5 reel video slot Combinations calculation

Hi,

I am not sure I am posting to the correct thread (correct me if I am wrong)

Can anyone explain how Combinations are calculated for Atkins Diet Slot machine described here:
and
(page 3)

For example I cannot get it why Combinations of Atkins 4 in a row is 28 (I would assume it is 31) and 3 in a row is 513.
Can anyone explain the formula?

Also if possible on Page 5 there is a Bonus feature: How is Expected base win calculated to be 0.704353. I would assume it is the same as the normal win: on page 4 Total = 0.63460

Thank you very much.

Read this thread.

The reel weights for Atkins, Steak, and total are as follows:

Atkins: 1 1 1 1 1
Steak: 2 3 2 2 3
Total: 32 32 32 32 32

What you are not taking into account is that four Atkins in a row with a Steak in position 5 will pay for 5 Steaks instead of 4 Atkins. So the hits are 1 * 1 * 1 * 1 * (32-1-3). In the last term, you see that I am eliminating getting a Steak or an Atkins.

Quote: nbetter

Also if possible on Page 5 there is a Bonus feature: How is Expected base win calculated to be 0.704353. I would assume it is the same as the normal win: on page 4 Total = 0.63460

The base win in the bonus equals the line wins (0.63460) plus the scatter wins (0.069756) from page 4.

This is a rudimentary slot game, and a good place to start if you are learning to analyze slots.

At the beginning I didn't understand why you eliminated only Steaks, but after reading more I understood that the rest 5x symbols just pay less than 4 Atkins.

Thank you very much both for the explanation.

How about getting 513 for 3 in a row? I really had a hard time getting the formula for possible win combination table.



I was only semi-succesful in 4s.

Formula(R* no of Symbol on Reel)

N = ((1+R1)*(1+R2)*(1+R3)*(1+R4)*(32-1-R5))-(32-1-R5)
Steaks Reel Distribution= 2 3 2 2 3

Steaks 4*row= ((1+2) * (1+3) * (1+2)* (1+2)*(32-1-3))-(32-1-3)
= 2,996

This works from Steak to Eggs, but having problem on Butter to Mayonnaise, Can somebody help we with this? THanks.
Also, for the computation for 5s, 3s, and 2s.


Atkins--------------28
Steak---------------2,996
Ham----------------5,157
Buffalo WIngs----5,348
Sausage-----------8,613
Eggs----------------6,692
********************
Butter---------------10,773
Cheese--------------13,972
Bacon----------------20,972
Mayonnaise---------20,972

Quote: kaikatsuna09

How about getting 513 for 3 in a row?

3 Atkins pays 50
If the fourth symbol is Steak, that's four Steaks, which is 200, which pays more than 3 Atkins, so it counts only as 4 Steaks here.
The same goes for Ham, Buffalo Wings, Sausage, and Eggs.
If the fourth symbol is Butter, 4 Butters is also 50, so Wizard is counting this as 3 Atkins (instead of 4 Butters).
However, if the fifth symbol is Butter or Atkins, that's 5 Butters, which pays more than 3 Atkins.
The same goes for Cheese.
If the fourth symbol is Bacon or Mayonnaise, then it doesn't matter what the fifth symbol is; 5 Bacon and 5 Mayonnaise both pay 50, so they are counted here as 3 Atkins.
If the fourth symbol is Scale, it doesn't matter what the fifth symbol is; this is 3 Atkins.
This means the number of "3 Atkins" combinations is the sum of:
(Fourth symbol Butter) x (Fifth symbol anything except Butter or Atkins) = 3 x 27 = 81
(Fourth symbol Cheese) x (Fifth symbol anything except Cheese or Atkins) = 4 x 28 = 112
(Fourth symbol Bacon, Mayonnaise, or Scale) x (Fifth symbol anything) = 10 x 32 = 320
81 + 112 + 320 = 513.

