A Beginner’s Guide To Slot Machine Symbols

Slot machine symbols are the images that appear on the spinning reels of a slot machine. Symbols are essential to the game, as predefined symbol combinations lead to player wins. There are several types: standard symbols, wilds, and scatters. Let's explain each type.

1. Standard Slot Symbols

Most of the spaces on the individual reels are made up of standard slot symbols. Standard symbols only have meaning when they appear together on a payline. Apart from that, they have no special features or impact on gameplay.

On any given spin, most of the matrix is ​​filled with standard symbols.

The specific images of the symbols vary. Traditional symbols like fruits (cherries, lemons, grapes), bars, and lucky 7s are still common in many slot games.

Image credit: Saranai/Shutterstock

Many modern games use playing card values ​​as standard symbols. For example, the popular online game Mega Moolah uses cards ranging from 10 to Ace as standard symbols. However, unlike playing card decks, the higher the value, the rarer the symbol on the reels. That is, three Ace symbols pay more than three King symbols.

In fact, the winnings of a slot symbol combination are always inversely proportional to the frequency of that symbol. For example, in the popular casino slot game "Buffalo Ascension," a line of three very common 9 symbols will earn you 5 times your initial bet, while a line of three of the rarest buffalo symbols will earn you 200 times your bet.

If you are playing a themed game, you may see standard slot symbols decorated to match the motif of the game. The most valuable standard symbols may be specially themed images. For example, in the popular "Wheel of Fortune" casino slot game, the high-value standard symbols are reminiscent of the prizes from the original game show, such as gold bars and images of cruise ships.

2. Wild Symbols

A wild is a slot symbol that has a special behavior that benefits the player. Like the wild card in poker, the wild can represent any other standard symbol on the board that is needed to make a winning combination. Also, in multi-payline games, the wild may substitute for one symbol on one payline and another symbol on the second payline.

The image below shows the result of a spin on One Night with Cleo, with a wild Cleo symbol appearing on reel 2 in the middle row.

Credit: Proprietary Games

In this case, the wild cleo is counted as a symbol of the second Horus eye for a combination of one victory in the central column. It is also counted as the middle of three emerald 9 symbols and wins additional awards.

3. Bonus Symbols

A bonus is a special slot symbol that triggers special game modes and prize money. To activate the bonus, you need to have three or more rare symbols in one spin. Whether the bonus is a free spin, a side game, or a temporary change in game play, it's always a good news for players.

The popular casino slot "Harley Davidson" adds a free spin to a bank where one bonus symbol accumulates for each spin. When multiple bonus symbols are displayed together, the free spin mode is triggered, and the player can ultimately use all spins accumulated in the bank.

If you are playing the game and do not know why the bonus symbol is not displayed, please check the rules. Depending on the game, the larger the bet amount per spin, the more frequently bonus symbols appear.

4. Scatter Symbols

The scatter symbol does not restrict the payline. When these special slot symbols are displayed on the matrix, the player wins, whether they are lined up in a row or scattered on the board.

Like bonus symbols, the scatter symbol sometimes sends great payouts and triggers bonus game modes. Usually, you need at least two or three scattered symbols to make a profit.

In the image below, you can see the welcome sight of "One Night with Cleo". In this game, Ankh's keyhole is the only scattered symbol of this game. If you scatter two ank's keyholes, you can get twice as much as the bet. If you have three, you will be 10 times the bet, and you will enter the bonus round, which has 15 free spins and prize money tripled.

Credit: Proprietary Games

As a scatter symbol, all three Ankh Keyhols are counted as players.

Other Special Slot Symbols

Slot games continue to evolve. Here, we will explain the symbols of other slot machines that you may encounter and how they will affect gameplay:

• Sticky: When these special symbols appear, they stay within multiple spins. Stricky may be a standard symbol or a special symbol. In any case, if STIKY accumulates on the matrix, you will have more opportunities to get bigger combinations and prize money.
• Stack: Slot symbol covers two or more spaces on one reel, greatly increasing the probability of winning combination.
• Bank: These symbols are a special symbol that will not bring the player immediately, but instead adds to the collection of bonus functions (such as free spins).

The fun part of the enlarged zoos of the throtthambol is that you can combine special benefits to players. For example, if the stack symbol that covers multiple frames on the reel is a wild symbol, it is more likely to have a lot of wild combination and a combination of victory.

