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Last Updated: August 19, 2016
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Deconstructing the Atkins Diet Slot Machine
Introduction
I designed the Atkins Diet slot machine in 2008 for a speaking engagement at a conference on slot machines in Sydney, Australia. It was used as an example of how video slots, sometimes known as pokies, are designed. I'll start with presenting the pay table and reel strips, and then I'll show the probability and return of the various ways to win.
Pay Table
The next table shows the Atkins Diet pay table. All wins must be left aligned. The Atkins symbol is wild and can substitute for any symbol except 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
The following are the reel strips for 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 look at the following example spin.
The way multiline video slots work is to pick one random number for each reel and map it onto the corresponding stop on the reel strip. Let's assume that the random number chosen designates where the reel will stop on the middle row. The symbols above and below will be those directly above and below on the reel strips.
Random numbers of 27, 14, 3, 31 and 27, for reels 1 to 5 respectively, would have resulted in the example above. The following table shows the position on the reel strips where all 15 visible symbols fall on the screen.
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 should also be noted that the reel strips wrap around. So, if the number chosen for the middle position is 1, then the top position would be 32. Likewise, if the middle position is 32, then the bottom position would be 1.
Symbol Distribution
The first step to calculating the return of a video slot is to count how often each symbol appears on each reel. The following table answers that question.
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
There are 32 × 32 × 32 × 32 × 32 = 33,554,432 possible outcomes in Atkins Diet. 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.
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 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 33,554,432. The total in the lower right cell reflects a hit frequency per line (probability of winning anything) of 5.45%.
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 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 63.46%.
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 serves as a scatter pay symbol. The player gets credit for a scatter pay if it appears anywhere on the screen. Unlike line pays, scatters don't need to be left aligned or on an active pay line. To be fair, 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.
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 probability and contribution to the return for 0 to 5 total scatter symbols. The lower right cell shows that the scatter pay feature returns 6.98% to the return of the game.
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
The player earns the bonus if he gets at least three scattered scales. The sum of the probability of 3 to 5 scales in the table above is 0.011185. During the bonus, the player will get ten free spins, and all wins are tripled.
In this game, free spins use the same reel strips as the base game. We have already shown that the expected line pay return is 0.634597 and the expected scatter return is 0.069756. So, if the win is tripled, then the expected win per spin is 3 × (0.634597 + 0.069756) = 2.113058.
Next, there is a rule that free spins can be won in free spins, infinitely. The expected number of total spins in a bonus is 10/(110×0.011185) = 11.259335.
So, with 11.259335 free spins, and an average win per spin of 2.113058, the expected final win per bonus is 11.259335 × 2.113058 = 23.791632.
The probability of winning the bonus in the first place is 0.011185, so the expected return per initial spin of the bonus feature is 0.011185 × 23.791632 = 0.266105.
Summary
The following table summarizes the three ways to win in the game. The bottom right cell shows an expected return of 97.046%. In other words, for every dollar the player bets, he can expect to get back 97¢.
Atkins Diet Summary
Item  Return 

Line Pays  63.460% 
Scatter  6.976% 
Bonus  26.610% 
Total  97.046% 
Internal Links
 Play Atkins Diet. Demo you can play for fun.
 Deconstructing the Atkins Diet Slot Machine. Earlier PDF version of this page.
 Slot machines main page.
 Appendix 4 shows how the return is calculated for my Wizard's Fruit Slot Machine.
 Appendix 5 analysis of the 21 Bell Slot Machine.
 Appendix 6 Analysis of Red, White, & Blue Slot Machine.
 Lock and Roll analysis of the skillbased slot machine found in North Carolina.
 Deconstructing Jackpot Party analysis of the video slot machine.
 Deconstructing Megabucks.
 Analysis of Lucky Larry's Lobstermania.
 Deconstructing Hexbreaker.
 Deconstructing Blazing Sevens.
Written by: Michael Shackleford