March 2nd, 2016 at 10:32:35 AM
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In the article "Deconstructing the Atkins Diet Slot Machine" on the Wizard of Odds site, I see the odds and payout for 2-5 Atkins (wild) symbols in a row as well as 2-5 of any other symbol in a row. However, what I don't see are the odds for any combination thereof, e.g. 2 Atkins and 1 steak. Why is that? Is this information missing, or is it covered in some way that is perhaps less than intuitive?

Thanks!

Benji

Thanks!

Benji

March 2nd, 2016 at 10:51:29 AM
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The "Pay Line Combinations" take wilds into account.

For example, "5 Steaks" includes all ways of getting 4 steaks and 1 Atkins, 3 steaks and 2 Atkins, 2 steaks and 3 Atkins, or 1 steak and 4 Atkins (but not 5 Atkins, which is its own payout).

If you treat all Atkins symbols as Steak symbols, there are 3 on reel 1, 4 on reel 2, 3 on reel 3, 3 on reel 4, and 4 on reel 5, for a total of 3 x 4 x 3 x 3 x 4 = 432, but that includes the 1 way to get 5 Atkins symbols, so there are 431 that pay off as 5 Steaks.

For example, "5 Steaks" includes all ways of getting 4 steaks and 1 Atkins, 3 steaks and 2 Atkins, 2 steaks and 3 Atkins, or 1 steak and 4 Atkins (but not 5 Atkins, which is its own payout).

If you treat all Atkins symbols as Steak symbols, there are 3 on reel 1, 4 on reel 2, 3 on reel 3, 3 on reel 4, and 4 on reel 5, for a total of 3 x 4 x 3 x 3 x 4 = 432, but that includes the 1 way to get 5 Atkins symbols, so there are 431 that pay off as 5 Steaks.

March 2nd, 2016 at 12:22:55 PM
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Thanks very much for this great answer! It's much appreciated.

Is there any chance you could also explain how the Atkins symbol Line Pay Combinations are calculated? In trying to reason about this, my thought process was that from 2 to 4 Atkins symbols in a row, in order for the line to count as an Atkins match and not that of some other symbol, the last Atkins symbol would need to be followed by a Scale symbol. Is that correct? In each case, the probability of an Atkins symbol or a scale is 1/32, so we'd have:

2 in a row: 33,554,432 * (1/32)^3 = 1024. Check.

3 in a row: 33,554,432 * (1/32)^4 = 32. (But the table shows 513.)

4 in a row: 33,554,432 * (1/32)^5 = 1. (But the table shows 28.)

5 in a row: 33,554,432 * (1/32)^5 = 1. Check.

What am I overlooking here? (Thanks for bearing with me!)

Is there any chance you could also explain how the Atkins symbol Line Pay Combinations are calculated? In trying to reason about this, my thought process was that from 2 to 4 Atkins symbols in a row, in order for the line to count as an Atkins match and not that of some other symbol, the last Atkins symbol would need to be followed by a Scale symbol. Is that correct? In each case, the probability of an Atkins symbol or a scale is 1/32, so we'd have:

2 in a row: 33,554,432 * (1/32)^3 = 1024. Check.

3 in a row: 33,554,432 * (1/32)^4 = 32. (But the table shows 513.)

4 in a row: 33,554,432 * (1/32)^5 = 1. (But the table shows 28.)

5 in a row: 33,554,432 * (1/32)^5 = 1. Check.

What am I overlooking here? (Thanks for bearing with me!)

March 2nd, 2016 at 1:06:46 PM
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The Pay Line Combinations table takes into account the fact that a particular line will pay only the highest amount if more than one winning combination exist.

For example, if the first four symbols on the line are Atkins, then the fifth one can be:

(a) Atkins, which is counted as 5 Atkins

(b) Steak, which means the line is both 4 Atkins and 5 Steaks; since 5 Steaks pays 1000 and 4 Atkins pays 500, it is counted as 5 Steaks

(c) anything else, which means the line is both 4 Atkins and 5 of whatever the fifth reel symbol is; since 5 in a row of anything other than Atkins or Steaks does not pay more than what 5 Atkins pays, it is counted as 4 Atkins. Note that 4 Atkins and 5 Hams both pay 500; The Wizard chose to count this as 4 Atkins, but could just as easily have counted it as 5 Hams.

There are 1 x 1 x 1 x 1 x (32 - 1 (Atkins) - 3 (Steak)) = 28 combinations that are counted as 4 Atkins.

Similarly, with Atkins symbols in reels 1-3, reel 4 has to be Butter, Cheese, Bacon, Mayonnaise, or Scale in order for the first 4 symbols not to pay more than 3 Atkins, and, if the fourth reel is Butter or Cheese, the fifth cannot be Atkins or the same as the fourth, as five of that symbol pays more than 50 (five Bacons or Mayonnaises pays 50, so it is counted as 3 Atkins, and five Scales pays zero)

Fourth reel Butter: 1 x 1 x 1 x 3 x 27 = 81

Fourth reel Cheese: 1 x 1 x 1 x 4 x 28 = 112

Fourth reel Bacon: 1 x 1 x 1 x 5 x 32 = 160 (remember, five Bacons pays the same as three Atkins)

Fourth reel Mayonnaise: 1 x 1 x 1 x 4 x 32 = 128 (five Mayonnaises pays the same as three Atkins)

Fourth reel Scale: 1 x 1 x 1 x 1 x 32 = 32 (five Scales pays zero)

The total = 81 + 112 + 160 + 128 + 32 = 513

For example, if the first four symbols on the line are Atkins, then the fifth one can be:

(a) Atkins, which is counted as 5 Atkins

(b) Steak, which means the line is both 4 Atkins and 5 Steaks; since 5 Steaks pays 1000 and 4 Atkins pays 500, it is counted as 5 Steaks

(c) anything else, which means the line is both 4 Atkins and 5 of whatever the fifth reel symbol is; since 5 in a row of anything other than Atkins or Steaks does not pay more than what 5 Atkins pays, it is counted as 4 Atkins. Note that 4 Atkins and 5 Hams both pay 500; The Wizard chose to count this as 4 Atkins, but could just as easily have counted it as 5 Hams.

There are 1 x 1 x 1 x 1 x (32 - 1 (Atkins) - 3 (Steak)) = 28 combinations that are counted as 4 Atkins.

Similarly, with Atkins symbols in reels 1-3, reel 4 has to be Butter, Cheese, Bacon, Mayonnaise, or Scale in order for the first 4 symbols not to pay more than 3 Atkins, and, if the fourth reel is Butter or Cheese, the fifth cannot be Atkins or the same as the fourth, as five of that symbol pays more than 50 (five Bacons or Mayonnaises pays 50, so it is counted as 3 Atkins, and five Scales pays zero)

Fourth reel Butter: 1 x 1 x 1 x 3 x 27 = 81

Fourth reel Cheese: 1 x 1 x 1 x 4 x 28 = 112

Fourth reel Bacon: 1 x 1 x 1 x 5 x 32 = 160 (remember, five Bacons pays the same as three Atkins)

Fourth reel Mayonnaise: 1 x 1 x 1 x 4 x 32 = 128 (five Mayonnaises pays the same as three Atkins)

Fourth reel Scale: 1 x 1 x 1 x 1 x 32 = 32 (five Scales pays zero)

The total = 81 + 112 + 160 + 128 + 32 = 513

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