How It All Comes Together: Reels, Rows, and Paylines

The old slot game was just a machine. The player pulled the lever, saw the mechanical reel rotating, and hoped that there would be a symbol that matched the payline (a single row in the center that crosses the vertical reel of three (or more)). These games were restricted by how many gears and levers could be pushed into the machine.

With the advent of online slot games, old mechanical restrictions have disappeared. Now your spin is displayed on the digital display. Most slot games stick to a handful of virtual reels and rows, but some types incorporate a visible frame that the slot symbol lands over after the spin. 。

The type of payline has also increased. Today's players can win by matching the symbols on any horizontal line in the matrix, zigzag, diagonal, and other patterns.

Let's look at the example of the payline. The online slot game "A Night with Cleo" uses 15 frame matrix with 3 lines and 5 reels. In this game, there are 20 kinds of payline as follows.

Credit: Proprietary Games

Important gameplay notes about paylines

• From left to right. Depending on the game, if you have two adjacent slot symbols, you may win. However, in almost all slot games today, the combination must start with the left end of the reel and continuously. In other words, while playing "88 Fortunes", if the golden torch symbol is aligned in the center frame of the reel 1, 2, 3, 5, the fifth reel symbol will not be counted as a combination. Aligning golden tores on the first three reels is 40 times worth the bet. If you spin again and look at the gold dentor in the center frame of reel 2, 3, 4, and 5, it may look good, but the combination of this slot symbol is continuous, but the leftmost reel. It is not worth it because it does not start.

• Depending on the multipeii game, two or more paylines may overlap to two or three reels on the left. For example, in the "night with Cleo", if there is a symbol of the two holus eyes in reel 1 and 2, 10 % of the betting amount will be paid. See the image of the payline in the above game. There are three different paylines starting from the central frame of reel 1 and 2. In other words, if the symbol of the two holus eyes is in these two frames, you can earn three times the prize as usual because the three paylines have a combination of your victory.

• Paperline. It's not so common in recent games, but you can also see slot games where the maximum number of paylines are valid only when you bet up to the maximum bed per spin. Check the rules as usual!

• Beyond the payline, some online slot games are called Waito Win Games, not payline games. In this system, there is no pr e-defined payline, so you can win if there is a symbol that matches any continuous reel. As usual, rules from left to right are valid (although some games are now using rules from right to left). Furthermore, as a flexible approach, there is a cluster dividend, and a continuous combination on reels is not required. In such a game, any cluster can configure any cluster, such as two symbols overlapping the same reel.

Slot Symbols Now and Forever

No matter where you go, a simpler slot machine is replaced by a more complex online slot game. The game will continue to evolve with visual charm and complexity. However, knowing the symbol of the slot machine is to the maximum experience of pulling the mechanical on e-arm dobanded lever, or whether you like the graphics that blink the latest digital games. This is an important condition for utilizing it.

Are you ready for the spin? Let's play the slot for free here!

Lead image Credit: PICS-XL/ShutterStock

An Introduction to Casino Slot Game Mathematics

This article introduces the basics of slot mathematics so that you can design the game from scratch using Microsoft Excel, code, or Slot Designer. It is assumed to be the basic understanding of the probability and the slot machine.

This is a quote from Chapter 1 of the free electronic book "Elements of Slot Design", assuming the probability and basic understanding of slot machines.

There is no standardization method, the design of the spreadsheet, and even the terms. For example, depending on the country or company, a symbol is called an icon, or a reel band is called a reel band. Therefore, this document uses the term defined by the author's commercial product, Slot Designer.

The Basics

First, let's consider a very simple slot game, with 10 symbols, one payline, one pille, one credit cost, each of which is a credit cost of 1 credit. Each reel has a total of 10 symbols, with one A and nine X symbols.

Figure 1. Simple 3X3 game

In one of the games of this game, if you have three A symbols of A on the payline, you will be given 1000 credits. When spinning the reel, the probability that A stops on the pay line of each reel is 1/10, so it can be seen that the probability of A in three reels is 1/1000.

Equation 1

If you win, the rules will give you 1000 credit, so the average win per game will be 1 credit.

Equation 2

When playing a game (turning the reel), you pay 1 credit, so the average cost (bet) to play each game is simply 1 credit.

Game RTP (Return to Player) is defined as a percentage of the average victory amount to the bet, and is 100%in this game.

