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Deconstructing Blazing Sevens

Introduction

In my continued efforts to show the world how video slot machines work, I set out to deconstruct how Blazing Sevens was designed by playing it. There are lots of different "Blazing Sevens" games. The one I am referring to is the five-reel video slot. Armed with a cell phone camera, I recorded about 30 minutes of play. Unlike most video slots, Blazing Sevens has no bonus round. To analyze the game, all I needed to do was piece together the reel strips based on my videos and then do the math.

Step One - Data Collection

Much like games I previously deconstructed, Jackpot Party and Hexbreaker, I chose Blazing Sevens because it didn't involve bonus spins. The only mystery was the reel stripping. So I found a game in the Fremont in downtown Las Vegas and recorded 30 minutes of play. These videos can be found on YouTube:

When I returned home, I asked for volunteers to record each sequence of three symbols on all five reels for every spin. I would like to thank Miplet for transcribing part 1 and ChesterDog for part 3. Those two videos I felt were sufficient.

Step Two - The Reel Strips

Then I tried to put together the order of the reel strips, based on the observed sequences of symbols. To make the reels balance and loop around, I assumed that some sequences appeared more than once on the same reel strip. These were chosen according to what completed the reels and which sequences occurred more frequently. The reel strips below I believe are very close approximations to the actual ones. However, due to repeating sequences, and a limited sample size of 617 spins, they are probably not exactly correct. I estimate that each reel may have about two incorrect symbols in terms of frequency.

The following table shows how often each three-symbol sequence appeared on each reel in videos 1 and 3. For example, the D-7-1 (dollar, plain seven, 1-bar) sequence appeared 14 times on reel 1.

Blazing Sevens Sequence CountsExpand

Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
Sequence Count Sequence Count Sequence Count Sequence Count Sequence Count
2B1 41 B2D 40 27D 38 1BD 30 F2D 34
B27 37 2D3 33 B27 35 F1B 30 BF2 29
3B2 29 1B2 28 7DB 32 17D 25 DBF 27
B1D 28 FDB 21 D3B 26 3F1 25 2F1 25
372 27 7DF 20 F2B 22 1D7 22 BD2 22
72B 27 DBF 20 1B7 21 7B3 21 2DB 21
73B 24 BF7 19 DBF 21 B2D 21 7B2 21
3D7 23 D71 19 FD3 21 BF3 20 7BF 20
7DB 21 7D2 18 1D3 19 D72 20 FBD 20
D37 21 B17 18 B2D 19 2BF 19 F1D 19
1B7 20 BF3 18 D1B 19 71B 19 F37 19
1D7 20 DFB 18 B7F 18 72B 19 DB1 18
B73 20 F7D 18 DF2 18 7D2 19 73B 17
F2B 19 371 17 3FB 17 3DF 18 F73 17
BD3 18 7D1 17 DB1 17 F17 18 173 16
27D 17 D2B 17 DB3 17 F3D 18 1DB 16
71B 17 D3B 17 1DB 16 B3D 17 3FB 16
D3B 17 3DB 16 3B1 16 D27 16 3FD 16
B37 15 D1B 16 B1D 16 F3B 16 7F2 16
B3D 15 F2B 16 D27 16 B3F 15 BF7 16
DB3 15 FB7 16 DB2 16 27B 14 F7B 16
1B2 14 2D1 15 FB2 16 2B3 14 2F3 15
B2D 14 B7D 15 2BF 15 2D1 14 B1F 15
D71 14 D1F 15 2DB 15 D1F 14 B7F 15
D73 14 17D 14 3B2 15 3B1 13 BF1 15
2D1 13 2B1 14 F1D 14 73F 13 D2F 15
3F2 13 BD7 14 7DF 13 D17 13 2B7 14
1D3 12 2BF 13 B17 13 DF1 13 F17 14
3BD 12 71B 13 BFD 13 1F3 12 FDB 14
D1B 12 F3D 13 FD2 13 B1D 12 1F7 12
2B3 11 1FD 12 7D1 12 BD1 12 B2F 12
273 9 3BD 12 BF1 12 D71 12 F2B 12
73F 8 71F 12 B3F 10 173 11 2D3 11
    1F2 11 17D 8 3D7 11 73F 10
    D37 11 7FD 8 BD2 11 D3F 9
    DB2 11     1B2 10 3BF 7
            D2B 10 37B 6
Total 617 Total 617 Total 617 Total 617 Total 617

My sidekick, JB, then wrote a program to assemble the combinations in order. It should be noted that given the sequences observed, multiple solutions are possible. The reel strips below are just one possibility. However, all of them would have the same expected return.

