# Lucky Larry's Lobstermania

## Introduction

In my continued effort to lift the veil of secrecy behind slot machines, I present the following analysis of the IGT game Lucky Larry's Lobstermania. The information regarding the design of this game is taken from the academic paper PAR Sheets, probabilities, and slot machine play: Implications for problem and non-problem gambling by Kevin A. Harrigan and Mike Dixon, University of Waterloo, Waterloo, Ontario, Canada.

The authors of the paper obtained par sheets for the game through the Canadian Freedom of Information and Protection of Privacy Act. I applaud the government of Canada for this release. The purpose of this page is to further the analysis of Lobstermania beyond what was presented in the Harrigan and Dixon paper.

It should be noted there are other versions of Lobstermania besides this one. As far as I can tell they differ by small changes to the pay table and details of the bonus round.

## Reel Strips

Harrigan and Dixon give the symbol distribution for two Lobstermania par sheets, one for 85.0% and the other for 96.2%. Both are presented below. Notice how the 96.2% version has more high-paying symbols and that any given symbol is distributed more uniformly across the 5 reels. To illustrate that the distribution is more choppy in the 85.0% version, notice that the number of clams per reel on the 85.0% version is 10,8,3,4,7. On the 96.2%, the distribution is 6-6-5-6-6. However, the number of key symbols (wild, scatter and bonus) are the same in both games.

### Lobstermania Symbol Distribution — 85.0%

Symbol Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
Wild 2 2 1 4 2
Logo 4 3 3 3 4
Buoy 3 4 3 8 5
Boat 4 3 4 3 4
Light House 3 4 6 3 7
Tuna 4 3 6 6 6
Clam 10 8 3 4 7
Sea Gull 3 9 4 10 5
Star Fish 10 3 10 7 8
Bonus 2 5 6 0 0
Scatter 2 2 2 2 2
Total 47 46 48 50 50

### Lobstermania Symbol Distribution — 96.2%

Symbol Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
Wild 2 2 1 4 2
Logo 4 4 3 4 4
Buoy 4 4 5 4 5
Boat 6 4 4 4 4
Light House 5 4 6 6 7
Tuna 6 4 5 6 7
Clam 6 6 5 6 6
Sea Gull 5 6 5 6 6
Star Fish 5 5 6 8 7
Bonus 2 5 6 0 0
Scatter 2 2 2 2 2
Total 47 46 48 50 50

Harrigan and Dixon do not indicate the exact reel stripping. However, as long as the scatter symbols are not so close on the same reel that they can appear at the same time, the symbol order does not matter for this game, as well as for most video slots. The following reel stripping is hypothetical, based on the 85.0% version.

### Lobstermania Symbol Distribution — 85.0% Reel Strips

Symbol Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
1 Tuna Clam Boat Sea Gull Clam
2 Star Fish Buoy Star Fish Tuna Wild
3 Clam Light House Clam Buoy Boat
4 Light House Clam Bonus Sea Gull Logo
5 Scatter Buoy Light House Scatter Buoy
6 Clam Light House Boat Buoy Star Fish
7 Star Fish Bonus Logo Star Fish Light House
8 Bonus Sea Gull Star Fish Sea Gull Tuna
9 Logo Clam Bonus Tuna Star Fish
10 Scatter Boat Light House Wild Light House
11 Buoy Sea Gull Star Fish Buoy Sea Gull
12 Clam Tuna Bonus Tuna Wild
13 Star Fish Boat Tuna Star Fish Tuna
14 Buoy Bonus Star Fish Logo Buoy
15 Clam Star Fish Clam Sea Gull Boat
16 Star Fish Sea Gull Sea Gull Tuna Clam
17 Logo Wild Star Fish Wild Tuna
18 Light House Bonus Wild Logo Buoy
19 Clam Sea Gull Bonus Light House Star Fish
20 Wild Light House Light House Buoy Clam
21 Sea Gull Logo Sea Gull Sea Gull Scatter
22 Star Fish Wild Star Fish Boat Buoy
23 Wild Buoy Tuna Clam Star Fish
24 Bonus Clam Clam Star Fish Tuna
25 Clam Bonus Boat Light House Clam
26 Boat Sea Gull Tuna Sea Gull Buoy
27 Star Fish Clam Star Fish Boat Boat
28 Tuna Scatter Bonus Clam Light House
29 Clam Logo Tuna Buoy Tuna
30 Star Fish Tuna Light House Sea Gull Logo
31 Tuna Sea Gull Star Fish Boat Light House
32 Logo Scatter Scatter Light House Sea Gull
33 Clam Star Fish Light House Star Fish Clam
34 Star Fish Clam Logo Tuna Logo
35 Boat Boat Sea Gull Sea Gull Star Fish
36 Light House Logo Star Fish Buoy Boat
37 Clam Sea Gull Scatter Star Fish Light House
38 Star Fish Clam Buoy Clam Tuna
39 Boat Bonus Tuna Buoy Sea Gull
40 Tuna Star Fish Logo Sea Gull Star Fish
41 Buoy Sea Gull Bonus Star Fish Light House
42 Sea Gull Buoy Star Fish Clam Clam
43 Logo Light House Light House Logo Logo
44 Clam Clam Sea Gull Wild Sea Gull
45 Star Fish Tuna Buoy Buoy Star Fish
46 Boat Sea Gull Boat Sea Gull Clam
47 Sea Gull   Tuna Star Fish Sea Gull
48     Buoy Scatter Light House
49       Tuna Scatter
50       Wild Star Fish