As for 4 Butters, you are forgetting to subtract the 81 combinations of {Atkins, Atkins, Atkins, Butter, (something besides Atkins or Butter)}, since 3 Atkins and 4 Butters both pay 50 and Wizard is counting these as 3 Atkins instead of 4 Butters
10,773 - 81 = 10,682.
Do the same for 4 Cheese, 4 Bacon, and 4 Mayonnaise.

Quote: ThatDonGuy

Re:How about getting 513 for 3 in a row?

Thank you so much.

Now I understand it well. I was confused because I never considered the paytable as basis of my computation for possible win combination.

(bow)

I think the following covers the entire game:

5 WILD COMBO: (1)*(1)*(1)*(1)*(1)
5 WILD COMBO: 1

5 Ham pays the same with 4 Wild = (1*1*1*1)*(4)
5 Buffalo Wings pays less than 4 Wild = (1*1*1*1)*(3)
5 Sausage pays less than 4 Wild = (1*1*1*1)*(4)
5 Eggs pays less than 4 Wild = (1*1*1*1)*(3)
5 Butter pays less than 4 Wild = (1*1*1*1)*(4)
5 Cheese pays less than 4 Wild = (1*1*1*1)*(3)
5 Bacon pays less than 4 Wild = (1*1*1*1)*(3)
5 Mayonnaise pays less than 4 Wild = (1*1*1*1)*(3)
5 Scale (S) pays less than 4 Wild = (1*1*1*1)*(1)
4 WILD COMBO: (1*1*1*1)*(4) + (1*1*1*1)*(3) + (1*1*1*1)*(4) + (1*1*1*1)*(3) + (1*1*1*1)*(4) + (1*1*1*1)*(3) + (1*1*1*1)*(3) + (1*1*1*1)*(3) + (1*1*1*1)*(1)
4 WILD COMBO: 28

4 Butter pays the same with 3 Wild = (1*1*1)*(3)*(32-4-1)
4 Cheese pays the same with 3 Wild = (1*1*1)*(4)*(32-3-1)
4 Bacon pays less than 3 Wild = (1*1*1)*(5)*(32)
4 Mayonnaise pays less than 3 Wild = (1*1*1)*(4)*(32)
4 Scale (S) pays less than 3 Wild = (1*1*1)*(1)*(32)
3 WILD COMBO: (1*1*1)*(3)*(32-4-1) + (1*1*1)*(4)*(32-3-1) + (1*1*1)*(5)*(32) + (1*1*1)*(4)*(32) + (1*1*1)*(1)*(32)
3 WILD COMBO: 513

3 Scale (S) pays less than 2 Wild = (1*1)*(1)*(32)*(32)
2 WILD COMBO: (1*1)*(1)*(32)*(32)
2 WILD COMBO: 1,024

5 Wild pays more than 5 Steak, so we subtract Wild from 5 Steak in a row
5 Steak COMBO: MAX = (2+1)*(3+1)*(2+1)*(2+1)*(3+1) => ((2+1)*(3+1)*(2+1)*(2+1)*(3+1) - (1*1*1*1*1)) = 431

4 Wild pays more than 4 Steak, so we subtract Wild from 4 Steak in a row
4 Steak COMBO: MAX = (2+1)*(3+1)*(2+1)*(2+1)*(32-3-1) => ((2+1)*(3+1)*(2+1)*(2+1) - (1*1*1*1))*(32-3-1) = 2,996

3 Wild pays more than 3 Steak, so we subtract Wild from 3 Steak in a row
3 Steak COMBO: MAX = (2+1)*(3+1)*(2+1)*(32-2-1)*(32) => ((2+1)*(3+1)*(2+1) - (1*1*1))*(32-2-1)*(32) = 32,480

2 Wild pays more than 2 Steak, so we subtract Wild from 2 Steak in a row
2 Steak COMBO: MAX = (2+1)*(3+1)*(32-2-1)*(32)*(32) => ((2+1)*(3+1) - (1*1))*(32-2-1)*(32)*(32) = 326,656

5 Ham pays the same with 4 Wild, so we subtract Wild from 4 Ham in a row
5 Ham COMBO: MAX = (2+1)*(3+1)*(3+1)*(3+1)*(4+1) => ((2+1)*(3+1)*(3+1)*(3+1) - (1*1*1*1))*(4+1) = 955

