- Appendices
- Slots Analysis
- Miscellaneous
Introduction
Click on this image to play.
May 06, 2017 Among the many games broken down to bits in his site, Shackleford also published the full design of a 20-lines slot he calls The Atkins Diet Slot. I am going to expand on Shakckleford’s webpage, adding simulations and some math for you to play with. If you wish to play the slot itself, for free, take a few spins here.
Atkins 20® Phase 1, also known as Induction, is designed to jumpstart your weight loss. An all-too-common misconception is that Phase 1 of Atkins is the whole program. In reality, it's the key to kick starting your fat burning metabolism. As you move through the diet. Avoid machines that use video representations of symbols. With these slots, there is absolutely no way to figure out what the payoff percentage of that machine is. Most casinos will hold a slot for you while you go to the restroom, take a short break or even go on a buffet run.
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 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.
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 |
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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.
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% |
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
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