The way the game would work would be to choose 5 random numbers, one for each reel, and map each random number to a position on the corresponding reel. For example, for reel 1 the game would draw a number from 1 to 47. For example, suppose this number were mapped to the symbol in the top row. If the random number for reel 1 were 37, then the symbols shown on reel 1 would be a Clam on top row, a Star Fish in the middle row, and a Boat on bottom row.

## Pay Table

The next table shows the Lobstermania pay table. All wins must be left aligned. The wild symbol can substitute for any line-pay symbol.

### Lobstermania Pay Table

Symbol 5 in a row 4 in a row 3 in a row 2 in a row
Wild 10000 500 100 5
Logo 1000 200 40 2
Buoy 500 100 25
Boat 500 100 25
Light House 500 50 10
Tuna 250 50 10
Clam 200 30 5
Sea Gull 200 30 5
Star Fish 150 30 5

## Line Pay Math

There are 47 × 46 × 48 × 50 × 50 = 259,440,000 possible outcomes in Lobstermania. The following table shows how many of these combinations result in each possible win. These figures are the result of a program with five nested loops that tallied the total for each win for each possible combination.

### Lobstermania Line Pay Combinations

Symbol 5 in a row 4 in a row 3 in a row 2 in a row Total
Wild 32 704 7,300 212,000 220,036
Logo 5,008 36,256 249,400 2,860,000 3,150,664
Buoy 9,968 59,856 220,400   290,224
Boat 6,204 44,968 313,900   365,072
Light House 13,086 59,122 442,900   515,108
Tuna 16,672 86,520 412,000   515,192
Clam 34,416 156,128 974,400   1,164,944
Sea Gull 26,838 163,142 459,000   648,980
Star Fish 72,440 288,640 1,201,200   1,562,280
Total 184,664 895,336 4,280,500 3,072,000 8,432,500

The next table shows the probability of each possible win. This is the number of winning combinations for that win, shown in the table above, divided by the total number of combinations of 259,440,000. The total in the lower right cell reflects a hit frequency per line (probability of winning anything) of 3.25%.

### Lobstermania Line Pay Probabilities

Symbol 5 in a row 4 in a row 3 in a row 2 in a row Total
Wild 0.00000012 0.00000271 0.00002814 0.00081714 0.00084812
Logo 0.00001930 0.00013975 0.00096130 0.01102374 0.01214409
Buoy 0.00003842 0.00023071 0.00084952   0.00111866
Boat 0.00002391 0.00017333 0.00120991   0.00140715
Light House 0.00005044 0.00022788 0.00170714   0.00198546
Tuna 0.00006426 0.00033349 0.00158804   0.00198578
Clam 0.00013265 0.00060179 0.00375578   0.00449023
Sea Gull 0.00010345 0.00062882 0.00176920   0.00250146
Star Fish 0.00027922 0.00111255 0.00462997   0.00602174
Total 0.00071178 0.00345103 0.01649900 0.01184089 0.03250270

The next table shows the contribution to the return for each possible win. Each cell is the product of the probability, from the table above, and the pay table. The right cell shows a total return from line pays of 55.28%.

