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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 nonproblem 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 highpaying 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 66566. 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 linepay 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%.
Written by: Michael Shackleford