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Deconstructing Lionfish
Introduction
In my endless effort to show how slot machines work, I offer this deconstruction of the slot machine Lionfish. The game can be found on many Game King machines. The reasons I chose this particular slot machine are its widespread availability and that it doesn't have a free spin bonus round. Usually, free spins utilize separate reel stripping, which would have required a prohibitive amount of play to put together the entire free spin reel strips. On the contrary, Lionfish is a simple 5reel video slot with no bonus round.
Data Collection
Much like games I previously deconstructed, Jackpot Party and Hexbreaker, I chose Lionfish because it didn't involve bonus spins. The only mystery was the reel stripping. I played a game at the Rampart casino in Las Vegas. It was located in a busy area near the security podium so I discretely put my camera in my shirt pocket. I posted on YouTube the . My apologies for the awful video quality.
I later went home and recorded every sequence of three symbols on every reel. Although many spins were not seen on camera, I still had enough to piece together the reel strips.
The Reel Strips
Many of the reel strips have the same sequence more than once. For example, the sequence 9shrimpJ appears twice on reel 3. Because of these repeating sequences, there are sometimes more than one way the reels could have been ordered. I chose one arbitrarily and it may or may not be the same as on the machine itself. However, it doesn't make any difference mathematically. I claim that the symbol frequency I came up with is exactly the same the actual game that I played and every possible sequence in the reels below is also possible on the actual game, and vice versa.
Lionfish Reel Strips
Position  Reel 1  Reel 2  Reel 3  Reel 4  Reel 5 

1  K  Sea anemone  K  J  J 
2  Q  10  A  9  Sea anemone 
3  Nautilus  A  Nautilus  Nautilus  K 
4  J  Starfish  10  Q  Q 
5  A  9  9  A  Starfish 
6  K  K  Nautilus  Starfish  9 
7  Sea anemone  Sea anemone  J  10  Sea anemone 
8  J  10  Q  Q  Q 
9  Q  Q  A  Lionfish  Starfish 
10  9  Starfish  Starfish  J  K 
11  Diver  10  K  9  Nautilus 
12  K  J  10  Sea anemone  A 
13  Q  Sea anemone  9  K  Sea anemone 
14  Sea anemone  A  Nautilus  Q  K 
15  10  9  K  Lionfish  9 
16  A  Lionfish  J  9  Lionfish 
17  Starfish  A  Q  J  K 
18  K  Sea anemone  Lionfish  Nautilus  10 
19  Q  10  10  9  Diver 
20  10  Nautilus  K  K  A 
21  Nautilus  Sea anemone  9  Nautilus  9 
22  J  K  Nautilus  10  Sea anemone 
23  A  A  J  A  K 
24  Sea anemone  Starfish  Q  Diver  10 
25  K  10  K  Q  Diver 
26  Q  9  Sea anemone  J  Nautilus 
27  Lionfish  Sea anemone  10  Nautilus  A 
28  A  Q  9  10  Sea anemone 
29  J  J  A  Q  9 
30  Nautilus  Diver  Diver  Nautilus  Lionfish 
The way multiline 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 of five random integers from 1 to 30. Let's assume this number gets mapped to the middle position on the screen. For example, if the game chose the number 23 for reel 1, then it would display JASea anemone, from top to bottom.
For another example, consider this screenshot:
The numbers associated with the symbols seen here, assuming the numbers were mapped to the symbol in the middle row, would be:
 Reel 1: 12
 Reel 2: 26
 Reel 3: 19
 Reel 4: 2
 Reel 5: 15
In the event the random number chosen is 1 or 30, then the reels wrap around, with position 1 coming after position 30.
Symbol Frequency
The next table shows the total number of each symbol on each reel.
Lionfish Symbol Distribution
Symbol  Reel 1  Reel 2  Reel 3  Reel 4  Reel 5 

Lionfish  1  1  1  2  2 
Starfish  1  3  1  1  2 
Nautilus  3  1  4  5  2 
Sea anemone  3  6  1  1  5 
A  4  4  3  2  3 
K  5  2  5  2  5 
Q  5  2  3  5  2 
J  4  2  3  4  1 
10  2  5  4  3  2 
9  1  3  4  4  4 
Diver  1  1  1  1  2 
Total  30  30  30  30  30 
Pay Table
The pay table is easily seen from the rule screens, which appears in the table below. The Lionfish is wild and may substitute for anything, including the Diver scatter pay. All line pay wins pay left to right.
Lionfish Pay Table
Symbol  5 pays  4 pays  3 pays  2 pays 