### Lobstermania Line Pay Probabilities

Symbol 5 in a row 4 in a row 3 in a row 2 in a row Total
Wild 0.00123343 0.00135677 0.00281375 0.00408572 0.00948967
Logo 0.01930311 0.02794943 0.03845205 0.02204749 0.10775208
Buoy 0.01921061 0.02307123 0.02123805   0.06351989
Boat 0.01195652 0.01733272 0.03024784   0.05953708
Light House 0.02521970 0.01139416 0.01707138   0.05368525
Tuna 0.01606537 0.01667438 0.01588036   0.04862010
Clam 0.02653099 0.01805365 0.01877891   0.06336355
Sea Gull 0.02068918 0.01886471 0.00884598   0.04839986
Star Fish 0.04188252 0.03337650 0.02314986   0.09840888
Total 0.18209143 0.16807354 0.17647818 0.02613321 0.55277636

## Scatter Pay

The player gets credit for a "scatter pay" symbol if it appears anywhere on the screen. Scatter pay wins are based on the total amount bet. The following table shows the number of scatters per reel, total symbols per reel, and the probability of a scatter on that reel, which is 3×(column 2)/(column 3). The reason for multiplying by 3 is there are three visible positions on each reel.

### Lobstermania Scatters per Reel

Reel Scatters Total Symbols
on Reel
Scatter
Probability
1 2 47 0.127660
2 2 46 0.130435
3 2 48 0.125000
4 2 50 0.120000
5 2 50 0.120000

The next table shows the probability and contribution to the return for 0 to 5 total scatter symbols. The lower right cell shows that the scatter pay feature returns 10.65% to the return of the game.

### Lobstermania Scatter Pay Probabilities and Returns

Scatters Pays Probability Return
5 200 0.000030 0.005994
4 25 0.001054 0.026351
3 5 0.014821 0.074106
2 0 0.104168 0.000000
1 0 0.365929 0.000000
0 0 0.513998 0.000000
Total   1.000000 0.106451

## Bonus

The player earns the bonus if he gets the bonus symbol on reels 1, 2 and 3 on any active pay line. The following table shows the probability of getting the bonus symbol on each of the first three reels. The lower right cell shows the probability of activating the bonus on any active pay line is 0.06%, or 1 in 1,730. If the player plays the maximum 15 pay lines, then the bonus probability per spin is 0.87%, or 1 in 115.

### Lobstermania Bonus Symbols per Reel

Reel Bonus
Symbols
Total Symbols
on Reel
Bonus
Probability
1 2 47 0.042553
2 5 46 0.108696
3 6 48 0.125000
Product     0.000578

There are three parts to the bonus game, as follows:

• Number of lobster traps.
• Number of lobsters per trap.
• Size/win of each lobster.

There are three possibilities for the number of lobster traps, 2, 3 and 4, each with equal probability. Thus, the expected number of traps is 3.

There are two possibilities for the number of lobsters per trap, 2 or 3, each with equal probability. Thus, the expected number of lobsters per trap is 2.5.

The prize per lobster can be anywhere from 5 to 250. Each prize has an associated weighting, as shown in the table below. The way the game might work is it would pick an integer from 1 to 322 and map it to a weight according to this table. The bottom right cell shows an average win of 44.02 per lobster.

### Lobstermania Bonus — Lobster Wins

Pays Weight Probability Return
5 5 0.015528 0.077640
6 5 0.015528 0.093168
7 5 0.015528 0.108696
8 5 0.015528 0.124224
10 20 0.062112 0.621118
12 10 0.031056 0.372671
15 10 0.031056 0.465839
20 20 0.062112 1.242236
22 20 0.062112 1.366460
25 20 0.062112 1.552795
27 20 0.062112 1.677019
30 19 0.059006 1.770186
35 22 0.068323 2.391304
45 24 0.074534 3.354037
50 19 0.059006 2.950311
55 15 0.046584 2.562112
60 15 0.046584 2.795031
65 15 0.046584 3.027950
70 15 0.046584 3.260870
75 15 0.046584 3.493789
100 10 0.031056 3.105590
150 8 0.024845 3.726708
250 5 0.015528 3.881988
Total 322 1.000000 44.021739

The average win per bonus is (average traps)×(average lobsters per trap)×(average win per lobster) = 3 × 2.5 × 44.021739 = 330.163043.

The expected return for the bonus feature is (bonus probability) × (average win per bonus) = 0.000578168 × 44.021739 = 0.190890.

## Summary

The following table summarizes the three ways to win in the game. The bottom right cell shows an expected return of 85.012%. In other words, for every dollar the player bets he can expect to get back 85¢.

### Lobstermania Summary

Item Return
Line Pays 55.278%
Scatter 10.645%
Bonus 19.089%
Total 85.012%

The Harrigan and Dixon paper mentioned they were given par sheets for seven versions of Lobstermania. The available returns were 85.0%, 87.5%, 90.0%, 92.5%, 94.0%, 95.0%, and 96.2%.

## More Deconstructions

I have deconstructed lots of slot machines. Here is a list of them: