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Casino Benefits Bonus Code: 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:. New Real Slots Games. For two non-independent lines, the outcome of one is influenced partially or totally by the outcome of the other. However, you can learn some basic casino math in order to take well-calculated risk. General formulas of the probability of the winning events related to one payline. Liberty Slots Casino is a brand new US friendly website offers exclusive collection of slots, video poker and table games.

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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 reel slot machines.

The standard length of a payline is 3. The common winning events on a payline are:. For the same parameters of the machine, the probabilities of the above events are the same regardless of the chosen graphic for the symbols. Winning event Case A Case B 8.

A specific symbol at least twice table formula and tables 9. A specific symbol three times or another specific symbol twice table formula A specific symbol three times or another specific symbol at least once table formula A specific symbol three times or any combination of that symbol with another specific symbol table formula The standard length of a payline is 4, but it could also have the length 3, 6, 7, or 8.

The reel 4 x 4-display slot machine could have 8 to 22 paylines of length 4, as follows: 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: The table notes the probabilities of the winning events on a payline of length 4.

Winning event Case A Case B 7. A specific symbol at least three times table formula 8. A specific symbol four times or another specific symbol at least three times tables formula A specific symbol four times or any combination of that symbol with another specific symbol tables formula The collection of probability results is presented along with the mathematics behind the slot games.

See the Books section for details. If the machine has blank stops, the blank should be considered as a symbol among them. Parameter p is specific to the machine. We denote by n the length of a certain payline. Each slot machine belongs to one of the two types: Type A — All reels have the same distribution of symbols; Type B — The reels have different numbers of stops and each symbol has different distributions on the stops of the reels.

With regard to the complexity of the events in respect to the ease of the probability computations, we have: 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: For an event E expressed through the number of instances of each symbol on a payline in case A, formula 1 is equivalent to: If E is the event exactly m instances of S , then: 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: 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.

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