Eddie s Math and Calculator Blog

Eddie's Math and Calculator Blog

A blog is that is all about mathematics and calculators, two of my passions in life.

Tuesday, January 7, 2014

Probability: Odds of Winning at Slot Machines

The Odds of Hitting it Big

The number of possible combinations is fairly easy to calculate. You multiply the number symbols each slot has together. For example for a three slot machine with six symbols a piece, the number possible combinations is 6 × 6 × 6 = 216. Although I have never played on one (knowingly), you could have a slot machine were each slot itself has a different amount of symbols.

Calculating the probability of winning on a slot machine is fairly simple. The odds of getting a certain combination is:

(number of winning combinations)/(number of possible combinations)

Different winning combinations offer different playoffs. The harder the combination, the bigger the reward. In gambling, the term payout percent is used when describing how "lucrative" the slot machine is. In general it is calculated like this:

?(winning combination k * payoff k)/(number of possible combinations)

Note that is different from the total of number of winning combinations over the number of possible combinations ratio. The payoff acts as a weight for each winning combination. (It is like weighted average, but not quite.)

Let us look at analyzing a pair of slot machines. For this blog entry, we will assume that the slot machine has one line and takes only one coin per roll.

Analyzing a Simple Slot Machine

The first machine has three slots. On each slot there is an apple, orange, lemon, banana, melon, and a Joker. The payouts are as follows:

(I) Three Jokers (Joker | Joker | Joker) pays 30 coins
(II) Any Three of the same fruit (example: Apple | Apple | Apple) pays 10 coins
(III) Any Two Jokers pays 4 coins
(IV) Any One Joker pays 1 coin (break even)

Number of Possible Combinations: 6 × 6 × 6 = 216

Number of Winning Combinations (see above):

(I): There is only one configuration for this: three Jokers.

(II): Three of a kind that isn't a Joker. One the first slot, you can get any of the five fruit (apple, orange, lemon, banana, melon). Once that fruit is selected, that fruit has to match on the next two slots. So, there are 5 such combinations: three apples, three oranges, three lemons, three bananas, and three lemons.

(III): Jokers can appear any two slots: slots 1 and 2, slots 1 and 3, and slots 2 and 3. The other slot must contain fruit. Hence the total number of winning combinations possible is 1 × 1 × 5 + 1 × 5 × 1 + 5 × 1 × 1 = 15.

(IV): Jokers can appear in any slot, the other two slots must have fruit. In this instance, it does not matter if the other two slots match. The number of combinations is 1 × 5 × 5 + 5 × 1 × 5 + 5 × 5 × 1 = 75.

There are a total of 1 + 5 + 15 + 75 = 96 winning combinations. The table below shows the calculation of slot's payout.

Calculating the payoff percentage:

The payoff percentage is 99.537%. That is pretty good in terms of slot machines. It could be a little misleading given that the harder combinations are given more weight.

Had everything paid equally, only 96/216, or about 44.444% of the combinations would win. I doubt no one would play a slot machine with less than a 50% chance of spinning a winning if there was no added incentive, such as a richer payoff.

A More Complex Slot Machine

We are still at one line, three slots. Here is the slot distribution:

There are 23 symbols per slot. So the number of possible combinations is 23 × 23 × 23 = 12,167.

Also note that the non-equal distribution of symbols on each slot. With the lack of BARs, cherries, and Sevens ( 7 ), it is obvious that getting winning combinations involving these three symbols offer higher playoffs.

The winning combinations, with payoffs are: (See the table above for the distribution of symbols)

(I) 3 BARs. Wins 60 coins. Number of winning combinations: 1

(II) 3 Sevens. Wins 40 coins. Number of winning combinations: 3 × 1 × 1 = 3

(III) 3 Cherries. Wins 20 coins.
Number of winning combinations: 4 × 3 × 3 = 36

(IV) 3 of any Fruit (3 Oranges, 3 Bananas, 3 Lemons)
Wins 10 coins.
Number of winning combinations:
For Oranges: 5 × 6 × 6 = 180
For Bananas: 5 × 6 × 6 = 180
For Lemons: 5 × 6 × 6 = 180
Total: 540

(V) Cherries in Any Two Slots:
Wins 4 coins.
Number of winning combinations:
Cherry, Cherry, Other: 4 × 3 × (23-3) = 240
Cherry, Other, Cherry: 4 × (23-3) × 3 = 240
Other, Cherry, Cherry: (23-4) × 3 × 3 = 171
Total: 651

(VI) Cherry in any one slot:
Wins 1 coin.
First Slot: 4 × 20 × 20 = 1600
Second Slot: 19 × 3 × 20 = 1120
Third Slot: 19 × 20 × 3 = 1120
Total: 3880

The following table calculates the payoff percentage for this machine:

This second table has a payoff percentage of 99.721%. If everything paid 1 coin equally, it would drop to just over 42%.

For more complex slot machines (more slots and multiple lines), the use of a spreadsheet or other computer program will come to the aid of calculating payoff since the number of calculations grow with complexity.

This blog is property of Edward Shore. 2014

Update: Due to the insane amount of spam on this blog thread, all comments on this article are surpressed. 7/24/2021

What Are the Odds of Winning a Jackpot on Slots

Learn what are the chances of winning a jackpot on slots, and the many ways to increase your odds, and what misconceptions you should disregard.

Walking out of a casino with millions of dollars in hand after winning a slot s jackpot prize, the fantasy of every casino patron. That s why people play slots after all they want to win the largest payouts ever!

What are the slot machine odds of being one of those people who took home one of the coveted jackpot prizes? Is there a way for you to improve your odds of winning the progressives?

Odds of Winning Large Jackpots In Slots

Your chances of winning any major jackpot start at 50 million to more than 100 million to one. The likelihood of winning a slot jackpot depends on the slot game s RTP rate and variance.

Take note that these odds are provided by a handful of software providers, which tend to be different from the actual probability of a game. Certain slots can reach up to 600 million to one likelihood of winning the jackpot.

Slot jackpot probability mentioned here is from local and wide area network progressive slots instead of fixed jackpots. When people spin the reels of these slots, the jackpot amount grows. Local progressives only count the spins from machines within the vicinity while wide area network progressives count spins from players around the world. Expect the former to have a low jackpot prize than the latter because of the availability of these games.

At this point, you are likely thinking of how to win jackpots on slot machines given the unsurmountable odds associated with progressive games. One method to improve your odds is in playing higher denomination slots.

Odds of Winning Large Jackpots In Slots

How Can Players Win Slot Jackpots

To understand how slots determine whether you win the jackpot or not, we need to cover the basics of the PRNG algorithm. Every online and video slot uses a PRNG algorithm to determine the results of each spin. This algorithm uses seeds and entropy data to create multiple authentic results. To achieve real randomness , entropy comes from real-world factors such as the system clock.

To have the jackpot within your reach, you need to spin the reels with the specific seed and entropy data (likely the specific time) set. Take note that this is just going to give you a chance at winning the jackpot. You also need to get one of the multiple results generated by the specific seed and entropy.

Play Higher Denomination Games Max Bets

When you play higher denomination games, you get a better payout upon your wins and a better edge against the house. When you play 1 to 5 cent denomination games, you only get a payback rate of 84% to 89% with a player edge of around 84% to 88%. Going for slots that costs a dollar to spin, you get a 93% to 95% return and an edge of up to 95%.

Higher denominations are one of the achievable slot machine tips to win the progressive jackpot prize since you are increasing the number of spins or chances. It is important to note that you are exchanging better jackpot win odds with higher risks. These denominations can result in losing more spins over a set period. On the other hand, the massive jackpot prize is worth taking on a bigger risk than playing it safe with small bets.

Popular Massive Jackpot Slots

Different slots have their gameplay mechanics in giving players a shot at the jackpot prize. Here are ways on how you can win the top progressive jackpot slots.

Mega Moolah (Microgaming)

With an RTP of 88.12%, Mega Moolah offers one of the largest jackpot prizes in any casino with a low edge against the house. You need to get into the Mega Moolah Jackpot Wheel to get the coveted prize, which is triggered by random during the base game. There are four different jackpots in the bonus mode that increase in amount as more people spin the reels: Mini, Minor, Major, Mega. You win one of the four jackpots when you land at its corresponding place on the reels.

Mega Moolah by MicroGaming

Aztec s Millions (RTG)

In the 3?5 reels and 25 payline Aztec s Millions (by Realtime Gaming), the progressive jackpot is obtainable by matching 5 Aztec s Millions symbols. Furthermore, you can win up to 25 free games by matching 5 Scattered Idols symbols to get a free shot at the progressive jackpot as well as tripling all non-bonus symbols payout.

Halls of Gods (NetEnt)

Halls of Gods progressive jackpot is hidden in the Bonus Feature of the game, which you can trigger by getting three Bonus symbols to appear on the reels. During the bonus game, you choose from 15 shields that contain three different jackpot symbols: Mega, Midi, Mini. You win the corresponding jackpot by revealing three of its symbols on the board.

Funky Fruits (Playtech)

Obtaining the jackpot in Funky Fruits from Playtech is straightforward and simple. You need to match eight or more of the Cherry symbol to win the jackpot. Do not mistake simply as easy though. The chances of having a Cherry symbol appear on the reels are incredibly low since this is the most valuable symbol in the game. Fortunately, Funky Fruits is a cluster pay slot where you get a free re-spin when you match any symbols.

Common Myths About Slot Machine Jackpots

Slots are somewhat esoteric with lots of people believing in random misconceptions. There have been several myths regarding slot jackpot probability such as ones where players can trigger the massive cash prize itself. Others involve finding slots with the best odds among the dark corners of the casino floor. Here are the two common myths of a win at slots jackpot payouts.

There Are Loose Slots Hidden in Plain Sight

Imaginations run wild among casino patrons when they see a worker servicing one of the machines. Questions such as Can resetting the machine refresh the algorithm to give the next player a better chance at winning the jackpot? can go around various players. When the service option appears on the screen, one cannot help but wonder if defragging or removing the money from a machine can loosen it up.

Unfortunately, there is no such thing as a loose slot that increases the slot machine odds. Hot or cold slots that pay high or low during specific times are also a myth.

Remember, every slot machine uses a PRNG algorithm to determine if a spin wins or loses as well as the corresponding symbols matched. An employee cannot change the algorithm programming when they service the machine.

Apart from being serviced by the staff, slot jackpot odds are also not affected by the payouts. Players who won the largest possible payout from a single title will not decrease the chances for the next person to get a high cash prize. All results are still created by the algorithm, which will not consider the money it paid out to players when determining the symbols appearing on the reels.

Players Can Trigger The Jackpot With a Button Sequence

A majority of casino patrons likely saw the clip of Brad Pitt entering a sequence of button presses and coin insert to win a slot s jackpot prize. Those who did watch Ocean s 13 tend to try their luck at pushing buttons at random to control their odds, which will not work.

Is the button sequence a myth? You will be surprised to know that this is real and was achieved by Ronald Dale Harris. Ronald was a programmer who has a job at the Nevada Gaming Control Board as an inspector of slot machines across Las Vegas casinos. During his career, he was able to create a chip that lets him win a high payout from any

game. To accomplish his goal, Ronald recruited friends to embed his chip onto targeted slots.

Ronald was able to get away with thousands of dollars from Las Vegas casinos. Unfortunately for him, the law caught up to Ronald in Atlantic City, and was sentenced to seven years.

Because of Ronald s illegal pursuit, casinos and manufacturers increased the security of each slot machine. Any random button presses on a slot machine will not increase a player s slot machine odds, but it can catch the attention of casino security.

Common myths and misconceptions about online slots.

With the massive payout provided by progressive jackpots, your odds of winning them are slimmer than winning the lottery. You can still increase your chances of winning the elusive jackpot prize by playing high denomination slots and raising the number of spins instead of following busted casino myths.

Understanding the Odds - Winning Slot Machine

Players who are interested in winning slot machines should spend some time understanding the odds and the secrets of the machine and of hitting the jackpot before they start to play slots for real money. The odds are basically the chances of hitting the jackpot in a slot machine or the chances of hitting any winning combination.

How are the Odds Calculated?

In all the modern slot machines the player's odds of hitting the winning combination of numbers and symbols would depend on how the reels are set up. Every stop on the reel can correspond to more than a single stop on the reel. The odds of hitting a particular symbol on the actual reel would also depend on how many stops would correspond to the actual stop. For this reason, it is a bit difficult to calculate the odds of hitting the winning combinations especially with machines that have many virtual stops.

The Odds of Hitting the Jackpot

In the typical slot machines the top jackpot for every reel would correspond to just one virtual stop. What this means is that the chance of the player hitting the jackpot in one reel is 1 to 64. If all the reels in the machine are set up that way, then the chance of hitting the jackpot symbol in all the 3 reels is 262,144. This means that for every player the chances of hitting the jackpot are very low. Also, in machines that have a bigger jackpot, the virtual reels would also have several more stops so this would again decrease the chances of hitting the jackpot immensely.

When there are blank stops below and above the jackpot symbols, these are losing stops, which means that the player would not win anything on those symbols. Also, these blank stops show that there are more virtual stops on the reel than images. A player is more likely to hit these blank stops rather than the jackpot images. It is creates an impression that they just missed winning the jackpot which again encourages them to keep playing more.

The Payback Percentage and the Odds

Every slot machine is designed and then tested in order to get a particular payback percentage. This percentage would be the money which is put into the slot machine and then later is paid to some of the players. The odds for a slot machine are built in the machine program on the computer chip. In most cases the casinos can only change the odds if they replace this chip. There is no way for a casino to instantly tighten up a slot machine despite the popular belief. Also do not believe in the loose slots machines.

Also, slot machines never loosen up if you play for a long period of time. The computer would keep on pulling up new numbers and with every spin you would still have the same odds of hitting the jackpot as you had at the last and the first spin. Slot machines are never ready to pay or are never due for a jackpot if it hasn't hit the jackpot in a long time. It is all based on the software.

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Slot Tips

You might be disappointed as the there are no strategies that actually work in slot games. It is a game of chance and only your destiny settles the outcome of the game.

But at the same time there are some specific moments you should pay your attention to. The primary one is what type of slots to gamble at. If you have never questioned yourself this simple thing, so you should start if you do not want to waste your time and cash. There are other important aspects of online gaming, which you should know and apply. Those are called slot tips.

How to Win at Slots Our Complete Guide on Slots Odds and More

Are you wondering how to win at slot machines? Or maybe you need some help to figure out slot odds? Look no further. The expert guide we ve written on this page covers everything you ll need to know on how slot machines work, and how you can pick the best slots to play online.

We ll also provide you with slot machine tips, debunk popular myths, and answer all the burning questions related to these beloved games. Ready to dive into the world of slots? Let s get started!

How Do Slot Machines Work?

To understand how to win at slot machines, we need to know how these games work. First thing you should be aware of is that slots outcomes are purely based on chance, which means there s no real slot machine strategy you can use to change those outcomes. Every player has the same odds of winning with any given slots game, and they cannot change these odds. You just spin the reels and hope to match symbols along the several paylines.

So, how does a slot ensure the same odds of winning for everyone? Why are the results random and unchangeable? Let s take a look at the answer below:

The Software Behind Slot Games

Every time you press the spin button, the slot will create a random sequence of numbers that determine the result. This process is in place because today s slot machines and their online counterparts use random number generator (RNG) software.

RNG Slot Results Are Always Random

The RNG works independently every time you play. This complex system churns out millions of potential results per second for the slot, even when no one is playing. This makes slot machines truly random and fair, which is why most casinos, including online casinos, offer RNG slots nowadays.

Each Spin Outcome Is Independent

Even when the reels appear to be spinning in the slot, the game is selecting one of the many results created by the RNG software. And while the game seems to go on winning or losing streaks, this isn t the case. Each spin is an independent event, so even if you hit spin a fraction of a second later, the RNG would have given a different outcome.

RNG Software and Fairness

You may wonder how one can be sure the RNG software is working as it should, and it isn t rigged. This is where software auditing companies, such as iTech Labs and eCOGRA come in. These companies test the software to make sure the spins of a particular slot are truly random and that over the long run, the returns from each game match up with the published amount.

Is There a Slot Machine Strategy?

Unlike skill-based games such as blackjack and poker, there is no strategy that you can apply to slot machines that will improve your chances of winning and give you an edge over the house. Simply put, slots are a game of luck, and nothing can change the outcome of each spin. Choosing which slot to play, on the other hand, is entirely in your control. You can improve your chances of winning by opting for slot machines with the best odds of winning.

Slot Machine Odds Explained

So far, we ve established that the results of modern slot machines are programmed to be random. However, as with other casino games, the odds of slots are set in a way that gives the house its edge. Casino games make money for the house by paying out less than the true odds of the winning bet. With table games, this can be quite simple. Let s take European roulette as an example. With numbers 1 through 36, plus a single 0, the true odds against any particular number are 36 to 1, but the casino pays single-number winners only 35 to 1.

Slots odds work in a similar way to our roulette example, except there are several more possibilities on slots. Because of the RNG software, there are thousands, and often millions, of reel combinations. It s also up to individual game designers to determine how much each winning combination pays. The number of winning combinations and the payouts per combination work together to determine an online slot s odds. But the vast number of possibilities makes the math of slots odds more complex than table games odds.

The player also doesn t know how the game was designed. Therefore, it s hard to quantify the odds of modern slot machines, whereas it was easier to figure out the true odds of an old-school mechanical game. You could have calculated your odds based on the number of reels and symbols per game. For example, a slot with 3 reels that holds 20 symbols per reel would give you a 7,999 to 1 chance of winning.

So, is there any way we can choose slots which offer better returns than others? And how can we know the house edge of a specific slot game? This is where RTP comes in, which we ll talk about next.

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