Equation 4, 5

In other words, if you play this game for a long time, you will be able to win 100 % of the bet amount even if you can only win 1000 games once. If RTP plays a game with more than 100%, players will earn money in the long term, and if they are less than 100%, players lose money.

If the prize money is changed from 1000 credits to 500 credits, the average winning amount (equation 2) will be 0. 5 credits and RTP (equation 3) will be 50%.

If you add the second A symbol to the first reel only (the symbol is 10), the probability of A on the reel will be doubled, so three A will appear on the payline. The probability is doubled.

In the original 1000 credit award, the average prize is 2 credits (Equation 2) and RTP is 200 % (Type 3). You can win 500 games once.

Combining the second A to the first reel with the 500 credit prize amount, the probability is doubled, the prize money is half, and the RTP remains 100%. If there are two A in the three reels, the probability is 8 times and the RTP is 400 % (500 credit prizes).

The three A-symbol victory patterns are called "combination", and a complete combination of a combination of a game is composed. You can write this as follows.

In Slot Designer you can implement your game with the script on the right and the basic statistics report of the pay rules on the left.

Counting Hits

Rather than performing all calculations as probabilities, we usually count the number of winning combinations over a game cycle and divide by the cycle at the end. This difference is subtle and although the end result is the same, it is easier to work with. We can rewrite Equation 1 using the number of hits instead of the probability.

Equation 5

Hit Rate and Hit Frequency

The hit rate tells you how many games you have to play on average to win a particular prize, while the hit rate tells you the percentage of games that win that prize. This is especially useful when looking at how often players trigger feature games.

Hit rate can be calculated in a few ways.

Equation 6, 7

And the hit frequency is

Equation 8

For the game in Equation 1, the hit rate is 1000, meaning there are 1000 games between hits.

Equation 9

And the hit frequency is 0. 1%

Equation 10

Volatility

If there is a game where you win 1 credit per play, the average win is 1 credit, and the average bet is 1 credit, then the RTP is 100% (Equation 3). In the previous section, we calculated that the RTP of a game where you win 1000 credits once in 1000 games and zero other plays is also 100%.

These two games have the same RTP, but they will be fundamentally different in terms of playing. The crucial difference between these two games is in the volatility. The game where you win every time has very low volatility, and the other has very high volatility. In fact, the volatility of both is so extreme that neither of them would be a practical design.

We can also see that in order to achieve the same RTP, as the probability of winning increases, the winning amount must be correspondingly lower.

Simple Pay Rules

If you get A's on the left two reels and no A's on the third reel, you win 100 credits. This is commonly called a left-to-right combination and can be written as combination.

When counting hits for this rule, reels 1 and 2 have the same "1" as before, but reel 3 has 9 hits with no "A". Another A on reel 3 matches the left 3 A pay rule, so the 10 hits of "any" symbols do not count as matching the reel 3 combination. The left 2 A and the left 3 A are mutually exclusive.

The number of hits is

Equation 11

The average win for this pay rule is 0. 9 credits (using equations 2 and 5).

Equation 12

Therefore, 90%of the RTP contributed to the game by this Pailul is used. The total RTP of the game is the total of individual contributions, and the total RTP is 190%because the left 3 A rule is 100%.

Instead of Pailul from left to right, you can add "Any" Pailul. This pilleul is composed of three combinations,,, and each combination has just two A symbols, exclusively. All two A have 27 hits

formula

Therefore, this Pailul's RTP is 270%, and the total RTP of this game is 370%.

Equation 14

If you add another "Any" rule that pays 10 credits to any 1 A, the combination,,,,,,. The hit by this Pilleul is 243 times.

Equation 15

Therefore, the RTP of this rule is 243%.

Equation 16

The RTP in this game is the total of RTP of each pilleul, and the RTP of the three "Any" rules is 613%.

Scatter

A normal symbol or a no n-scattered symbol is paid (hit) only when it is on the payline. The scattered symbol is hit when it is displayed on the reel, above, or below, on a play window.

If the reel moves in the window and the scatter symbol (S) moves to three possible (top, middle, lower), consider what will happen.

Since the reel stops at 10 possible positions on the payline, the hits are not once, but three times. The number of hits of this combination

Hit (S, S, S) = 3 x 3 x 3 = 27

And the number of hits of S on the left 2 is

Hits (S, S,! S) = 3 x 3 x (10-3) = 63

If the height of the window is 4 symbols, it will be 4 hits per reel, and the left 3 S hits will be 64.

