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In
slots, the problem of calculating the probabilities of occurrence of
the various combinations is most similar to the one from the dice case.
Let n be the number of symbols on each reel. The
total number of possible combinations that can occur after the machine is
actuated is
n x n x n for
a three-reel slot machine and n x n x
n x n for a four-reel slot machine.
The following tables list the probabilities of occurrence of the various
winning combinations for slot machines having three and four reels, which
have 5, 6, 7, 8, 9 or 10 symbols:
3
reels, n = 5
|
Event
|
P
( / )
|
P
( % )
|
|
certain
triple
|
1/125
|
0.8
|
|
triple
|
1/25
|
4
|
|
certain
double
|
12/125
|
9.6
|
|
double
|
12/25
|
48
|
|
certain
double and certain symbol
|
3/125
|
2.4
|
3 reels, n = 6
|
Event
|
P
( / )
|
P
( % )
|
|
certain
triple
|
1/216
|
0.46296
|
|
triple
|
1/36
|
2.77777
|
|
certain
double
|
5/72
|
6.94444
|
|
double
|
5/12
|
41.66666
|
|
certain
double and certain symbol
|
1/72
|
1.38888
|
3 reels, n = 7
|
Event
|
P
( / )
|
P
( % )
|
|
certain
triple
|
1/343
|
0.29154
|
|
triple
|
1/49
|
2.04081
|
|
certain
double
|
18/147
|
12.24489
|
|
double
|
18/49
|
36.73469
|
|
certain
double and certain symbol
|
3/343
|
0.87463
|
...........................................
missing tables
.....................................................................
4
reels, n = 5
|
Event
|
P
( / )
|
P
( % )
|
|
4
identical certain symbols
|
1/625
|
0.16
|
|
4
identical symbols
|
1/125
|
0.8
|
|
certain
triple
|
16/625
|
2.56
|
|
triple
|
16/125
|
12.8
|
|
certain
double
|
96/625
|
15.36
|
|
double
|
12/25
|
48
|
|
2
certain doubles
|
6/625
|
0.96
|
|
2
doubles
|
12/125
|
9.6
|
4
reels, n = 6
|
Event
|
P
( / )
|
P
( % )
|
|
4
identical certain symbols
|
1/1296
|
0.07116
|
|
4
identical symbols
|
1/216
|
0.46296
|
|
certain
triple
|
5/324
|
1.54320
|
|
triple
|
5/54
|
9.25925
|
|
certain
double
|
25/216
|
11.57407
|
|
double
|
35/72
|
48.61111
|
|
2
certain doubles
|
1/216
|
0.46296
|
|
2
doubles
|
5/72
|
1.38888
|
4 reels, n = 7
|
Event
|
P
( / )
|
P
( % )
|
|
4
identical certain symbols
|
1/2401
|
0.04164
|
|
4
identical symbols
|
1/343
|
0.29154
|
|
certain
triple
|
24/2401
|
0.99958
|
|
triple
|
24/343
|
6.99708
|
|
certain
double
|
216/2401
|
8.99625
|
|
double
|
162/343
|
47.23032
|
|
2
certain doubles
|
6/2401
|
0.24989
|
|
2
doubles
|
18/343
|
5.24781
|
...........................................
missing tables
.....................................................................
|
Sources |
|
All
tables and the complete formulas of calculus are in the section titled Slots
of the book PROBABILITY GUIDE TO GAMBLING: The Mathematics of Dice,
Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets. See
the Books
section for details. |
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