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.

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.

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.

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.

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%.

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%.

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.

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.

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.

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.

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¢.

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:

• Deconstructing Jackpot Party analysis of the video slot machine.
• Deconstructing Lion's Share analysis of the classic MGM progressive game.
• Deconstructing Cleopatra analysis of the popular IGT game.
• Deconstructing Lionfish analysis of the slot game found on many Game Maker machines.
• Deconstructing Megabucks.
• Deconstructing the Atkins Diet slot machine.
• Deconstructing Lucky Larry's Lobstermania.
• Deconstructing Hexbreaker.
• Deconstructing Blazing Sevens.
• Deconstructing Hot Roll.

Written by: Michael Shackleford