5 Reel Game Combinations

Hello Im new in forum and i want to have some info because im too comfused about the way to calculate the combinations of
a slot machine game.
Lets start with a game with 3x5 reel and 9 line

the symbols :
R1 R2 R3 R4 R5
ITEM1 2 2 2 2 3
ITEM2 4 2 6 8 2
ITEM3 6 4 7 4 3
ITEM4 7 8 5 8 6
ITEM5 8 10 10 7 7
ITEM6 9 11 4 5 9
ITEM7 10 11 7 4 10
ITEM8 11 11 10 7 8
ITEM9 11 6 12 9 8
ITEM0 11 7 11 12 9
SCATER 2 2 2 2 3
SUM 81 74 75 68 68


Can please anyony explaine the way to make mathimatec all the combinations?

Thank you

I suggest you read the following articles, as well as some of the items that are linked.

https://wizardofodds.com/play/slots/atkins-diet/
https://wizardofodds.com/games/slots/

Yes but there is no mathematic formula tha i can use for make all the combinations?
5 in a row for example is r1*r2*r3*r4*r5......

There are two basic approaches:

1) The mathematical approach. Come up with formulas for each X in a row of symbol Y. Keep in mind that with a Wild symbol, the formulas will get a little more complicated for two reasons: the extra symbol, and the possibility of X in a row of Wild symbols paying more than Y in a row of symbol Z. Typically only the higher-paying combination is paid in such situations.

2) The brute-force approach. Write some computer code to iterate through every possible combination to determine the highest-paying win. I recommend using only the unique combinations and weighting them accordingly to keep the processing time under 1 second.

Also keep in mind that scatter symbols are calculated differently than payline symbols.

Im interest for an example of mathematic approache if you can.
The brute force is not a academic way but a practic to see if the theory is ok.

Thank you.

I use the brute-force approach myself because it is less susceptible to errors, and reusable regardless of how many symbols there are. I'll let others chime in with mathematical examples if they wish.

So you have a program you put the symbols and get the results?
All like practice?
You dont want to see if the theoritical is the same to practice?


Thank you.

Quote: billyboy

So you have a program you put the symbols and get the results?
All like practice?
You dont want to see if the theoritical is the same to practice?


Thank you.

I use both. I start by using a program, which is not a simulator; it actually counts all win combinations. When I get close to what I want, I insert formulas, which give identical results. The reason I do this is so the client can alter things and have them update real time in excel. When they're done, I make sure that all the numbers are still right.

Can you please give me a link for your program?

Quote: billyboy

Can you please give me a link for your program?

It is custom software that I wrote. My apologies, but I will not be distributing it.

Need a program like this if anyone can give me a link for test.

Thank you

Mine is also custom written, and unfortunately I will not be making it available either.