Slot game Line Pay Combinations

I was reading the articles "Deconstructing the Atkins Diet Slot Machine"and trying to understand how to calculate Line Pay Combinations, but I could not figure it out myself. Would anybody available to explain it to me please? Many many thanks!!!

For example, for Atkins, 4 in a row, in the list it was 28, however, shouldn't it be 1x1x1x1x(32-1)=31? or, for Steak, 3 in a row, I thought it should be 2x3x2x(32-2)x32=11520, however it is listed as 32480.

I am so frustrated, anybody please? big thanks!

Read this thread. If you still have questions, feel free to ask. I'm leaving for Vegas in few hours so I might be able to help until Saturday night.

I can attempt a simple explanation with example.

Lets say there are 20 spots a each wheel, and 5 wheels (20^5 = 3.2 million combinations).

Lets say Symbol "A" occurs 3-6-4-2-3 times (3 on the 1st wheel, 6 on the 2nd wheel, etc.).

Given these conditions, to match the first 4 wheels A-A-A-A the chances are
3*6*4*2 = 144 possibilities, BUT there is a 5th wheel... on it there are 3 A's.
So that means there are 20 - 3 = 17 spots that will cause the A-A-A-A to win the 4 A's prize.
(If an A appears on the 5th wheel, one wins the Five A's prize: not the Four A's prize.)

Solving this is 3*6*4*2*17 / 3,200,000 or a chance of 0.000765 (about 1 in 1307)
Since there are many winning combinations other than just "A", the payout to the winner is usually substantially less... 100 per coin
might be expected.

Hope this helps.

4 Atkins is only 28 combinations because 5 Steak is more valuable than 4 Atkins and only the highest winner is paid. So on the 5th reel we have to exclude getting a Steak or an Atkins to determine the combinations of 4 Atkins. 1 Atkins and 3 Steak exist on Reel 5. 1x1x1x1x(32-1-3) = 28

As for 3 Steak, remember that Atkins is Wild.

So...
Reel 1 has 1 Atkins and 2 Steak
Reel 2 has 1 Atkins and 3 Steak
Reel 3 has 1 Atkins and 2 Steak
Reel 4 has 1 Atkins and 2 Steak

We need Reels 1-3 to either have Atkins or Steak. But not 3 Atkins because 3 Atkins pays more than 3 Steak. Then the fourth reel may be anything but Atkins or Steak, and the fifth reel can be anything.

[(1+2)*(1+3)*(1+2) - 1*1*1]*(32-1-2)*32 = 35*29*32 = 32,480

Hope this clears things up a bit for you.

Many many thanks! still reading it and it was already helpful =)

Quote: tringlomane

4 Atkins is only 28 combinations because 5 Steak is more valuable than 4 Atkins and only the highest winner is paid. So on the 5th reel we have to exclude getting a Steak or an Atkins to determine the combinations of 4 Atkins. 1 Atkins and 3 Steak exist on Reel 5. 1x1x1x1x(32-1-3) = 28

As for 3 Steak, remember that Atkins is Wild.

So...
Reel 1 has 1 Atkins and 2 Steak
Reel 2 has 1 Atkins and 3 Steak
Reel 3 has 1 Atkins and 2 Steak
Reel 4 has 1 Atkins and 2 Steak

We need Reels 1-3 to either have Atkins or Steak. But not 3 Atkins because 3 Atkins pays more than 3 Steak. Then the fourth reel may be anything but Atkins or Steak, and the fifth reel can be anything.

[(1+2)*(1+3)*(1+2) - 1*1*1]*(32-1-2)*32 = 35*29*32 = 32,480

Hope this clears things up a bit for you.

Got it! big thanks! however, when I get down to 3 Atkins in a row, I tried the same method, I am deducting Atkins(1), Steak(2), Ham(3), Drumstick(2), Sausage(4) and Eggs(3) on the 4th reel since they all have a higher pay, then I get this
1*1*1*(32-1-2-3-2-4-3)*32=544
it is still 31 off from 513 in the chart.
Would you know where I went wrong at all? Thanks!

Yeah unfortunately that method wont work with the Atkins symbol because it's wild and sometimes it will make 5 of a kind with higher pays if you multiply by all 32 reels in reel 5.

So let's look at the symbols that pay 50 or less for 4 of a kind and the number of symbols for each in Reel 4/Reel 5:
4 Butter 50; 5 Butter 100; 3/4
4 Cheese 50; 5 Cheese 100; 4/3
4 Bacon 25; 5 Bacon 50; 5/3
4 Mayo 25; 5 Mayo 50; 4/3
Scale (brick for line pay); 1 on Reel 4

There is also 1 "Atkins" Symbol in Reel 5 that may need to be subtracted out as well.

So now:
3 Atkins with Butter in Reel 4: 1*1*1*3*(32-4-1) = 81
3 Atkins with Cheese in Reel 4: 1*1*1*4*(32-3-1) = 112
3 Atkins with Bacon in Reel 4: 1*1*1*5*32 = 160 (note we use all 32 now because 5 Bacon also pays 50 like 3 Atkins does)
3 Atkins with Mayo in Reel 4: 1*1*1*4*32 = 128
3 Atkins with Scale in Reel 4: 1*1*1*1*32 = 32

Total combinations: 513

Also as a general warning, we are placing payouts that are of equal value under the Atkins symbol here as well as those that pay higher. So later on, when doing something like 4 Butter which is also 50, you will also need to subtract out 1*1*1*3*(32-4-1), similar to what was done for the 3 Steak calculation. As you can see, doing this by hand is not super straightforward.

I see. I was about to write an excel sheet to generate numbers, I guess it's a bit too complicated.
Thanks so much for explaining the details though!!! Slot odds cal is very interesting =)

Quote: sheldor

I see. I was about to write an excel sheet to generate numbers, I guess it's a bit too complicated.
Thanks so much for explaining the details though!!! Slot odds cal is very interesting =)

If you're careful though, you can do it via spreadsheet. It's just not that easy. If you know the phyisical positions of the reels, it's likely easier to calculate with 5 nested loops running through all of possibilities and calculating the return from there.