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Last Updated: August 19, 2016

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%.

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