If you add the second scatter symbol to the reel, there are six hits (2x2) in the reel 3, and the total number of 3 s hits is 3x3 x 6 = 54.

Similarly, S is not hit (not displayed in the window), the last reel is stopped, and it is a 3x3x4 = 36 hit.

In the following example, two S symbols overlap in reel 3. If you look carefully at the reel 3 while rotating the play window, you can see that there are only four stops that cause hits due to scattered symbols. However, the two hits on the reel are the same (six times), as the two stops are hit twice instead of one of these four stops.

The total number of hits for a cycle remains the same, so the RTP remains the same. However, the prizes awarded by the game are different. For a win with two stacked symbols, the number of hits is doubled, and the total wins for that prize are also doubled. The RTP remains the same, but the volatility has changed slightly.

Previously, if there were two scatter symbols on a reel, a hit of "S" would count as four, but now there are six hits, and the hit count for each remains zero. So, we can see that the reel strip layout changes the RTP for games with scatter symbols. Scatter symbols are usually separated on the reels, so that there can never be more than one on the same reel at a time.

When designing games, especially when using Excel, calculations are usually made assuming that the scatters are spread on the reels so that this effect does not occur, and when the actual game is built, the symbols are spread to fit this assumption. If the scatters are not properly separated, an error will occur.

Slot Designer allows you to globally scatter symbols with the Scatter command. Scatter A

You can also make it scatter only where it is used in a combination by adding an 's ' after the symbol.

Pays 100 for three A's to the left;

A wild or substitute symbol is a symbol that can be used in place of other symbols in a combination on the paytable.

Wild Symbols

In the game in Figure 1 (page 4), one of the X symbols has been replaced by the wild symbol 'W' on reel 3.

In this combination, there is one hit on reels 1 and 2, but on reel 3, both the A and the W hit, so there are two hits where there was only one before.

Another notation for this combination with an embedded wild is as follows:

The symbol indicates that an A or W counts on the third reel of the payline.

This is equivalent to adding a second A on reel 3, but the wild symbol can substitute for other symbols other than A if there are other symbols or combinations.

A popular substitution variation is to double the winnings if the wild matches the combination. In this case, you simply need to count the hits of the various combinations and determine the RTP from the appropriate winning value.

The RTP of this game is 100 credits for 3×A, 30% for W as wild, doubling the winnings, and 1 credit bet.

Equation 17

Slot designers can replace several ways. You can include the wildocyvol "w" in Pailul.

Lay 3 A | Pay 100;

You can also automatically change all combinations to include wildcymbols using the SubstitionUtment command.

SUBSTITUTE W = all; pay 100 on Left 3 a;

Wild symbols are not usually applied to the scattered symbol "S".

All except SUBSTITUTE W = S;

If you use a wildocycle, you can automatically double the prize money.

All except Substitute W = S on Pay = Pay * 2;

By scattered the wildocybol, it is assigned to the Payline combination if the wildcymbol is somewhere on the reel. Wild symbols are usually substituted only when they are on the payline. In this example, a wildcymbol W on the payline is scattered, and a combination has been established.

Expanding Wild

Like other types of scattered symbols, there are multiple hits on the reel when the combination symbol is on the payline (1 hit), the top or bottom of the payline (and one hit). There is a possibility.

Expanding wild usually displays animations that expand to cover the entire reel, and the payline combination symbol cannot be seen, so the hit of the payline symbol is not usually counted. After that, you can use the RTP contribution stored in another part of the game that looks like a player.

In the slot designer's expanded wild, Wild Shymbol W is a substitute for A, and W is scattered, and when counts multiple (2) hits in both A on the payline and the scattered wild outside the payline, the following: You can implement it like.

Pay 100 to the left three A | W;

If you want to reduce multiple (2) hits to one hit, use the MERGE attribute.

Pay 100 to the left 3

Use Merge ';< A|W's >Let's consider a game where Wild Symbol W is a substitute for symbol A and B, and the reel stops with a symbol on the payline. This matches both the left 3 A and the left 2 B pilleul (combination and each).

Prioritisation

It is possible to pay both, but it is common to pay only for the highest win. For this reason, slot games generally have the rule that the highest win is paid to each payline. This is also called priority, and decides which rules to pay for payment rules.

Hits when prioritization, including wild, are as follows.