4 Wild pays more than 4 Ham, so we subtract Wild from 4 Ham in a row
4 Ham COMBO: MAX = (2+1)*(3+1)*(3+1)*(3+1)*(32-4-1) => ((2+1)*(3+1)*(3+1)*(3+1) - (1*1*1*1))*(32-4-1) = 5,157

3 Wild pays more than 3 Ham, so we subtract Wild from 3 Ham in a row
3 Ham COMBO: MAX = (2+1)*(3+1)*(3+1)*(32-3-1)*(32) => ((2+1)*(3+1)*(3+1) - (1*1*1))*(32-3-1)*(32) = 42,112

2 Wild pays more than 2 Ham, so we subtract Wild from 2 Ham in a row
2 Ham COMBO: MAX = (2+1)*(3+1)*(32-3-1)*(32)*(32) => ((2+1)*(3+1) - (1*1))*(32-3-1)*(32)*(32) = 315,392

4 Wild pays more than 5 Buffalo Wings, so we subtract Wild from 4 Buffalo Wings in a row
5 Buffalo Wings COMBO: MAX = (3+1)*(3+1)*(3+1)*(2+1)*(3+1) => ((3+1)*(3+1)*(3+1)*(2+1) - (1*1*1*1))*(3+1) = 764

4 Wild pays more than 4 Buffalo Wings, so we subtract Wild from 4 Buffalo Wings in a row
4 Buffalo Wings COMBO: MAX = (3+1)*(3+1)*(3+1)*(2+1)*(32-3-1) => ((3+1)*(3+1)*(3+1)*(2+1) - (1*1*1*1))*(32-3-1) = 5,348

3 Wild pays more than 3 Buffalo Wings, so we subtract Wild from 3 Buffalo Wings in a row
3 Buffalo Wings COMBO: MAX = (3+1)*(3+1)*(3+1)*(32-2-1)*(32) => ((3+1)*(3+1)*(3+1) - (1*1*1))*(32-2-1)*(32) = 58,464

2 Wild pays more than 2 Buffalo Wings, so we subtract Wild from 2 Buffalo Wings in a row
2 Buffalo Wings COMBO: MAX = (3+1)*(3+1)*(32-3-1)*(32)*(32) => ((3+1)*(3+1) - (1*1))*(32-3-1)*(32)*(32) = 430,080

4 Wild pays more than 5 Sausage, so we subtract Wild from 4 Sausage in a row
5 Sausage COMBO: MAX = (3+1)*(3+1)*(3+1)*(4+1)*(4+1) => ((3+1)*(3+1)*(3+1)*(4+1) - (1*1*1*1))*(4+1) = 1,595

4 Wild pays more than 4 Sausage, so we subtract Wild from 4 Sausage in a row
4 Sausage COMBO: MAX = (3+1)*(3+1)*(3+1)*(4+1)*(32-4-1) => ((3+1)*(3+1)*(3+1)*(4+1) - (1*1*1*1))*(32-4-1) = 8,613

3 Wild pays more than 3 Sausage, so we subtract Wild from 3 Sausage in a row
3 Sausage COMBO: MAX = (3+1)*(3+1)*(3+1)*(32-4-1)*(32) => ((3+1)*(3+1)*(3+1) - (1*1*1))*(32-4-1)*(32) = 54,432

4 Wild pays more than 5 Eggs, so we subtract Wild from 4 Eggs in a row
5 Eggs COMBO: MAX = (4+1)*(2+1)*(3+1)*(3+1)*(3+1) => ((4+1)*(2+1)*(3+1)*(3+1) - (1*1*1*1))*(3+1) = 956

4 Wild pays more than 4 Eggs, so we subtract Wild from 4 Eggs in a row
4 Eggs COMBO: MAX = (4+1)*(2+1)*(3+1)*(3+1)*(32-3-1) => ((4+1)*(2+1)*(3+1)*(3+1) - (1*1*1*1))*(32-3-1) = 6,692

