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• Appendices
• Slots Analysis
• Miscellaneous

Introduction

Click on this image to play.

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.

Mills Novelty Slot Machine

The way multi-line 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.

Mills Slot Machine

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/(1-10×0.011185) = 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.

Mills Atkins Slot Machine Reproduction

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

Mills Novelty Slot Machines

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%

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.

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 skill-based slot machine found in North Carolina.
  

Written by: Michael Shackleford