Last Updated: August 19, 2016

# Deconstructing Hexbreaker

## Introduction

In my continued efforts to show the world how video slot machines work, I set out to deconstruct how Hexbreaker was designed by playing it. Armed with a cell phone camera, I recorded about 45 minutes of play. With information about the symbol frequency, pay table, and bonus rules only, it is possible to analyze the odds of any slot machine. This is what I endeavored to do with Hexbreaker.

## Step One - Data Collection

Much like a game I previously deconstructed, Jackpot Party, I chose Hexbreaker because it didn't involve bonus spins and the bonus rules were fully disclosed. The only mystery was the reel stripping. So I found a game in a quiet corner of the Main Street Station in downtown Las Vegas and recorded 45 minutes of play. These videos can be found on YouTube:

When I returned home, I hired my brother in law to record, by hand, the three visible symbols on each reel for all 506 spins in the first and second videos. This took many hours, at my financial expense.

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 twice on the same reel strip. These were chosen according to what completed the reels and which sequences occurred more frequently. My webmaster 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.

## Step Two - The Reel Strips

As stated above, I am not claiming these are the exact reel strips in Hexbreaker. However, the symbol frequency I believe is very close to the actual game at the Main Street Station. The following table shows my best guess as to what the Hexbreaker reels look like.

### Hexbreaker Reel Strips

Position Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
1 13 Umbrella Umbrella 13 Cat
2 Hex Mirror Crow Umbrella Salt
3 Crack Penny Salt Mirror Crack
4 Penny Salt Mirror Crack Hex
5 Cat Mirror Penny Salt Crow
6 Salt Umbrella Voodoo doll Cat Salt
7 13 13 13 Voodoo doll Voodoo doll
8 Mirror Voodoo doll Penny Jinx Jinx
9 Crack Salt Mirror Crack Cat
10 13 Mirror Umbrella Penny Voodoo doll
11 Salt Crack Salt Mirror Mirror
12 Crow Crow Mirror Voodoo doll Umbrella
13 Voodoo doll Umbrella Crack Penny 13
14 Mirror Jinx 13 Mirror Penny
15 Salt Penny Penny Crack Cat
16 13 Cat Hex Voodoo doll Crow
17 Mirror Crack Voodoo doll Cat Salt
18 Crack Jinx Salt Penny Mirror
19 Umbrella Umbrella Mirror Umbrella Crack
20 Mirror Penny Voodoo doll Mirror 13
21 Salt Mirror Penny Penny Penny
22 Crack Salt Mirror Voodoo doll Jinx
23 Cat Crack Salt 13 Crack
24 Jinx Cat Umbrella Salt 13
25 Salt Penny Mirror Hex Salt
26 13 Umbrella Voodoo doll Crack Jinx
27 Hex Ladder 13 Crow Crack
28 Voodoo doll Salt Penny Penny 13
29 Cat Penny Umbrella Umbrella Umbrella
30 Salt Mirror Jinx Ladder Penny
31 Mirror Umbrella Voodoo doll Penny Hex
32 Voodoo doll Penny Penny Crow Crow
33 Jinx Ladder Crow Voodoo doll Voodoo doll
34 Crow Salt Salt Mirror Mirror
35 Crack Voodoo doll Voodoo doll Crack 13
36 Mirror Mirror Mirror Penny Salt
37 Voodoo doll Salt Crack Voodoo doll Mirror
38 Crow Crow Voodoo doll Umbrella Voodoo doll
39 Cat Crack Salt Crow Crow
40 Umbrella Salt Mirror Voodoo doll Crack
41 Mirror Ladder Voodoo doll Mirror Mirror
42 Crow Crack Salt Crack Salt
43 Crack Penny Penny Voodoo doll 13
44 13 Hex Cat Crow Mirror
45 Salt Salt Voodoo doll Umbrella Penny
46 Hex Crow Mirror Jinx Crack
47 Crack Crack Crack Crack 13
48 Voodoo doll Voodoo doll Salt 13 Cat
49 Cat Mirror 13 Umbrella Umbrella
50 Penny Salt Umbrella Mirror Mirror
51 Crow Crack Penny Crack Crow
52 Voodoo doll Hex Jinx Salt Salt
53 Mirror Penny Salt 13 Mirror
54 Crack Voodoo doll Umbrella Crack Crow
55 Crow 13 Crow Voodoo doll Crack
56 Jinx Penny Penny Mirror Cat
57 Umbrella Mirror Hex Penny Salt
58 Penny Umbrella Salt Crack Penny
59 Hex Voodoo doll Crack Hex Hex
60 Voodoo doll Crow Mirror Umbrella Salt
61 Salt Penny Cat Penny Crow
62 Mirror Crack Umbrella Mirror 13
63 Crack Mirror Salt Salt Crack
64 Cat Penny Cat Umbrella Mirror
65 13 Salt Penny Crow Crow
66 Salt Cat Voodoo doll Crack Crack
67 Mirror Crack Jinx Penny Mirror
68 Crow       Umbrella
69 Voodoo doll       Crow

