Davita
Davita
  • Threads: 7
  • Posts: 18
Joined: Nov 20, 2014
November 20th, 2014 at 11:46:44 AM permalink
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
miplet
miplet
  • Threads: 5
  • Posts: 2105
Joined: Dec 1, 2009
November 20th, 2014 at 12:08:44 PM permalink
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.
“Man Babes” #AxelFabulous
AxelWolf
AxelWolf
  • Threads: 164
  • Posts: 22272
Joined: Oct 10, 2012
November 20th, 2014 at 12:41:08 PM permalink
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.
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
Davita
Davita
  • Threads: 7
  • Posts: 18
Joined: Nov 20, 2014
November 20th, 2014 at 1:53:16 PM permalink
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
Mission146
Mission146
  • Threads: 142
  • Posts: 16832
Joined: May 15, 2012
November 20th, 2014 at 2:11:56 PM permalink
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.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
JB
Administrator
JB
  • Threads: 334
  • Posts: 2089
Joined: Oct 14, 2009
Thanked by
MichaelBluejay
November 20th, 2014 at 2:47:32 PM permalink
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.
Davita
Davita
  • Threads: 7
  • Posts: 18
Joined: Nov 20, 2014
November 21st, 2014 at 3:19:33 AM permalink
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 :)
Davita
Davita
  • Threads: 7
  • Posts: 18
Joined: Nov 20, 2014
November 21st, 2014 at 9:16:44 AM permalink
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?
Davita
Davita
  • Threads: 7
  • Posts: 18
Joined: Nov 20, 2014
November 21st, 2014 at 9:39:56 AM permalink
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
DRich
DRich
  • Threads: 86
  • Posts: 11596
Joined: Jul 6, 2012
November 21st, 2014 at 10:02:18 AM permalink
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.
At my age, a "Life In Prison" sentence is not much of a deterrent.
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1909
Joined: May 10, 2011
Thanked by
DorukanjrrrMichaelBluejay
November 21st, 2014 at 10:38:35 AM permalink
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.
I heart Crystal Math.
Mission146
Mission146
  • Threads: 142
  • Posts: 16832
Joined: May 15, 2012
November 21st, 2014 at 1:57:44 PM permalink
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.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
  • Jump to: