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The 21 Bell slot machine
Analysis of 21 Bell Slot Machine
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 |
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 |
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).
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%.