,
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
)


(the symbols from the examples are just for illustrating the winning combinations and may be replaced by symbols of any graphic. For the same parameters of the machine, the probabilities of the above events are the same regardless of the chosen graphic for the symbols.)
unions of winning events on a payline (disjunctions of the previous events

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
through
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
, operated with or):


8. A specific symbol at least twice


9. A specific symbol at least once


10. A specific symbol three times or another specific symbol twice


11. A specific symbol three times or another specific symbol once


12. A specific symbol three times or another specific symbol at least once


13. A specific symbol three times or any combination of that symbol with another specific symbol


14. A specific symbol twice or another specific symbol once


15. A specific symbol twice or any combination of at least one of three other specific symbols


On a 3-reel 2 x 3- or 3 x 3-display slot machine, any two paylines are linked; therefore we cannot estimate the probabilities of the winning events related to several lines.


16-reel slot machines
the 16-reel slot machines usually have the 4 x 4 configuration of the display. The standard length of a payline is 4, but it could also have the length 3, 6, 7, or 8. The 16-reel 4 x 4-display slot machine could have 8 to 22 paylines of length 4, as follows: 4 horizontal, 4 vertical, 2 oblique (diagonal), or 12 trapezoidal lines. It could also have 4 transversal stair lines of length 7, 12 double-stair lines of length 6, or 10 double-stair lines of length 8. It could also have 4 oblique lines of length 3.


The common winning events on a payline are:


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– A specific symbol four times (on a payline of length at least 4; for example, (
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
))


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– any symbol four times (quadruple; on a payline of length at least 4)


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– A specific symbol exactly three times (on a payline of length at least 3; for example, (
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
any))


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– any symbol exactly three times (triple) (on a payline of length at least 3)


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– any combination of two specific symbols (on a payline of length at least 3; for example, (mix
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
&
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
) , that is (
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
) or (
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
) or (
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
), for a payline of length 4)


Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
– any combination of at least one of three specific symbols (on a payline of length at least 3; for example, (any bar any bar any bar any bar), with three bar symbols like
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
,
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
,
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
, for a payline of length 4).


The table notes the probabilities of the winning events on a payline of length 4.


Unions of winning events on a payline (disjunctions of the previous events

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
through
Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.
, operated with or):


7. A specific symbol at least three times


8. A specific symbol four times or another specific symbol three times


9. A specific symbol four times or another specific symbol at least three times


10. A specific symbol four times or any combination of that symbol with another specific symbol


11. A specific symbol three times or any combination of at least one of three other specific symbols


Winning events on several paylines
for the probabilities of these events, we considered only paylines of the regular length 4 in case A.


1.1 A winning event on any of the horizontal lines
1.2 A winning event on any of the vertical lines
1.3 A winning event on any of the horizontal or vertical lines
1.4 A winning event on either or both of the diagonals
1.5 A winning event on any of the horizontal or diagonal lines
1.6 A winning event on any of the vertical or diagonal lines
1.7 A winning event on any of the horizontal, vertical, or diagonal lines
1.8 A winning event on any of the left-right trapezoidal lines
1.9 A winning event on any of the horizontal or left-right trapezoidal lines


All slots probabilities and other statistical indicators, for the most common types of slot machines and the most common winning events, are covered in the book the mathematics of slots: configurations, combinations, probabilities . The collection of probability results is presented along with the mathematics behind the slot games. See the books section for details.

Online Slots Math - Understanding The Numbers Can Help You Choose The Best Slot Games, slot games mathematics.