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Play Five-Line Australian Reels Slot Machine for Free

Last Update: Dec 21, 2008

This page shows how my Five-Line Australian Reels slot machine was designed. Everything you need to know about the return can be found in the pay table and reel strips. Here is the pay table:

Australian Reels — Pay Table
Win	1 coin	2 coins	3 coins
Three flags	2500	5000	8000
Blue 7, white 7, red 7 (in order)	200	400	600
Three blue 7's	80	160	240
Three white 7's	60	120	180
Three red 7's	40	80	120
Three kangaroos	20	40	60
Three platypuses	15	30	45
Three echidnas	10	20	30
Any three 7's	2	4	6
Any three kangaroo,platypus,echidna	1	2	3

The next table shows the reel strips. The game picks 3 random numbers from 1 to 64, one for each reel. Then it maps each number to the corresponding position on the reels. This will decide the symbol in the middle row. The symbols on the top and bottom lines will be above and below the randomly chosen stops on the reel strips.

Australian Reels — Reel Strips
Stop	Reel 1	Reel 2	Reel 3
1	flag	echidna	white 7
2	red 7	blue 7	blue 7
3	white 7	platypus	red 7
4	kangaroo	echidna	echidna
5	platypus	white 7	blue 7
6	red 7	kangaroo	platypus
7	white 7	platypus	echidna
8	echidna	echidna	white 7
9	kangaroo	blue 7	platypus
10	platypus	white 7	echidna
11	red 7	echidna	kangaroo
12	white 7	red 7	platypus
13	platypus	platypus	echidna
14	red 7	echidna	white 7
15	kangaroo	kangaroo	platypus
16	white 7	red 7	blue 7
17	echidna	echidna	echidna
18	kangaroo	kangaroo	platypus
19	platypus	blue 7	red 7
20	echidna	echidna	echidna
21	white 7	kangaroo	platypus
22	platypus	red 7	white 7
23	kangaroo	echidna	echidna
24	echidna	kangaroo	platypus
25	platypus	blue 7	kangaroo
26	red 7	echidna	echidna
27	kangaroo	red 7	platypus
28	platypus	platypus	white 7
29	red 7	echidna	echidna
30	kangaroo	red 7	platypus
31	platypus	kangaroo	blue 7
32	white 7	echidna	echidna
33	kangaroo	red 7	platypus
34	red 7	kangaroo	white 7
35	echidna	echidna	echidna
36	platypus	red 7	platypus
37	kangaroo	flag	kangaroo
38	echidna	echidna	echidna
39	red 7	kangaroo	platypus
40	kangaroo	platypus	white 7
41	white 7	echidna	echidna
42	platypus	red 7	flag
43	red 7	kangaroo	platypus
44	white 7	echidna	echidna
45	platypus	blue 7	kangaroo
46	blue 7	platypus	platypus
47	white 7	echidna	blue 7
48	red 7	kangaroo	echidna
49	kangaroo	red 7	platypus
50	white 7	echidna	white 7
51	platypus	kangaroo	echidna
52	kangaroo	blue 7	platypus
53	red 7	echidna	kangaroo
54	white 7	red 7	echidna
55	kangaroo	kangaroo	blue 7
56	red 7	echidna	platypus
57	platypus	blue 7	white 7
58	kangaroo	kangaroo	echidna
59	blue 7	echidna	blue 7
60	platypus	red 7	platypus
61	kangaroo	kangaroo	echidna
62	red 7	echidna	blue 7
63	platypus	blue 7	platypus
64	kangaroo	red 7	echidna

The first step to calculating the return is to count the number of times each symbol occurs on each reel.

Australian Reels — Symbol Count
Symbol	Reel 1	Reel 2	Reel 3
Flag	1	1	1
Blue 7	2	8	8
White 7	11	2	9
Red 7	13	12	2
Kangaroo	16	14	5
Platypus	15	6	19
Echidna	6	21	20
Total	64	64	64

Grouping symbols into groups makes the math easier. Here are pertinent groups to the math.

