5 reel video slot Combinations calculation

Now, I now this is a rehash of<-- this thread, but I didn't really understand the magic behind combination calculation.
We have 5 reel, each of one with 32 symbols. Can anyone explain in laymen's term how to calculate each winning combination?

Thank you very much

Lots of threads on this. The one you link to plus:
https://wizardofvegas.com/forum/questions-and-answers/math/4639-scatter-math-question/
https://wizardofvegas.com/forum/gambling/slots/4596-looking-for-information-on-atkins-diet-5-reel-slot-machine-on-wizard-of-odds/

Ask any other questions you may have after reading all the posts in those threads.

Quote: Davita

Now, I now this is a rehash of https://wizardofvegas.com/forum/questions-and-answers/gambling/6269-5-reel-video-slot-combinations-calculation/ <-- this thread, but I didn't really understand the magic behind combination calculation.
We have 5 reel, each of one with 32 symbols. Can anyone explain in laymen's term how to calculate each winning combination?

Thank you very much

do u understand that the number of symbols are not the key? its how often the symbols hit the paylines. You have to track that.

Thanks for the links. Actually, I'm looking for a scatter free game formulas. I'm trying to build a game with line winnings + wild. no scatters. That's why I'm looking how to calculate all possible winning combinations to calculate payrate. I'm a newbie here, so sorry if I'm asking something obvious.

Thanks

Quote: Davita

Thanks for the links. Actually, I'm looking for a scatter free game formulas. I'm trying to build a game with line winnings + wild. no scatters. That's why I'm looking how to calculate all possible winning combinations to calculate payrate. I'm a newbie here, so sorry if I'm asking something obvious.

Thanks

Okay, you said you have five reels and thirty-two symbols per reel.

Let's say you have cherries and you have Free Games, now, let's say you put four cherries on each of the first three reels, two cherries on the fourth reel and two cherries on the fifth reel. We're going to look at the probabilities per line bet, here, and we'll say that either three, four or five cherries pays.

The probability of hitting five cherries is:

1/(4/32 * 4/32 * 4/32 * 2/32 * 2/32) = 1 IN 131072.077846 (Obviously, this is ridiculous for five cherries, but I just picked some numbers off the top of my head for the reels)

The probability of hitting four cherries is the same, except the fifth thing is anything that is not a cherry:

1/(4/32 * 4/32 * 4/32 * 2/32 * 30/32) = 1 IN 8738.13333333

The probability of hitting three cherries is the same, except the fourth thing is anything that is not a cherry:

1/(4/32 * 4/32 * 4/32 * 30/32) = 1 IN 546.133333333

There would probably be more cherries than that, though, if cherries are the lowest-paying winning result.

Anyway, figuring something out like probabilities for a five-reel thirty-two assignment slot machine is pretty easy, really. You just figure out your Line Pays, Bonus Rules and then determine the probabilities using the number of stops.

You're better off writing a program to analyze it, as there is less opportunity for error. This is especially true when, for example, 2 wilds pays more than 4 Aces, and you're studying Wild-Wild-Ace-Ace combinations. Just iterate through the possibilities, seeing which pays are possible, and picking the highest one (incrementing its combination count accordingly). Using only formulas for a 5-reel game is of course possible, but much more of a headache, when you can just write an analyzer once and reuse it for many games.

I see. Thank you very much, I'll go that way then. If I'll have any questions, I'll ask here if you don't mind :)

Quote: Mission146

Okay, you said you have five reels and thirty-two symbols per reel.

Let's say you have cherries and you have Free Games, now, let's say you put four cherries on each of the first three reels, two cherries on the fourth reel and two cherries on the fifth reel. We're going to look at the probabilities per line bet, here, and we'll say that either three, four or five cherries pays.

