Atkinson Diet Slot Problem

Dear Wizard / Hi guys,

I have a problem with understanding something on the Atkinson Diet slot which was designed by the wizard.
It's regarding the total possible cases of Wild 4-in-a-row.
The wizard mentions that 28 cases of this are existed.
What I don't understand is how come 28 and not 31.
Let's say all of the four reels are "Wild". Now, the fifth reel can have 32 different cases - The "wild" case is excluded because then it will be 5-in-a-row.
Still, I have 31 different symbols which can occur. Each one of them will give me the case of wild 4-in-a-row.

Even if I try to calculate it:
The probability of four in a row is (1/32)X(1/32)X(1/32)X(1/32)X(31/32)
total cases number is 32 X 32 X 32 X 32 X 32
The number of cases of 4-in-a-row: Probability X total cases number = 31

What am I missing?

Thanks

The game pays the highest line combination. If there are symbols that pay more for 5 of a kind than the 4 wild pay, you must subtract those hits.

For instance, if 5 AA symbols pays 2000 and 4 WW symbols pay 1000, then the combination WW WW WW WW AA will be evaluated as 5 AA and not 4 WW.

Thanks, I was loosing sleep over this one.

So, number of options should be caculated manually?

Quote: wizardofslots

So, number of options should be caculated manually?

For someone like me, I find it easier and faster to iterate through each possible combination to determine its highest-paying outcome, and then update a running total for that outcome. To me, this is easier than figuring out the formula for each outcome.

Also, you don't have to iterate through every single reel position, just each unique possible combination, and weight the result accordingly before updating the running total.

They often are - broken out by sub-type, etc. There are as many ways to do these sorts of calculations as there are slot machines. I've got a very complicated (but very fast) set of formulas that is trade-secret and which forms the basis of my consulting work. Regardless of whatever method you choose, just make sure you abide by the rule "only highest award paid per line." If your calculations don't accurately reflect that, but the game implementation pays that way, your math will be off.

I do my work with manual calculations and with an automatic hit counting program. Often, I will start developing a game with the automatic hit counter, then I will later add formulas so the game designers can mess around with numbers if they want to. Also, formulas make it very easy when changing the reel weights.