Equation 18

Equation 19 RTP for no n-priority games is 860%.

Ceremony 20

Let's consider the winning combination. If all wins are paid, both the left 2 B and the left 3 A will be hit. If only the highest win is paid, it is necessary to decide whether to pay either the left 2 B or the left 3 A. In order to exclude the hits paid as the left 3 A, it is necessary to adjust (discount) the left 2 b.

Instead of the left 2 B, the combination of the left 3 A is a stop on the pay line, and there are eight hits.

Formation 21

The number of hits on the left 2 B is 54-8 = 46 hits.

The RTP of this game is 780%, which is considerably lower from 860%of the no n-priority.

Equation 22

If Pailul has the same prize amount, the priority is selected by the game designer.

In actual games using Excel, discounts are quite complicated.

The priority of Slot Designer is implemented as follows.

Increase priority

Most games have multiple paylines and more than 100. There is no standard layout of the payline.

Multiline

RTP tends to depend on the number of i n-game payline, so the number of paylines and their layouts are usually rarely concerned mathematically. RTP is usually calculated only for one payline. Adding a payline increases the number of hits and wins linearly, so the bet amount increases to keep RTP constant.

The hit of the scatter combination does not depend on the payline, so the prize money is multiplied by a bed to keep RTP constant.

The maximum number of paylines in the game is the height of each reel window, which can be described as "how to win" in the game used. In a 5-reel thre e-row game, this is a way to win 5 or 243 lines or wins. Similarly, in the 5x4 game, it will be up to 4 or 1024 payline. The game in which 3, 4, 5, 4, and 3 symbols are displayed in reel 1-5, respectively, has a paying of up to 3 x 4 × 5 × 4 × 3 = 720.

The above five paylines were created by the following slot designer code.

// Payline LINE01 to define a payline

Payline LINE02< 2,2,2,2,2 >Payline line 03< 1,1,1,1,1 >Payline line 04< 3,3,3,3,3 >Payline LINE05< 1,2,3,2,1 >// Payline that makes the payline into a game into a game Payline01, LINE02, LINE03, LINE04, LINE05;< 3,2,1,2,3 >Virtual reels were originally used in mechanical stepper games to implement symbol weights, as described in the Telnaes patent (US 4448419). It is not common, but some game designers are also used in video slots.

Virtual Reels

In the mechanical stepper machine, the reel is a physical device, and the number of symbols around the reel is limited to about 22 due to mechanical restrictions on the size of the reel and the symbol. For example, if one reel has 100 symbols, each symbol is too small to see it on the player, or conversely, the game console becomes huge to match the huge reel.

Considering a thre e-reel game, it will be limited to 223 cycles, that is, 10648 types. Even if only one of the 10648 games hits a 20K credit prize money, the RTP from one prize is about 188 %. This significantly restricts the maximum prize money of the payout and the flexibility of the game design.

The virtual reel is modeled on a longer virtual reel, which maps multiple virtual stops on one physical stop on the actual reel.

In this example, there is a virtual reel stacked one by one with a 6 x-a symbol and one 1xA symbol. The virtual symbol is attached to a physical reel, and when the virtual reel rotates and the stop position is determined, the corresponding stop position on the physical reel is determined.

By rotating a virtual reel, you can see that the probability of hitting the six A symbol stack is six times the probability of hitting one A symbol and the probability of hitting a B symbol. Therefore, it can be seen that the weighting of the symbol on the virtual reel affects the probability of stopping the symbol on the physical reel.

Let's consider an example of a single combination of a thre e-reel game that gets a 20k credit. You can easily create a virtual reel consisting of 100 symbols and give a 1003 = 1 million game cycle. The prize RTP was 188%without virtual reels, but only 0. 2%.

In stepper machines, virtual reels greatly increase the prize money, increasing the flexibility of the pa y-table design.

Unlike regular games, the prize money of each combination (so RTP) is different for each payline, so the Excel spreadsheet becomes very complicated. To understand why this happens, consider a virtual reel with a very large weight in a certain position. When the reel spin stops, the symbol is very likely to stop to the payline 1, and it is very unlikely that it will stop at or lower the position below (that is, another payline).

It is possible to balance the symbol on the reel so that the RTP of each payline is the same.

The symbol must be placed on the reel so that the symbols just above and just below each pivot point exist, mainly pivot points, and the weights are balanced.

In the figure on the right, the weight of the pair of the symbol A and B at the position of 6 and 7 around the pivot is 3, 2, and the weight of the pair of B and A at 13, 14 positions is 3 and 2. 。

Only the symbols adjacent to the pivot are required.

Symbol layout may not be balanced, such as when converting a video game into a stepper format. In this case, not only calculates the RTP of each payline, but also if the player may select and play with different numbers, it is considerable effort to keep the RTP almost the same for each player selection. It may be. As the number of paylines increases, the same or increased RTP may be a regulation requirement.

Most games have normal 3x3 or 5x3 windows, but some games have a more unusual shape. The RTP of these games can be easily calculated using the same principles that we have given to now. Regardless of the height of the windows, the combination of the normal payline is only scattered by the height of the window.

Irregular Window

In this example, a window shows a 3, 5, 5, 5, 3 symbols in reel 1 to 5, respectively.

For example, the number of hits of the scattered symbol in all five reels is 1125.

Slot Designer describes the window in the following code, first defines the maximum size of the window, and then defines which location in the window is used.

Window 5, 5 ,,,,;;

Depending on the game, there is one that presents a series of hidden options (boxes, etc.) to the player and selects one or more. Each time the prize is selected, the value of the prize becomes clear, and the player gets the total of the selected prizes. These are also known as pick games.

Player Choice

The average win of this simple case

Equation 23

There are many variations for this type of feature, such as choosing other feature games, mult i-pliers, or prizes that end immediately. It is quite complicated and exceeds the scope of this article.

General game features are free spins, and bass games are triggered by a series of free games.

Free Games

First, consider the case where the free game does not trigger additional free games. The average wins of the base and free games are B0 and B1, respectively, and the base game triggers n1 free games with a trigger probability of p1. Thus, the average number of free games is n1p1.

Equation 24

The final win, F, of the combination of base and free games is

Equation 25

As usual, the RTP is the win divided by the bet amount.

Equation 26

Now consider the case where the free game can retrigger n2 games with probability p2. The average number of free spins is

Equation 27

Then, the RTP is the average win of the base and free games times the average number of free games divided by the bet.

The standard deviation σ is calculated by multiplying the probability of each prize in the base and feature games by the difference between the credit value of that prize and the average credit winnings over the entire series of base/feature games (Equation 29).

Standard Deviation

Equation 29

The standard deviation suitable for regulatory approval can be calculated in Excel. The probability of each prize in a feature game is the total probability of reaching that feature game multiplied by the probability of that prize being awarded in the feature game.

The probability of the base game itself is 1. 0, and the probability of the free game is the expected value of the free spins calculated with Equation 27.

We should also include hits with zero wins (i. e., misses), which cannot be calculated analytically in Excel for games with matching wins (most, if not all). We can either leave it out, or make an approximation of cycles minus the sum of hits, which is wrong either way. A related issue is that Excel models only one payline, so even with multi-line games the standard deviation is one line, and multi-line games have even more overlapping wins than single-line games.

Furthermore, only non-overlapping wins can be calculated using Excel, but players experience overlapping wins. For example, when a player wins 100 credits and 200 credits from simultaneous scatter and line wins, should this be considered as one win of 300 credits or separate wins of 100 credits and 200 credits? The player experiences it as 300 credits, but it cannot be calculated theoretically. A full cycle simulation can be done to determine the correct distribution of wins, or a random simulation can be done to get an approximation.

If you win a free game, you can accidentally win a series of games, and you can calculate the standard deviation. The only way to estimate this type of standard deviation is to perform random simulation.

There are several ways to calculate the standard deviation, and which one to use depends on what you are trying to achieve.

The trust interval shows the range of RTP of the game machine after N game.

Volatility Index and Confidence Intervals

Here, the volatility index based on the 95%confidence interval

Equation 31

If the measured RTP is out of this range, it can be said that it is not moving as expected with 95%reliability. This calculation assumes that the game has a normal distribution, but it may not be the case.

Slot Designer displays 90, 95, 99%reliable levels to show the margins expected by game operators.

The volatility indexes based on the 90%and 99%confidence intervals are 1. 64σ and 2. 58σ, respectively. < SPAN> If you win a free game, you can accidentally win a series of games, which can also calculate the standard deviation. The only way to estimate this type of standard deviation is to perform random simulation.

There are several ways to calculate the standard deviation, and which one to use depends on what you are trying to achieve.