3 Wild pays more than 3 Eggs, so we subtract Wild from 3 Eggs in a row
3 Eggs COMBO: MAX = (4+1)*(2+1)*(3+1)*(32-3-1)*(32) => ((4+1)*(2+1)*(3+1) - (1*1*1))*(32-3-1)*(32) = 52,864

4 Wild pays more than 5 Butter, so we subtract Wild from 4 Butter in a row
5 Butter COMBO: MAX = (4+1)*(3+1)*(4+1)*(3+1)*(4+1) => ((4+1)*(3+1)*(4+1)*(3+1) - (1*1*1*1))*(4+1) = 1,995

4 Butter pays the same with 3 Wild, so we subtract Wild from 3 Butter in a row
4 Butter COMBO: MAX = (4+1)*(3+1)*(4+1)*(3+1)*(32-4-1) => ((4+1)*(3+1)*(4+1) - (1*1*1))*(3+1)*(32-4-1) = 10,692

3 Wild pays more than 3 Butter, so we subtract Wild from 3 Butter in a row
3 Butter COMBO: MAX = (4+1)*(3+1)*(4+1)*(32-3-1)*(32) => ((4+1)*(3+1)*(4+1) - (1*1*1))*(32-3-1)*(32) = 88,704

4 Wild pays more than 5 Cheese, so we subtract Wild from 4 Cheese in a row
5 Cheese COMBO: MAX = (3+1)*(4+1)*(4+1)*(4+1)*(3+1) => ((3+1)*(4+1)*(4+1)*(4+1) - (1*1*1*1))*(3+1) = 1,996

4 Cheese pays the same with 3 Wild, so we subtract Wild from 3 Cheese in a row
4 Cheese COMBO: MAX = (3+1)*(4+1)*(4+1)*(4+1)*(32-3-1) => ((3+1)*(4+1)*(4+1) - (1*1*1))*(4+1)*(32-3-1) = 13,860

3 Wild pays more than 3 Cheese, so we subtract Wild from 3 Cheese in a row
3 Cheese COMBO: MAX = (3+1)*(4+1)*(4+1)*(32-4-1)*(32) => ((3+1)*(4+1)*(4+1) - (1*1*1))*(32-4-1)*(32) = 85,536

5 Bacon pays the same with 3 Wild, so we subtract Wild from 3 Bacon in a row
5 Bacon COMBO: MAX = (4+1)*(4+1)*(4+1)*(5+1)*(3+1) => ((4+1)*(4+1)*(4+1) - (1*1*1))*(5+1)*(3+1) = 2,976

3 Wild pays more than 4 Bacon, so we subtract Wild from 3 Bacon in a row
4 Bacon COMBO: MAX = (4+1)*(4+1)*(4+1)*(5+1)*(32-3-1) => ((4+1)*(4+1)*(4+1) - (1*1*1))*(5+1)*(32-3-1) = 20,832

3 Wild pays more than 3 Bacon, so we subtract Wild from 3 Bacon in a row
3 Bacon COMBO: MAX = (4+1)*(4+1)*(4+1)*(32-5-1)*(32) => ((4+1)*(4+1)*(4+1) - (1*1*1))*(32-5-1)*(32) = 103,168

5 Mayonnaise pays the same with 3 Wild, so we subtract Wild from 3 Mayonnaise in a row
5 Mayonnaise COMBO: MAX = (4+1)*(5+1)*(4+1)*(4+1)*(3+1) => ((4+1)*(5+1)*(4+1) - (1*1*1))*(4+1)*(3+1) = 2,980

3 Wild pays more than 4 Mayonnaise, so we subtract Wild from 3 Mayonnaise in a row
4 Mayonnaise COMBO: MAX = (4+1)*(5+1)*(4+1)*(4+1)*(32-3-1) => ((4+1)*(5+1)*(4+1) - (1*1*1))*(4+1)*(32-3-1) = 20,860

