Slot Machine appendix 4: The Wizard's fruit slot

Last update: September 19, 2001

This appendix explains how the Wizard's Fruit Slot was designed. This is a typical three reel slot machine, designed in the same way similar multi-payline machines work in the casinos.

The paytable for this game is as follows.

Payline	Pays
Three globes	500
Three bars	100
Three plums	50
Three bells	20
Three oranges	15
Three cherries	10
cherry-cherry-any	5
cherry-any-any	2

The next table shows how often each symbol occurs on each reel.

Symbol	Reel 1	Reel 2	Reel 3
Cherry	5	2	3
Orange	4	4	4
Bell	3	4	4
Globe	1	1	1
Plum	3	3	1
Lemon	3	5	6
Bar	1	1	1
Total	20	20	20

Once we know the paytable and how often each symbol occurs on each reel is it just a matter of simple math to determine the return of each paying combination.

Probability of three globes = (1/20)*(1/20)*(1/20)=1/8000=0.000125
Probability of three bars = (1/20)*(1/20)*(1/20)=1/8000=0.000125
Probability of three plums = (3/20)*(3/20)*(1/20)=9/8000=0.001125
Probability of three bells = (3/20)*(4/20)*(4/20)=48/8000=0.006000
Probability of three oranges = (4/20)*(4/20)*(4/20)=64/8000=0.008000
Probability of three cherries = (5/20)*(2/20)*(3/20)=30/8000=0.003750
Probability of two cherries = (5/20)*(2/20)*(17/20)=170/8000=0.021250 note: must be left aligned
Probability of one cherry = (5/20)*(18/20)*(20/20)=1800/8000=0.225000 note: must be left aligned

The return of each paying combination is the product of the probability and what it pays:

Return of three globes = (1/8000)*500 = .062500
Return of three bars = (1/8000)*100 = 0.012500
Return of three plums = (9/8000)*50 = 0.056250
Return of three bells = (48/8000)*20 = 0.120000
Return of three oranges = (64/8000)*15 = 0.120000
Return of three cherries = (30/8000)*10 = 0.037500
Return of two cherries = (170/8000)*5 = 0.106250
Return of one cherry = (1800/8000)*2 = 0.450000

The total of all the returns is 0.965000. In other words the theoretical return of this machine is 96.5%.

Go black to slot machines.

The Wizard's other sites: Wizard of Vegas, Wizard of Macau, Math Problems The Wizard recommends: The Bear Growls, Casinomeister, Online Casino Suite