Lionfish  5000  1000  100  5 
Starfish  2000  500  50  0 
Nautilus  200  80  20  0 
Sea anemone  200  80  20  0 
A  150  50  10  0 
K  150  50  10  0 
Q  120  40  10  0 
J  120  40  10  0 
10  100  20  5  2 
9  100  20  5  2 
The diver is a scatter pay. This means the player is paid according to the number that appear on the screen anywhere. The player is paid a multiple of his total amount bet and the number of diver symbols. Following is the scatter pay table.
 5 Pays: 60
 4 Pays: 10
 3 Pays: 2
As mentioned before, the wild Lionfish can substitute for the scatter pay symbol, which is unusual in terms of slot machine design. In fact, it can substitute for two things at once, a scatter and as a line pay symbol.
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 player qualifies for only the highest possible win per line. In the event of a tie, the win is counted under the category of the Lionfish. For example, if the player got LionfishLionfishLionfish99, then he would qualify for a win of 100 for either three wilds or five 9's. As mentioned, the player qualifies for only the highest, of which there is a tie. The way I scored this win is three wilds.
Lionfish Line Pay Combinations
Symbol  5 in a row  4 in a row  3 in a row  2 in a row  Total 

Lionfish  4  52  727  6,780  7,563 
Starfish  188  1,196  12,150    13,534 
Nautilus  1,112  7,098  26,910    35,120 
Sea anemone  1,162  3,795  44,550    49,507 
A  1,990  9,900  77,220    89,110 
K  3,010  9,844  83,460    96,314 
Q  2,008  12,922  48,990    63,920 
J  1,074  9,558  42,480    53,112 
10  1,780  11,570  63,750  382,500  459,600 
9  1,404  5,616  25,200  157,500  189,720 
Total  13,732  71,551  425,437  546,780  1,057,500 
Be warned that the math is tedious and errorprone to calculate these combinations by hand. If you're up to the challenge and you can code, then I recommend coding five nested loops and cycle through all 30^5=24,300,000 possible outcomes.
The next table shows the probability of each possible win. The lower right cell shows a hit frequency per line of 4.35%.
Lionfish Line Pay Probabilities
Symbol  5 in a row  4 in a row  3 in a row  2 in a row  Total 

Lionfish  0.00000016  0.00000214  0.00002992  0.00027901  0.00031123 
Starfish  0.00000774  0.00004922  0.00050000    0.00055695 
Nautilus  0.00004576  0.00029210  0.00110741    0.00144527 
Sea anemone  0.00004782  0.00015617  0.00183333    0.00203733 
A  0.00008189  0.00040741  0.00317778    0.00366708 
K  0.00012387  0.00040510  0.00343457    0.00396354 
Q  0.00008263  0.00053177  0.00201605    0.00263045 
J  0.00004420  0.00039333  0.00174815    0.00218568 
10  0.00007325  0.00047613  0.00262346  0.01574074  0.01891358 
9  0.00005778  0.00023111  0.00103704  0.00648148  0.00780741 
Total  0.00056510  0.00294449  0.01750770  0.02250123  0.04351852 
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 50.33% of his bet per spin from line pays.
Lionfish Line Pay Returns
Symbol  5 in a row  4 in a row  3 in a row  2 in a row  Total 

Lionfish  0.00082305  0.00213992  0.00299177  0.00139506  0.00734979 
Starfish  0.01547325  0.02460905  0.02500000    0.06508230 
Nautilus  0.00915226  0.02336790  0.02214815    0.05466831 
Sea anemone  0.00956379  0.01249383  0.03666667    0.05872428 
A  0.01228395  0.02037037  0.03177778    0.06443210 
K  0.01858025  0.02025514  0.03434568    0.07318107 
Q  0.00991605  0.02127078  0.02016049    0.05134733 
J  0.00530370  0.01573333  0.01748148    0.03851852 
10  0.00732510  0.00952263  0.01311728  0.03148148  0.06144650 
9  0.00577778  0.00462222  0.00518519  0.01296296  0.02854815 
Total  0.09419918  0.15438519  0.20887449  0.04583951  0.50329835 
Scatter Pay
The game pays based on the number of Diver and Lionfish symbols anywhere on the screen. Remember the wild can count for both a scatter pay and a line pay symbol. Scatter pay wins are based on the total amount bet.
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 39.68%, which is quite high compared to other slot machines, probably because there is no bonus round.
Lionfish — Scatter Pay
Scatters  Pays  Combinations  Probability  Return 

5  60  23,328  0.000960  0.057600 
4  10  369,360  0.015200  0.152000 
3  2  2,274,480  0.093600  0.187200 
2  0  6,765,120  0.278400   
1  0  9,642,240  0.396800   
0  0  5,225,472  0.215040   
Total  24,300,000  1.000000  0.396800 
Summary
The final table below shows the return of each win category in Lionfish. The lower right cell shows a total return for the game of 90.010%.
Lionfish Summary
Type of Win  Return 

Line Pays  50.330% 
Scatter (fixed wins)  39.680% 
Total  90.010% 
The returns of other Lionfish 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 range of options tends to be 85% to 97%.
Internal Links
 My main slot machine page.
 Deconstructing Jackpot Party analysis of the video slot machine.
 Deconstructing Megabucks.
 Deconstructing the Atkins Diet slot machine. (PDF)
 Analysis of Lucky Larry's Lobstermania.
 Deconstructing Hexbreaker.
External Links
 at my forum at Wizard of Vegas.
Written by: Michael Shackleford