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Appendix 4

Analysis of 21 Bell Slot Machine

This appendix attempts to show how return for the 21 Bell Slot Machine is calculated.

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%.

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