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Breaking Down the Atkins Diet Slot Machine
Introduction
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:
- Deconstructing Jackpot Party analysis of the video slot machine.
- Deconstructing Lion's Share A detailed look at the classic MGM progressive game.
- Deconstructing Cleopatra analysis of the popular IGT game.
- Deconstructing Lionfish Analysis of a slot game commonly found on various Game Maker machines.
- Deconstructing Megabucks .
- Breaking down the Atkins Diet slot machine. .
- Examining Lucky Larry's Lobstermania. .
- Deconstructing Hexbreaker .
- Deconstructing Blazing Sevens .
- Deconstructing Hot Roll .
Internal Links
- Play Atkins Diet . Demo you can play for fun.
- Breaking Down the Atkins Diet Slot Machine . Earlier PDF version of this page.
- Slot machines main page.
- Appendix 4 Demonstrates how I calculate the returns for my analyses.Wizard's Fruit Slot Machine .
- Appendix 5 analysis of the 21 Bell Slot Machine.
- Appendix 6 Evaluating the Red, White, & Blue Slot Machine.
- Lock and Roll Insights into the skill-based slot machine located in North Carolina.