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Introduction
to Slot Machines
The slot machine consists of a 3-bar in blue,
2-bar in white and 1-bar which is in red.
When a bet is
placed by pressing the spin button, the machine
will select 3 random numbers, with each reel
selected differently. These random numbers are
chosen from a generator which randomly selects
these numbers at a rate of thousands per second.
The final outcome would be the numbers chosen
when the play is initiated, which means that the
result is pre-determined from the moment the
spin is made.
Conversely, in
terms of the Red, White and Blue, each random
number has 64 equally likely outcomes. A
“Look-up Table” is set when each random number
is mapped to a stop position. The following
TABLE illustrates the Red White and Blue lookup
table on the assumption that the total number of
stops per symbol per reel.
As soon as the
random numbers are chosen, they will be mapped
to a stop on the machine using the Look-up Table
where the outcome will be scored and player will
be rewarded if he wins anything. For instance,
if the random numbers chosen were 26, 8, and 43 the player
would get Blue 7, Blank, Red 7. It
should be noted that there will be clusters of
the same symbol in a row. For example, stops at
60 to 62 on reel 1 are all mapped to a 1 bar
symbol. These will be directed to the same 1 bar
symbol on the actual reel. There are exactly 22
groups of like symbols on each reel, which is
the standard number of stops on an
electro-mechanical three-reel slot machine,
known as a "Stepper Slot." In
addition, there is only stop 45 on reel 1 mapped
to the red 7 symbol. There will be 5 positions
each on the blanks above and below it which
often causes near miss effect when the reel
stops directly above or below the highest paying
symbol.
The
return of the machine can be calculated by
summing up the number of position for each
symbol on each reel to get the total symbol
weightings. The following TABLE shows the
summation of the total weights.
With the weighting of each
symbol and reel known, it is easy to calculate
the return. The following table shows the win,
number of combinations, probability, and
contribution to the return for all possible
events. For example, the table above shows the
number of white 7's are 6, 1, and 7, for reels
1, 2, and 3 respectively. The total number of
winning combinations for three white sevens is
thus 6 × 1 × 7 = 42. 
The lower right cell shows a return of
86.58%. That means that for every dollar bet at
the one coin level, the player will get back
86.58 cents, on average. Doing the same table
for two coins results in a return of 86.58% as
well, and three coins has a higher return of
87.47%, due to the disproportionately high win
on the top two pays. The standard deviation is
9.03 for 1 or 2 coins, and 10.80 for 3 coins.
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