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The Wizard's Fruit Slot
Introduction
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.
Click image to play.
The paytable for this game is as follows.
Fruit Slot Pay Table
| 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 Distribution
| 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.