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Breaking Down the Atkins Diet Slot Machine

Introduction


Click on this image to play.

In 2008, I created the Atkins Diet slot machine for a presentation at a conference in Sydney focused on slot machines. This machine was intended to illustrate the design elements of video slots, often referred to as pokies. I will start by showing the payout structure along with the reel symbols, followed by an analysis of winning probabilities and returns.

Pay Table

The subsequent table presents the payout structure for the Atkins Diet slot machine. All winnings must align from left to right. The Atkins symbol acts as a wild card, substituting for any other symbol except for the scale.

Atkins Diet Pay Table

Symbol 5 in a row 4 in a row 3 in a row 2 in a row
Atkins 5000 500 50 5
Steak 1000 200 40 3
Ham 500 150 30 2
Buffalo Wings 300 100 25 2
Sausage 200 75 20 0
Eggs 200 75 20 0
Butter 100 50 15 0
Cheese 100 50 15 0
Bacon 50 25 10 0
Mayonnaise 50 25 10 0

Reel Strips

Next, we have the reel symbols for the Atkins Diet.

Atkins Diet Reel Strips

Stop Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
1 Scale Mayonnaise Ham Ham Bacon
2 Mayonnaise Buffalo Wings Butter Cheese Scale
3 Ham Steak Eggs Atkins Steak
4 Sausage Sausage Scale Scale Ham
5 Bacon Cheese Cheese Butter Cheese
6 Eggs Mayonnaise Mayonnaise Bacon Sausage
7 Cheese Ham Butter Cheese Butter
8 Mayonnaise Butter Ham Sausage Bacon
9 Sausage Bacon Sausage Steak Buffalo Wings
10 Butter Steak Bacon Eggs Cheese
11 Buffalo Wings Sausage Steak Bacon Sausage
12 Bacon Mayonnaise Buffalo Wings Mayonnaise Ham
13 Eggs Ham Butter Sausage Butter
14 Mayonnaise Atkins Mayonnaise Cheese Steak
15 Steak Butter Cheese Butter Mayonnaise
16 Buffalo Wings Eggs Sausage Ham Eggs
17 Butter Cheese Eggs Mayonnaise Sausage
18 Cheese Bacon Bacon Bacon Ham
19 Eggs Sausage Mayonnaise Buffalo Wings Atkins
20 Atkins Buffalo Wings Buffalo Wings Sausage Butter
21 Bacon Scale Ham Cheese Buffalo Wings
22 Mayonnaise Mayonnaise Sausage Eggs Mayonnaise
23 Ham Butter Bacon Butter Eggs
24 Cheese Cheese Cheese Buffalo Wings Ham
25 Eggs Bacon Eggs Bacon Bacon
26 Scale Eggs Atkins Mayonnaise Butter
27 Butter Buffalo Wings Buffalo Wings Eggs Steak
28 Bacon Mayonnaise Bacon Ham Mayonnaise
29 Sausage Steak Butter Sausage Sausage
30 Buffalo Wings Ham Cheese Steak Eggs
31 Steak Cheese Mayonnaise Mayonnaise Cheese
32 Butter Bacon Steak Bacon Buffalo Wings

Example Spin

Let’s examine the outcome of a sample spin.

Multi-line video slots operate by randomly selecting a number for each reel, which corresponds to a specific stop on the reel. Let's say the random number for the middle row dictates where the reel will land. The symbols that appear above and below this position correspond to their placements on the reel.

The example outcome illustrated above stems from random numbers of 27, 14, 3, 31, and 27 for reels one through five respectively. The following table indicates where these 15 on-screen symbols land on the reel strips.

Atkins Diet Reel Strips

Stop Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
Top 26 13 2 30 26
Middle 27 14 3 31 27
Bottom 28 15 4 32 28

It is important to note that the reel strips wrap around. For instance, if the number for the center position is 1, then the top position becomes 32. Conversely, if the middle number is 32, the bottom would revert to 1.

Symbol Distribution

To calculate a video slot's return, the first step is assessing the frequency of each symbol appearing on each reel. The table below provides those details.

Atkins Diet Symbol Distribution

Symbol Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
Atkins 1 1 1 1 1
Steak 2 3 2 2 3
Ham 2 3 3 3 4
Buffalo Wings 3 3 3 2 3
Sausage 3 3 3 4 4
Eggs 4 2 3 3 3
Butter 4 3 4 3 4
Cheese 3 4 4 4 3
Bacon 4 4 4 5 3
Mayonnaise 4 5 4 4 3
Scale 2 1 1 1 1
Total 32 32 32 32 32

Line Pay Math

In the Atkins Diet slot machine, there are a total of 33,554,432 possible combinations, derived from 32 × 32 × 32 × 32 × 32. The next table illustrates how many of these combinations yield a win, calculated through a program using five nested loops to tally results for every possible win scenario.