The probability of hitting five cherries is:

1/(4/32 * 4/32 * 4/32 * 2/32 * 2/32) = 1 IN 131072.077846 (Obviously, this is ridiculous for five cherries, but I just picked some numbers off the top of my head for the reels)

The probability of hitting four cherries is the same, except the fifth thing is anything that is not a cherry:

1/(4/32 * 4/32 * 4/32 * 2/32 * 30/32) = 1 IN 8738.13333333

The probability of hitting three cherries is the same, except the fourth thing is anything that is not a cherry:

1/(4/32 * 4/32 * 4/32 * 30/32) = 1 IN 546.133333333

There would probably be more cherries than that, though, if cherries are the lowest-paying winning result.

Anyway, figuring something out like probabilities for a five-reel thirty-two assignment slot machine is pretty easy, really. You just figure out your Line Pays, Bonus Rules and then determine the probabilities using the number of stops.

Correct me if I'm wrong, but this works only in this pattern CCCCX, where C = Cherry and X anything else. So the probability of CCCCX = 1 IN 8738.13333333, but XCCCC also is a win and has a different probability, which is =1/(28/32 * 4/32 * 4/32 * 2/32 * 2/32) = 18724.57143
so I guess to calculate the winning probability I should add 8738.13333333(CCCCX) to 18724.57143(XCCCC) wich would be 27462.70476?

Thanks again.

P.S. BTW, could you also please explain how line pay works? If I have a probability of winning say 4 cherries, how do I calculate how much to give back?

Quote: JB

You're better off writing a program to analyze it, as there is less opportunity for error. This is especially true when, for example, 2 wilds pays more than 4 Aces, and you're studying Wild-Wild-Ace-Ace combinations. Just iterate through the possibilities, seeing which pays are possible, and picking the highest one (incrementing its combination count accordingly). Using only formulas for a 5-reel game is of course possible, but much more of a headache, when you can just write an analyzer once and reuse it for many games.

Thanks for the info JB. I'm quite familiar with software development, I've just have no idea how to do the analyzing part. Should it be done with brute force style? I mean, looking at each possible combination and picking the winners? Or is there a better way to do it?
Thanks again

Quote: Davita

Thanks for the info JB. I'm quite familiar with software development, I've just have no idea how to do the analyzing part. Should it be done with brute force style? I mean, looking at each possible combination and picking the winners? Or is there a better way to do it?
Thanks again

Just do brute force. A 5 reel with 32 symbols per reel should only take a fraction of a second to run through with modern computers.

Quote: Davita

Thanks for the info JB. I'm quite familiar with software development, I've just have no idea how to do the analyzing part. Should it be done with brute force style? I mean, looking at each possible combination and picking the winners? Or is there a better way to do it?
Thanks again

This is the easiest way.

I calculate nearly all of my games in Excel and via brute force. I like using Excel because I can change the reels and have a real time update to the return, but I always verify my calculations with a brute force program to make sure my manual calculations are correct.

Quote: Davita

Correct me if I'm wrong, but this works only in this pattern CCCCX, where C = Cherry and X anything else. So the probability of CCCCX = 1 IN 8738.13333333, but XCCCC also is a win and has a different probability, which is =1/(28/32 * 4/32 * 4/32 * 2/32 * 2/32) = 18724.57143
so I guess to calculate the winning probability I should add 8738.13333333(CCCCX) to 18724.57143(XCCCC) wich would be 27462.70476?

Thanks again.

P.S. BTW, could you also please explain how line pay works? If I have a probability of winning say 4 cherries, how do I calculate how much to give back?

I'm afraid you are incorrect, unless you want to design a machine that plays two ways, and they do exist, but for most machines, the first reel would have to be a cherry to pay for cherries.

You calculate how much to give back based on all possible winning combinations and the probability thereof, so if you want to return a certain percentage overall, you can decide whether to make the bulk of the return Bonus heavy, low pays heavy, mid-pays heavy, high pays heavy or a combination. I would suggest most modern slot machines the bulk of the return comes from low pays and Free Games/Bonuses.