 

Blazing Sevens Reel Strips

Position Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
1 2 D 7 7 2
2 D F D D F
3 1 B B 2 3
4 B 7 3 B 7
5 2 D F 3 B
6 7 2 B D 2
7 D B 2 7 F
8 B 1 D 2 1
9 3 7 B B 7
10 7 D 2 F 3
11 2 1 7 3 B
12 B B D D F
13 1 2 B F 7
14 D D 1 1 3
15 3 3 D 7 F
16 B B B 3 D
17 2 D F F B
18 7 7 1 1 F
19 3 1 D B 2
20 F B 3 D D
21 2 2 B 2 B
22 B D 2 7 F
23 3 1 7 B 1
24 D F D 3 D
25 7 D F F B
26 1 B 2 1 1
27 B F B B F
28 7 3 F D 7
29 3 D D 1 B
30 B B 3 F F
31 D 2 B 3 2
32 3 D 1 B B
33 7 3 7 1 7
34 2 7 D D F
35 B 1 1 7 2
36 1 F B 1 D
37 D 2 7 B 3
38 7 B F 2 F
39 3 F D D B
40 B 7 2 1 D

 

Key:
F = Blazing seven
7 = Seven
D = Dollar sign
B = Bell
3 = 3-bar
2 = 2-bar
1 = 1-bar

The way multi-line video slots work is they draw random numbers, one for each reel, to determine where on the reel strips to stop. In this case, the game would choose five random integers from 1 to 40, one for each reel. Suppose, for example, the game chose the numbers 24,24,37,11,4 for reels 1 to 5 respectively. Then assume the game maps these number to the top row seen on the screen. In this example, the screen would look like this:

The next table shows the total number of each symbol on each reel, based on the estimated reel strips above.

 

Blazing Sevens Symbol Distribution

Symbol Code Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
Blazing seven F 1 5 5 5 10
Seven 7 7 5 5 5 5
Dollar D 6 9 9 7 5
Bell B 9 8 9 7 8
3-bar 3 7 3 3 5 4
2-bar 2 6 5 5 4 5
1-bar 1 4 5 4 7 3
Total   40 40 40 40 40

Step Three - The Pay Table

The pay table is easily seen from the rule screens and game glass. Most video slots simply multiply all awards by the number of coins bet per line. Blazing Sevens is different. The first coin enables wins on the dollar, bell, and all bar symbols. The second coin enables wins on all types of sevens. The third coin doubles the wins on plain sevens and mixed sevens, and more than doubles the wins on blazing sevens. The following three tables show the pay table for 1, 2, and 3 coins bet per line respectively. All wins must be left-aligned.

Blazing Sevens Pay Table — 1 Coin Bet

Symbol 5 in a Row 4 in a Row 3 in a Row
Blazing sevens 0 0 0
Sevens 0 0 0
Mixed sevens 0 0 0
Dollar 100 50 20
Bell 75 25 10
3-bar 300 150 30
2-bar 200 100 20
1-bar 100 50 10
Mixed bars 30 10 5

Blazing Sevens Pay Table — 2 Coins Bet

Symbol 5 in a Row 4 in a Row 3 in a Row
Blazing sevens 7500 500 200
Sevens 300 150 50
Mixed sevens 200 80 25
Dollar 100 50 20
Bell 75 25 10
3-bar 300 150 30
2-bar 200 100 20
1-bar 100 50 10
Mixed bars 30 10 5

Blazing Sevens Pay Table — 3 Coins Bet

Symbol 5 in a Row 4 in a Row 3 in a Row
Blazing sevens 20000 2000 500
Sevens 600 300 100
Mixed sevens 400 160 50
Dollar 100 50 20
Bell 75 25 10
3-bar 300 150 30
2-bar 200 100 20
1-bar 100 50 10
Mixed bars 30 10 5

Step Four - The Math

The next table shows the number of combinations for each possible win. In cases where two equal wins are possible, for example three 3-bars or five mixed bars, the game counts it as the one composed of fewer symbols.

 

 

Blazing Sevens Line Pay Combinations

Symbol 5 in a Row 4 in a Row 3 in a Row Total
Blazing sevens 1,250 3,750 35,000 40,000
Sevens 4,375 21,875 210,000 236,250
Mixed sevens 111,875 200,000 960,000 1,271,875
Dollar 17,010 119,070 641,520 777,600
Bell 36,288 145,152 855,360 1,036,800
3-bar 1,260 11,340 88,200 100,800
2-bar 3,000 21,000 216,000 240,000
1-bar 1,680 20,720 105,600 128,000
Mixed bars 509,184 1,188,096 2,545,920 4,243,200
Total 685,922 1,731,003 5,657,600 8,074,525

 

The next table shows the probability of each possible win. The values in each cell are the number of combinations from the table above divided by the number of combinations of 405 = 102,400,000. The lower right cell shows the hit frequency per line of 7.01%.

