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- Appendices
- Slots Analysis
- Miscellaneous
Analysis of 21 Bell Slot Machine
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This appendix attempts to show how return for the 21 Bell Slot Machine is calculated.
Click image to play.
Table 1 shows the frequency of each symbol(s) on each reel. Each stop is equally likely.
Table 1 — Reel Strips
| Stop | Reel 1 | Reel 2 | Reel 3 |
|---|---|---|---|
| 1 | orange | cherry | bell |
| 2 | melon | plum | orange |
| 3 | plum | cherry | plum |
| 4 | cherry | 7 and orange | bell |
| 5 | plum | cherry | orange |
| 6 | orange | bell | lemon |
| 7 | 7 | plum and bar | bell |
| 8 | bell and bar | bell | melon and orange |
| 9 | orange | cherry | bell |
| 10 | cherry | orange | plum |
| 11 | bar | bell | lemon |
| 12 | plum | melon and orange | bell |
| 13 | orange | plum | plum |
| 14 | plum | bell | bell |
| 15 | melon | cherry | 7 and bar |
| 16 | plum | bar | lemon |
| 17 | orange | orange | bell |
| 18 | plum | cherry | melon and orange |
| 19 | bar | bell | bell |
| 20 | plum | melon and orange | lemon |
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Table 2 shows the frequency of each symbol on each reel.
Table 2 — Symbol Frequency
| Symbol | Reel 1 | Reel 2 | Reel 3 |
|---|---|---|---|
| 7 | 1 | 1 | 1 |
| Bar | 3 | 2 | 1 |
| Melon | 2 | 2 | 2 |
| Bell | 1 | 5 | 8 |
| Plum | 7 | 3 | 3 |
| Orange | 5 | 5 | 4 |
| Cherry | 2 | 6 | 0 |
| Lemon | 0 | 0 | 4 |
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Table 3 shows the number of combinations of each paying combination (probability combinations) and the expected return for each paying combination over all possible outcomes (return combinations).
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Table 3 — Probability and Return Combinations
| Win | Pays | Probability Combinations | Return Combinations |
|---|---|---|---|
| 3 sevens | 200 | 1 | 200 |
| 3 bars | 100 | 6 | 600 |
| 3 melons | 100 | 8 | 800 |
| melon, melon, bar | 100 | 4 | 400 |
| 3 bells | 18 | 40 | 720 |
| bell, bell, bar | 18 | 5 | 90 |
| 3 plums | 14 | 63 | 882 |
| plum, plum, bar | 14 | 21 | 294 |
| 3 oranges | 10 | 100 | 1000 |
| orange, orange, bar | 10 | 25 | 250 |
| cherry, cherry, any | 5 | 240 | 1200 |
| cherry, any, any | 2 | 560 | 1120 |
| Total | 1073 | 7556 |
The bottom row of table 3 shows 1073 probability combinations and 7556 return combinations. With 20 stops on each reel the total combinations is 203=8000. So the probability of any win (hit frequency) is 1073/8000 =13.41%. The machine's expected return is 7556/8000 =94.45%.
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Written by: Michael Shackleford