Australian Reels — Symbol Group Count
Symbol	Reel 1	Reel 2	Reel 3
Blue 7 or Flag	3	9	9
White 7 or Flag	12	3	10
Red 7 or Flag	14	13	3
Kangaroo or Flag	17	15	6
Platypus or Flag	16	7	20
Echidna or Flag	7	22	21
Any 7 or Flag	27	23	20
Any three Kangaroo, Platypus, Echidna, or Flag	38	42	45

Next comes the fun part, calculating the number of combinations for each win in the pay table.

Three flags = 1 × 1 × 1 = 1.
Blue 7, white 7, red 7 = 3 × 3 × 3 - 1 = 26. We subtract 1 because I included the flag in each group. If the player got three flags he would win the jackpot instead.
Three blue 7's = pr(blue 7 or flag on reel 1) × pr(blue 7 or flag on reel 2) × pr(blue 7 or flag on reel 3) - pr(flag on reel 1) × pr(flag on reel 2) × pr(flag on reel 3) - pr(blue 7 on reel 1) × pr(flag on reel 2) × pr(flag on reel 3) = 3 × 9 × 9 - 1 × 1 × 1 - 2 × 1 × 1 = 240. Here we multiply the weights for a blue 7 or flag for each reel, and then subtract for the higher paying combnations of three flags, and blue7-flag-flag, which can form the higher paying blue7-white7-red7.
Three white 7's = pr(white 7 or flag on reel 1) × pr(white 7 or flag on reel 2) × pr(white 7 or flag on reel 3) - pr(flag on reel 1) × pr(flag on reel 2) × pr(flag on reel 3) - pr(flag on reel 1) × pr(white 7 on reel 2) × pr(flag on reel 3) = 12 × 3 × 10 - 1 × 1 × 1 - 1 × 2 × 1 = 357. Here we multiply the weights for a white 7 or flag for each reel, and then subtract for the higher paying combnations of three flags, and flag-white7-flag, which can form the higher paying blue7-white7-red7.
Three red 7's = pr(red 7 or flag on reel 1) × pr(red 7 or flag on reel 2) × pr(red 7 or flag on reel 3) - pr(flag on reel 1) × pr(flag on reel 2) × pr(flag on reel 3) - pr(flag on reel 1) × pr(flag on reel 2) × pr(red 7 on reel 3) = 14 × 13 × 3 - 1 × 1 × 1 - 1 × 1 × 2 = 543. Here we multiply the weights for a red 7 or flag for each reel, and then subtract for the higher paying combnations of three flags, and flag-flag-red7, which can form the higher paying blue7-white7-red7.
Any three 7's = 27 × 23 × 20 - (1+26+242+359+545) = 11247. Here we subtract out all the higher pays of three of a kind.
Three kangaroos = 17 × 15 × 6 - 1 × 1 × 1 = 1529.
Three platypuses = 16 × 7 × 20 - 1 × 1 × 1 = 2239.
Three echidnas = 7 × 22 × 21 - 1 × 1 × 1 = 3233.
Any three kangaroo,platypus,echidna= 38 × 42 × 45 - (1+1529+2239+3233) = 64818. Again, we subtract out higher pays, consisting of three of the same animal or flag.

The next table shows for each win, with one coin bet: what it pays, combinations, probability (combinations divided by 64³, and return (product of pays and probability). The lower right cell shows a return of 96.973%.

With 3 coins bet the return per coin bet for three flags is 8000/3=2666.67. That increases the win for three flags by 166.667. That increases the return by (1/64³)×166.667 = 0.000636. The return for 3 coins bet is thus 96.840% + 0.064% = 96.903% (total not equal to sum of parts due to rounding).

Australian Reels — Summary
Win	Pays	Combinations	Probability	Return
Three flags	2500	1	0.000004	0.009537
Blue 7, white 7, red 7	200	26	0.000099	0.019836
Three blue 7's	80	240	0.000916	0.073242
Three white 7's	60	357	0.001362	0.081711
Three red 7's	40	543	0.002071	0.082855
Any three 7's	2	11253	0.042927	0.085854
Three kangaroos	20	1529	0.005833	0.116653
Three platypuses	15	2239	0.008541	0.128117
Three echidnas	10	3233	0.012333	0.123329
Any three kangaroo,platypus,echidna	1	64818	0.247261	0.247261
Total		84238	0.321342	0.968395

This design is for educational purposes only. It is my design. Permission is NOT given to steal it to make a real money game. For such permission, please contact me.