 

Blazing Sevens Probabilities

Symbol 5 in a Row 4 in a Row 3 in a Row Total
Blazing sevens 0.000012 0.000037 0.000342 0.000391
Sevens 0.000043 0.000299 0.002393 0.002734
Mixed sevens 0.001093 0.001587 0.006641 0.009320
Dollar 0.000166 0.001163 0.006265 0.007594
Bell 0.000354 0.001418 0.008353 0.010125
3-bar 0.000012 0.000111 0.000861 0.000984
2-bar 0.000029 0.000205 0.002109 0.002344
1-bar 0.000016 0.000202 0.001031 0.001250
Mixed bars 0.004710 0.009771 0.020861 0.035342
Total 0.006436 0.014792 0.048855 0.070084


The next three tables show the expected return for each win, for one to three coins bet respectively. This is the (amount of the win)*(probability of win). The overall return is shown in the lower right cell of each table.

 

 

Blazing Sevens Returns — 1 Coin Bet

Symbol 5 in a Row 4 in a Row 3 in a Row Total
Win 5 in a row 4 in a row 3 in a row Total
Blazing sevens 0.000000 0.000000 0.000000 0.000000
Sevens 0.000000 0.000000 0.000000 0.000000
Mixed sevens 0.000000 0.000000 0.000000 0.000000
Dollar 0.016611 0.058140 0.125297 0.200048
Bell 0.026578 0.035438 0.083531 0.145547
3-bar 0.003691 0.016611 0.025840 0.046143
2-bar 0.005859 0.020508 0.037969 0.064336
1-bar 0.001641 0.010117 0.009469 0.021227
Mixed bars 0.141553 0.103206 0.110578 0.355338
Total 0.195934 0.244020 0.392684 0.832637

Blazing Sevens Returns — 2 Coins Bet

Symbol 5 in a Row 4 in a Row 3 in a Row Total
Win 5 in a row 4 in a row 3 in a row Total
Blazing sevens 0.091553 0.018311 0.068359 0.178223
Sevens 0.012817 0.032043 0.102539 0.147400
Mixed sevens 0.218506 0.134277 0.175781 0.528564
Dollar 0.016611 0.058140 0.125297 0.200048
Bell 0.026578 0.035438 0.083531 0.145547
3-bar 0.003691 0.016611 0.025840 0.046143
2-bar 0.005859 0.020508 0.037969 0.064336
1-bar 0.001641 0.010117 0.009469 0.021227
Mixed bars 0.141553 0.103206 0.110578 0.355338
Total 0.518810 0.428651 0.739363 1.686824

Blazing Sevens Returns — 3 Coins Bet

Symbol 5 in a Row 4 in a Row 3 in a Row Total
Win 5 in a row 4 in a row 3 in a row Total
Blazing sevens 0.244141 0.073242 0.170898 0.488281
Sevens 0.025635 0.064087 0.205078 0.294800
Mixed sevens 0.437012 0.268555 0.351563 1.057129
Dollar 0.016611 0.058140 0.125297 0.200048
Bell 0.026578 0.035438 0.083531 0.145547
3-bar 0.003691 0.016611 0.025840 0.046143
2-bar 0.005859 0.020508 0.037969 0.064336
1-bar 0.001641 0.010117 0.009469 0.021227
Mixed bars 0.141553 0.103206 0.110578 0.355338
Total 0.902721 0.649904 1.120223 2.672847

Summary

The following table shows the gross return for (1) Dollars, Bells, and Bars, (2) All Sevens, and (3) Combined. The net return is the gross return divided by the number of coins bet. It shows the more the player bets per line, the greater the return, with a maximum return of 89.09%.

Blazing Sevens — Summary

Coins
Bet		 Bar, $, Bell
Return		 Sevens
Return		 Gross
Return		 Net
Return
3 0.832637 1.840210 2.672847 0.890949
2 0.832637 0.876012 1.708650 0.854325
1 0.832637 0.000000 0.832637 0.832637

Disclaimer

If I didn't make myself clear above, I am not claiming this page is an exact depiction of Blazing Sevens. Due to repeating symbols, I had to make some judgment calls to fill in the blanks. As explained above, there are also different reel strip orders possible given what was observed at the machine.

 

 

Acknowledgments

I would like to thank miplet for doing the data entry on video 1 and ChesterDog for video 3. I would also like to thank JB for piecing together the 40 different sequences of three symbols for each reel into a complete reel strip, as well as for confirming my math was correct.

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Written by: Michael Shackleford