Atkins Diet Line Pay Combinations

Symbol 5 in a row 4 in a row 3 in a row 2 in a row Total
Atkins 1 28 513 1,024 1,566
Steak 431 2,996 32,480 326,656 362,563
Ham 955 5,157 42,112 315,392 363,616
Buffalo Wings 764 5,348 58,464 430,080 494,656
Sausage 1,595 8,613 54,432 - 64,640
Eggs 956 6,692 52,864 - 60,512
Butter 1,995 10,692 88,704 - 101,391
Cheese 1,996 13,860 85,536 - 101,392
Bacon 2,976 20,832 103,168 - 126,976
Mayonnaise 2,980 20,860 128,736 - 152,576
Total 14,649 95,078 647,009 1,073,152 1,829,888

The subsequent table breaks down the probabilities for each winning outcome. This figure is derived by dividing the number of winning combinations by the grand total of 33,554,432. The total shown in the bottom right indicates a 5.45% hit frequency per pay line, or the likelihood of winning something.

Atkins Line Pay Probabilities

Symbol 5 in a row 4 in a row 3 in a row 2 in a row Total
Atkins 0.00000003 0.00000083 0.00001529 0.00003052 0.00004667
Steak 0.00001284 0.00008929 0.00096798 0.00973511 0.01080522
Ham 0.00002846 0.00015369 0.00125504 0.00939941 0.01083660
Buffalo Wings 0.00002277 0.00015938 0.00174236 0.01281738 0.01474190
Sausage 0.00004753 0.00025669 0.00162220 - 0.00192642
Eggs 0.00002849 0.00019944 0.00157547 - 0.00180340
Butter 0.00005946 0.00031865 0.00264359 - 0.00302169
Cheese 0.00005949 0.00041306 0.00254917 - 0.00302172
Bacon 0.00008869 0.00062084 0.00307465 - 0.00378418
Mayonnaise 0.00008881 0.00062168 0.00383663 - 0.00454712
Total 0.00043657 0.00283355 0.01928237 0.03198242 0.05453491

The following table demonstrates each winning possibility's contribution to the overall return. Each cell represents the product of the winning probability (from the previous table) and the payout structure. The rightmost cell sums this up, revealing a total return of 63.46% from line pays.

Atkins Diet Expected Returns

Symbol 5 in a row 4 in a row 3 in a row 2 in a row Total
Atkins (wild) 0.000149 0.000417 0.000764 0.000153 0.001483
Steak 0.012845 0.017858 0.038719 0.029205 0.098627
Ham 0.014231 0.023054 0.037651 0.018799 0.093734
Buffalo Wings 0.006831 0.015938 0.043559 0.025635 0.091963
Sausage 0.009507 0.019252 0.032444 - 0.061202
Eggs 0.005698 0.014958 0.031509 - 0.052165
Butter 0.005946 0.015932 0.039654 - 0.061532
Cheese 0.005949 0.020653 0.038238 - 0.064839
Bacon 0.004435 0.015521 0.030746 - 0.050702
Mayonnaise 0.004441 0.015542 0.038366 - 0.058349
Total 0.070029 0.159124 0.331651 0.073792 0.634597

Scatter Pay

The scale functions as a scatter symbol. Players receive scatter pays for its appearance anywhere on the screen, which differs from line pays as scatters do not require left alignment or a place on an active pay line. To ensure fairness, scatter pay values are based on the total bet. The table following outlines the number of scatters per reel, total symbols on each reel, and the scatter probability calculated as 3 × (column 2)/(column 3), with the factor of three reflecting all three visible positions on the reels.

Atkins Diet Scatters per Reel

Reel Scatters Total Symbols
on Reel
Scatter
Probability
1 2 32 0.18750
2 1 32 0.09375
3 1 32 0.09375
4 1 32 0.09375
5 1 32 0.09375

The next table shows the probabilities and contributions to the return from 0 to 5 scatter symbols. The bottom right cell reveals that the scatter pay feature contributes 6.98% to the game’s return.

Atkins Diet Scatter Pay Probabilities and Returns

Scatters Pays Combinations Probability Return
5 100 486 0.000014 0.001448
4 25 20,898 0.000623 0.015570
3 5 353,916 0.010548 0.052738
Total   33,554,432 0.011185 0.069756

Bonus

Players earn a bonus when they land at least three scattered scales. The cumulative probability for landing 3 to 5 scales, as noted in the earlier table, is 0.011185. During this bonus round, players enjoy ten free spins, and all winnings are tripled.

In this particular game, the free spins employ the same reel strips as the main game. As previously indicated, the anticipated line pay return is 0.634597, while the expected scatter return is 0.069756. Therefore, if the winnings are tripled, the expected win for each spin becomes 3 × (0.634597 + 0.069756) = 2.113058.

There is also a stipulation that players can win free spins even during the free spins round, ad infinitum. The expected total spins during a bonus period equate to 10/(1-10 × 0.011185) = 11.259335.

Thus, with 11.259335 free spins and an average win of 2.113058 per spin, the anticipated total win for the bonus round becomes 11.259335 × 2.113058 = 23.791632.

The probability of initially winning the bonus is 0.011185, leading to an expected return from the initial spin of the bonus feature calculated as 0.011185 × 23.791632 = 0.266105.

Summary

The forthcoming table encapsulates the three winning methods within the game. The cell in the bottom right showcases an expected return of 97.046%. This implies that for every dollar wagered, the player can anticipate receiving back 97 cents.

Atkins Diet Summary

Item Return
Line Pays 63.460%
Scatter 6.976%
Bonus 26.610%
Total 97.046%

More Deconstructions

I have extensively analyzed various slot machines. Here’s a compilation of those studies:

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