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, one for each reel. The random number should be from 1 to 69 for reels 1 and 5, and 1 to 67 for reels 2 to 4. Suppose, for example, the game chose the numbers 55,41,24,29,11 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. Again, this is according to my best estimate.

### Hexbreaker Symbol Distribution

Symbol Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
Hex 4 2 2 2 3
13 7 2 4 4 8
Crow 7 4 3 5 9
Umbrella 3 7 7 8 4
Voodoo doll 8 5 10 9 4
Penny 3 11 10 10 5
Salt 9 10 11 4 9
Crack 9 9 4 11 9
Cat 6 3 3 2 5
Mirror 10 9 10 9 10
Ladder 0 3 0 1 0
Jinx 3 2 3 2 3
Total 69 67 67 67 69

## Step Three - The Pay Table

The pay table is easily seen from the rule screens, which appears in the table below. The Logo is wild and may substitute for any line pay combination. The cat symbol is unique because if the player achieves at least three cats with no wilds, then it pays more than if wilds are used. Finally, unlike most slots, line pay wins in Hexbreaker pay in both directions. If the player can win both ways, only the highest win on that pay-line is awarded.

### Hexbreaker Pay Table

Symbol 5 pays 4 pays 3 pays 2 pays
Logo 10000 1000 100 5
Cat (natural) 2500 750 100
Cat (with wilds) 500 150 20
13 400 100 13
crow 300 75 15
Umbrella 250 50 10
Voodoo doll 200 30 10
Penny 200 30 5
Salt 150 25 5
Crack 150 25 5

## Step Four - Line Pay Math

The next table shows the number of combinations for each possible win. Cells are left blank if they don't produce a win. The wild symbol, special rule about the cat symbol, and paying both directions make a mathematical analysis of line pay wins tedious, complicated, and error prone. In my strong opinion, the safest and easiest way to analyze the line pay wins is to score every possible outcome with five nested loops.

The lower right cell shows the total winning combinations is 53,972,083. There are 69*67*67*67*69 = 1,431,932,643 total possible combinations in Hexbreaker. That makes the hit frequency per line 53,972,083/1,431,932,643 = 3.77%.

### Hexbreaker Line Pay Combinations

Symbol 5 4 3 2 Total
Logo 96 3,672 107,172 2,200,752 2,311,692
Cat (natural) 540 12,582 363,078   376,200
Cat 6,376 92,934 1,265,692   1,365,002
13 16,904 174,728 2,674,260   2,865,892
crow 27,168 265,606 2,982,472   3,275,246
Umbrella 39,394 685,296 4,604,811   5,329,501
Voodoo doll 77,200 1,038,032 7,547,922   8,663,154
Penny 104,504 1,704,512 7,720,226   9,529,242
Salt 145,416 1,304,064 11,213,614   12,663,094
Crack 133,248 1,186,842 6,272,970   7,593,060
Total 550,846 6,468,268 44,752,217   53,972,083

The next table shows the probability of each possible win. The lower right cell shows a hit frequency per line of 3.77%, which was also derived above.

