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Introduction
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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 |
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 |
How To Play Slot Machines
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 |
Slot Machine Math Odds
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
Playing the slot machines is not complicated. The game is all about luck, with no strategy component to cause stress. Slot machines are entertaining, because they are a low impact casino diversion. That doesn’t mean you should avoid all suggestions or basic strategy tips. Below is what you should know about slot machines.
Don’t Buy Advice Books – Buying a book of tips for beating the slot machines is like buying a book of tips for how to cheat death. Most slot machines have a house edge between 5% and 15%. No strategy lowers that house edge. Gamblers put money in the machine. They hit the spin button. No matter what people say, you cannot calculate which fraction of the second to click the button, because the machine spits out thousands of reel combinations per second. The people selling books are just insulting your intelligence. Don’t let them.
Don’t Sweat Lost Wins – Imagine you walk away from the machine and see someone walk up to your machine immediately. You pause a second to see how they do, then (to your horror) see them hit spin once and win a big jackpot. If this happens, don’t step out on the ledge. The chances may be 5000:1 that you would have hit the button at the exact same time as the player who walked up. In other words, they didn’t steal your jackpot–it just kind of happened.
Use the Slots Cards – Always use your slots card. Most slot clubs save a player 1% to 2%. Players get free stuff for doing what they were going to do anyway: play. Slots clubs offer players free rooms, free meals, cashback, and other comps. Never turn down free stuff.
Understand the Law of Averages – The law of averages states that something which hasn’t happened in a while is more likely to happen soon. This is a fallacy in slots gambling. Every spin of the reels is completely separate from every other spin. If you hit a jackpot last spin, you have exactly the same chance of hitting it the next round. If you haven’t hit a bonus round in 100 spins, you have the same chance of hitting it on the 101st spin as you did on the other hundred. The law of averages is one of those common sense ways of looking at the world which is wrong.
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Slow Down – Players like the play faster, as if it’s an advantage to do so. Don’t play faster; play slower. The casino gets a big advantage over you. When you speed up play, this only increases that advantage. Don’t play multiple games at once. Don’t use the auto-spin function. Do nothing that speeds up your session. Instead, take your time and savor your gambling experience. Not only can you appreciate the game more, you’ll save money.
Play Full Coin Progressives – When playing the progressives, always place the max bet. This is the only way you activate the progressive jackpot feature. Don’t make this mistake, only to find out later you could have had a progressive jackpot prize if you’d only followed instructions.
Multi Line Slot Machines
Don’t Play Multiple Line Machines – The multiple payline slot machines might seem like they pay out more often. They tend to have worse odds than the single payline machine. Many of those extra winning spins provide negligible paybacks. They might not even pay for the cost of the spin.
Keep a Gambling Log – Keep a log of your gambling wins and losses. You might think this is only to your disadvantage, but it’s not. Imagine you hit a jackpot worth $10,000. If you want to stay legal, you’ll have to pay taxes on those winnings. If you’ve kept a log of your gambling losses throughout the year, you’ll be able to offset the money you won by adding in the money you lost. In most players’ cases, this can save you a ton of money. Also, having a record of your monthly losses gives you an idea what you’re losing on trips to the casino, so you’ll be a little more discriminating about what you play.
Compare Payouts –Remember to compare the top payout on all the similar looking machines. Sometimes, one slot machine is going to have a much larger payout than a machine right next to it with the same theme. Of course, this applies for progressive jackpots. This is less common with the progressives, now that networked jackpots are becoming a norm.
Slot Machine Mathematics
Choose Your Max Bet Denomination – Don’t think I’m saying to find the biggest denomination and play it. Not everyone can place $10 or $25 bets on a slot spin. Once again, don’t bet one penny more than you can comfortably afford to lose. What I’m saying is you should find the biggest denomination in your range and play that machine. The higher the slot denomination, the better the payback percentage. Casinos want to cater to people who wager a lot of money.