3 Wild pays more than 3 Mayonnaise, so we subtract Wild from 3 Mayonnaise in a row
3 Mayonnaise COMBO: MAX = (4+1)*(5+1)*(4+1)*(32-4-1)*(32) => ((4+1)*(5+1)*(4+1) - (1*1*1))*(32-4-1)*(32) = 128,736

5 SCAT on Reels 1, 2, 3, 4, 5 = (2*3)*(1*3)*(1*3)*(1*3)*(1*3)
5 SCAT COMBO: (2*3)*(1*3)*(1*3)*(1*3)*(1*3)
5 SCAT COMBO: 486

4 SCAT on Reels 1, 2, 3, 4 = (2*3)*(1*3)*(1*3)*(1*3)*(32-1*3)
4 SCAT on Reels 1, 2, 3, 5 = (2*3)*(1*3)*(1*3)*(32-1*3)*(1*3)
4 SCAT on Reels 1, 2, 4, 5 = (2*3)*(1*3)*(32-1*3)*(1*3)*(1*3)
4 SCAT on Reels 1, 3, 4, 5 = (2*3)*(32-1*3)*(1*3)*(1*3)*(1*3)
4 SCAT on Reels 2, 3, 4, 5 = (32-2*3)*(1*3)*(1*3)*(1*3)*(1*3)
4 SCAT COMBO: (2*3)*(1*3)*(1*3)*(1*3)*(32-1*3) + (2*3)*(1*3)*(1*3)*(32-1*3)*(1*3) + (2*3)*(1*3)*(32-1*3)*(1*3)*(1*3) + (2*3)*(32-1*3)*(1*3)*(1*3)*(1*3) + (32-2*3)*(1*3)*(1*3)*(1*3)*(1*3)
4 SCAT COMBO: 20,898

3 SCAT on Reels 1, 2, 3 = (2*3)*(1*3)*(1*3)*(32-1*3)*(32-1*3)
3 SCAT on Reels 1, 2, 4 = (2*3)*(1*3)*(32-1*3)*(1*3)*(32-1*3)
3 SCAT on Reels 1, 2, 5 = (2*3)*(1*3)*(32-1*3)*(32-1*3)*(1*3)
3 SCAT on Reels 1, 3, 4 = (2*3)*(32-1*3)*(1*3)*(1*3)*(32-1*3)
3 SCAT on Reels 1, 3, 5 = (2*3)*(32-1*3)*(1*3)*(32-1*3)*(1*3)
3 SCAT on Reels 1, 4, 5 = (2*3)*(32-1*3)*(32-1*3)*(1*3)*(1*3)
3 SCAT on Reels 2, 3, 4 = (32-2*3)*(1*3)*(1*3)*(1*3)*(32-1*3)
3 SCAT on Reels 2, 3, 5 = (32-2*3)*(1*3)*(1*3)*(32-1*3)*(1*3)
3 SCAT on Reels 2, 4, 5 = (32-2*3)*(1*3)*(32-1*3)*(1*3)*(1*3)
3 SCAT on Reels 3, 4, 5 = (32-2*3)*(32-1*3)*(1*3)*(1*3)*(1*3)
3 SCAT COMBO: (2*3)*(1*3)*(1*3)*(32-1*3)*(32-1*3) + (2*3)*(1*3)*(32-1*3)*(1*3)*(32-1*3) + (2*3)*(1*3)*(32-1*3)*(32-1*3)*(1*3) + (2*3)*(32-1*3)*(1*3)*(1*3)*(32-1*3) + (2*3)*(32-1*3)*(1*3)*(32-1*3)*(1*3) + (2*3)*(32-1*3)*(32-1*3)*(1*3)*(1*3) + (32-2*3)*(1*3)*(1*3)*(1*3)*(32-1*3) + (32-2*3)*(1*3)*(1*3)*(32-1*3)*(1*3) + (32-2*3)*(1*3)*(32-1*3)*(1*3)*(1*3) + (32-2*3)*(32-1*3)*(1*3)*(1*3)*(1*3)
3 SCAT COMBO: 353,916