### Hexbreaker Line Pay Probabilities

Symbol 5 4 3 2 Total
Logo 0.00000007 0.00000256 0.00007484 0.00153691 0.00161439
Cat (natural) 0.00000038 0.00000879 0.00025356   0.00026272
Cat 0.00000445 0.00006490 0.00088390   0.00095326
13 0.00001181 0.00012202 0.00186759   0.00200142
crow 0.00001897 0.00018549 0.00208283   0.00228729
Umbrella 0.00002751 0.00047858 0.00321580   0.00372189
Voodoo doll 0.00005391 0.00072492 0.00527114   0.00604997
Penny 0.00007298 0.00119036 0.00539147   0.00665481
Salt 0.00010155 0.00091070 0.00783110   0.00884336
Crack 0.00009305 0.00082884 0.00438077   0.00530267
Total 0.00038469 0.00451716 0.03125302 0.00153691 0.03769178

The next table shows the product of each winning probability and what it pays. The lower right cell shows that the player can expect to win 53.22% of his bet per spin from line pays.

### Hexbreaker Line Pay Returns

Symbol 5 4 3 2 Total
Logo 0.00067042 0.00256437 0.00748443 0.00768455 0.01840377
Cat (natural) 0.00094278 0.00659004 0.02535580   0.03288863
Cat 0.00222636 0.00973516 0.01767809   0.02963962
13 0.00472201 0.01220225 0.02427864   0.04120290
crow 0.00569189 0.01391158 0.03124245   0.05084592
Umbrella 0.00687777 0.02392906 0.03215801   0.06296484
Voodoo doll 0.01078263 0.02174750 0.05271143   0.08524157
Penny 0.01459622 0.03571073 0.02695736   0.07726431
Salt 0.01523284 0.02276755 0.03915552   0.07715591
Crack 0.01395820 0.02072098 0.02190386   0.05658304
total 0.07570112 0.16987923 0.27892561 0.00768455 0.53219051

## Step Five - Scatter Pays

The game pays based on the number of Jinx symbols anywhere on the screen. Scatter pay wins are based on the total amount bet. The game pays 150 for five scatters, 13 for four, and 4 for three. For those unfamiliar with Chinese superstitions, the number four is very unlucky, because it sounds like the Chinese word for "death."

The following table shows the probability and contribution to the return for each number of scatter pays. The lower right cell shows a total return of 5.89%.

### Hexbreaker — Scatter Pay

Scatters Pays Probability Return
5 150 0.000018 0.002749
4 13 0.000735 0.009557
3 4 0.011654 0.046617
2 0 0.091300 0.000000
1 0 0.353708 0.000000
0 0 0.542585 0.000000
Total 0 1.000000 0.058923

## Step Six - The Mirror Miror Bonus

The player will play the Mirror Mirror Bonus if he gets at least four consecutive mirrors on any active pay-line. Wins are based on the amount bet per line.

In the Mirror Mirror Bonus, there are 13 mirrors. The game will randomly place 13 prizes behind the mirrors. The prizes are larger if the bonus is triggered with five mirror symbols. Then, the player gets to break any five of the mirrors and keep the associated prizes.

In addition, the game randomly places five Treasure Symbols behind the mirrors. It is possible that one mirror will have more than one symbol. I assume the way the game works is that one of the 13 mirrors is chosen at random for each Treasure Symbol, even if another symbol was already placed with that mirror.

To see examples, here are my three videos and the starting times of the Mirror Mirror bonuses.

The following table shows the 13 prizes according to whether the bonus was triggered with four or five mirror symbols.

### Mirror Mirror Bonus — Mirror Prizes

Prize
Number
Four Mirrors Five Mirrors
1 5 10
2 10 20
3 12 25
4 15 30
5 20 35
6 25 40
7 25 45
8 30 50
9 35 75
10 40 100
11 50 100
12 50 150
13 100 200
Average 32.0769231 67.692308

As mentioned above, if the player finds at least one treasure symbol, then he will get a bonus within the bonus. The following table shows the prize according to the number of Treasure Symbols found and whether the bonus was triggered with four or five mirrors.

### Mirror Mirror Bonus — Treasure Wins

Treasures
Found
Four
Mirrors
Five
Mirrors
5 1000 3000
4 125 1000
3 75 500
2 25 150
1 15 35
0 0 0

The next table summarizes all the pieces of the Mirror Mirror Bonus. The lower right cell shows that this feature contributes 17.15% to the return of the game.

### Mirror Mirror Bonus — Summary

Statistic 4 Mirrors 5 Mirrors Total
Probability 0.000667 0.000057 0.000724
Mirror win 160.384615 338.461538 174.296875
Icon win 45.748237 261.677435 62.617705
Win per bonus 206.132852 600.138974 236.914580
Win per spin 0.137592 0.033948 0.171540

## Step Seven - Money Ladder Bonus

The player will play the Money Ladder Bonus if he gets the ladder symbol anywhere on reels 2 and 4. All wins in the Money Ladder Bonus are based on the total amount bet on the initiating spin.

The bonus features a ladder with 12 steps on each side. Starting with the bottom step on the right side, and going counter-clockwise, the prizes are: 1,1,1,1,1,1,1,2,2,2,3,4,16,4,3,2,2,2,1,1,1,1,1,1,1. In the image above I bet 13 coins, so all the wins per step were multiplied by 13.

Hoo Doo the cat will start at the bottom of the ladder and move around it counter-clockwise. The player will touch a Ouija Board, which will pick a number from 1 to 13. Then the cat will move that many steps around the ladder. As the player stops on each step, he will collect the prize on that step. Then the prize associated with that step will zero out. Every time the cat moves across the floor to do another lap around the ladder, each remaining prize will increase by the total amount bet. If the cat ever stops on a step he previously stopped on, or at the top of the ladder, then the bonus will be over.

To see examples, here my three videos and the starting times of the Money Ladder bonuses.

The following table shows the probability and expected return from each Money Ladder bonus win. This table was based on a random simulation of over seven billion bonuses. The lower right cell shows an average win of 18.707.

### Money Ladder Bonus — Possible Outcomes

Win Probability Return
2 0.0013653239 0.0027306477
3 0.0072470481 0.0217411442
4 0.0149546295 0.0598185181
5 0.0241636009 0.1208180047
6 0.0292061860 0.1752371157
7 0.0315978315 0.2211848207
8 0.0318368166 0.2546945328
9 0.0316930017 0.2852370154
10 0.0319982128 0.3199821282
11 0.0323937555 0.3563313102
12 0.0325625326 0.3907503907
13 0.0322976359 0.4198692668
14 0.0313532229 0.4389451208
15 0.0299063881 0.4485958217
16 0.1049632134 1.6794114143
17 0.0673635272 1.1451799616
18 0.0511508430 0.9207151749
19 0.0385602678 0.7326450890
20 0.0329660694 0.6593213875
21 0.0263324701 0.5529818730
22 0.0273527415 0.6017603139
23 0.0278317529 0.6401303170
24 0.0282474808 0.6779395394
25 0.0268856881 0.6721422022
26 0.0244441412 0.6355476705
27 0.0213845707 0.5773834077
28 0.0182927666 0.5121974637
29 0.0154596540 0.4483299650
30 0.0132194741 0.3965842238
31 0.0116497410 0.3611419701
32 0.0105126952 0.3364062462
33 0.0097625719 0.3221648739
34 0.0091497825 0.3110926045
35 0.0085378784 0.2988257457
36 0.0078602887 0.2829703947
37 0.0071118873 0.2631398287
38 0.0063196567 0.2401469534
39 0.0055131938 0.2150145572
40 0.0047426800 0.1897071993
41 0.0040515458 0.1661133769
42 0.0034594245 0.1452958294
43 0.0029702607 0.1277212115
44 0.0025768766 0.1133825704
45 0.0022647400 0.1019132990
46 0.0020143209 0.0926587600
47 0.0018081746 0.0849842053
48 0.0016291277 0.0781981279
49 0.0014638848 0.0717303574
50 0.0013085984 0.0654299190
51 0.0011589908 0.0591085287
52 0.0010165461 0.0528603952
53 0.0008812066 0.0467039481
54 0.0007565567 0.0408540631
55 0.0006447815 0.0354629819
56 0.0005458610 0.0305682138
57 0.0004615357 0.0263075340
58 0.0003905274 0.0226505914
59 0.0003324059 0.0196119473
60 0.0002843733 0.0170623998
61 0.0002451469 0.0149539583
62 0.0002127818 0.0131924700
63 0.0001856658 0.0116969433
64 0.0001629026 0.0104257674
65 0.0001426304 0.0092709738
66 0.0001247963 0.0082365542
67 0.0001086134 0.0072771011
68 0.0000942307 0.0064076901
69 0.0000808496 0.0055786216
70 0.0000688669 0.0048206852
71 0.0000583695 0.0041442339
72 0.0000490601 0.0035323298
73 0.0000410229 0.0029946709
74 0.0000341942 0.0025303708
75 0.0000285068 0.0021380118
76 0.0000237678 0.0018063560
77 0.0000197916 0.0015239519
78 0.0000166252 0.0012967694
79 0.0000139878 0.0011050341
80 0.0000119308 0.0009544612
81 0.0000101425 0.0008215385
82 0.0000086540 0.0007096252
83 0.0000074086 0.0006149127
84 0.0000063059 0.0005296992
85 0.0000054029 0.0004592465
86 0.0000046133 0.0003967444
87 0.0000039163 0.0003407150
88 0.0000032660 0.0002874074
89 0.0000027123 0.0002413907
90 0.0000022985 0.0002068695
91 0.0000018937 0.0001723230
92 0.0000015398 0.0001416622
93 0.0000012852 0.0001195223
94 0.0000010415 0.0000979022
95 0.0000008426 0.0000800490
96 0.0000006946 0.0000666841
97 0.0000005701 0.0000552985
98 0.0000004731 0.0000463668
99 0.0000003925 0.0000388597
100 0.0000003122 0.0000312198
101 0.0000002622 0.0000264777
102 0.0000002074 0.0000211570
103 0.0000001855 0.0000191093
104 0.0000001551 0.0000161308
105 0.0000001308 0.0000137333
106 0.0000001049 0.0000111214
107 0.0000000823 0.0000088076
108 0.0000000772 0.0000083372
109 0.0000000650 0.0000070817
110 0.0000000525 0.0000057705
111 0.0000000387 0.0000042923
112 0.0000000350 0.0000039170
113 0.0000000267 0.0000030202
114 0.0000000200 0.0000022852
115 0.0000000188 0.0000021581
116 0.0000000118 0.0000013688
117 0.0000000125 0.0000014637
118 0.0000000097 0.0000011407
119 0.0000000070 0.0000008290
120 0.0000000048 0.0000005800
121 0.0000000057 0.0000006881
122 0.0000000036 0.0000004336
123 0.0000000037 0.0000004546
124 0.0000000021 0.0000002644
125 0.0000000018 0.0000002310
126 0.0000000011 0.0000001433
127 0.0000000010 0.0000001264
128 0.0000000011 0.0000001456
129 0.0000000006 0.0000000734
130 0.0000000007 0.0000000924
131 0.0000000004 0.0000000559
132 0.0000000004 0.0000000563
133 0.0000000006 0.0000000756
134 0.0000000001 0.0000000191
135 0.0000000004 0.0000000576
136 0.0000000004 0.0000000580
137 0.0000000001 0.0000000195
138 0.0000000001 0.0000000196
139 0.0000000001 0.0000000198
146 0.0000000001 0.0000000208
Total 1.0000000000 18.7069413032

The Money Ladder bonus probability is (9/67)×(3/67) = 0.006015, or 1 in 166.26. The contribution to the return of the game is 0.006015 × 18.706941 = 0.112517.

## Step Eight - Summary

The final table below shows the return of each win category in Hexbreaker. The lower right cell shows a total return for the game of 87.517%.

### Hexbreaker Summary

Type of Win Return
Line pays 53.219%
Scatter pay 5.892%
Mirror bonus 17.154%
Total 87.517%

The returns of other Hexbreaker games likely vary. With most video slots, there are several different versions available, differing mostly by the reel stripping. The casino manager may choose which version to put into the game.

The purpose of this page was not to endorse Hexbreaker as a good or bad game to play but to illustrate general concepts in slot machine design.

## Disclaimer

If I didn't make myself clear above, I am not claiming this page is an exact depiction of Hexbreaker. 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 J.B. for piecing together the 67 to 69 different sequences of three symbols for each reel into a complete reel strip.