Slot Mathematics

[SlotDesigner]

I'm not sure if this is of interest here or not, but I've written a brief introduction to Slot mathematics.

http://slotdesigner.com/publications/

First post to keep my account alive.

[ROCKET]

 
GOOD READING MATERIAL THANK YOU ..  

[a69mopar]

Hi Robert,
   Interesting read, thanks for posting.  Makes me want to try the slot designer software.

Thanks,
Wayne

[CommTech]

Welcome to New Life Games Robert! 
Thanks for that great information! 

[SlotDesigner]

Thanks for the feedback. I probably won't be posting here very often, but I'll try and let you know when I make updates.

If anyone has any suggestions for topics that I could include in future updates please let me know (I can't promise to add everything as there's quite a narrow focus to the book).

Robert

[dpalmi]

Wow!  That made my head hurt....

 

Good stuff

Dan #2

[SlotDesigner]

There's a second edition of the math book on the website now.

[TZtech]

Thanks again for making this available publically - Great info
Have you considered working with someone like Quixant (http://www.quixant.com/) or Heber (http://www.heber.co.uk/our-expertise/gaming/) to produce a fully integrated package for a rapid application developement platform for slot machines ?

Also any thoughts on this thread - http://newlifegames.net/nlg/index.php?topic=241.msg21985#msg21985 (Reply 42) from a gaming mathematician perspective would be great.
In the unit I currently work in we need to investigate any games that have a 3% +  - from the theoretical RTP over a 12 month rolling period.

[StatFreak]

Robert, you old SOB!!! I never thought I'd be touching base with you again. It's been five years. You were working on the ReelPower portion of the software when we last talked.

I just found this thread and as soon as I saw the Australian address on your linked page I knew it had to be you. Then I checked the Home page and saw the familiar screen image of your software.

       We're very glad to have you with us!!



I haven't had a chance to peruse the book yet but I will certainly do so.   Okay, I couldn't resist reading it before I finished posting.

I do have a question regarding free games. The examples and code sample shows a scenario with a closed set of free games. If the theme has an open-ended number of free games (where more can be won during the free bonus round) but has a fixed maximum number of games, do you call the free game calc subroutine recursively to calculate the total RTP or use the average number of free games expected for the calculations? (equations 27 and 28)

If the bonus has no maximum number of free spins, how does using a calculated average of the number of free games and RTP affect the detailed breakdown analysis of the bonus?


I hope your software company is doing well. The finished product looks fantastic.

Stat

[SlotDesigner]

Hi TZTech, I've thought about rapid application development for slot machines, but the tools I have are really only for mathematics design and prototyping. I've done a lot of platform development before and I'm not really interested these days, apart from the bits that relate to maths. Maths is great and there seems to be no end to it. Regarding the other forum thread, its not really my thing, but I've asked a game designer I know if he's interested in answering it - Leo has a PhD in maths and is a serious gaming mathematician.

Statfreak, 5 years, hard to believe. I'm doing pretty well, just way to busy (hence not much posting here). There's another equation you can use when there's a maximum number of free games. I'll have to look it up and I'll see about adding it to the next version. I think Leo can answer your questions better than I can.

[StatFreak]

Thanks Robert. I had forgotten about that old thread TZTech mentioned and am also interested in hearing what Leo has to say about it -- in particular: whether it's possible to offer viable (from the casino's perspective regarding risk) high volatility themes in games with very long cycles and how to address the casinos concerns, why many of these games seem to have incomplete PAR sheet data, and if there is a solution to the problem.

..and the answer to my question. 

[Leo]

...but I've asked a game designer I know if he's interested in answering it - Leo has a PhD in maths and is a serious gaming mathematician.

Thanks for your introduction, Mr. SlotDesigner. It's good to be here!

If the bonus has no maximum number of free spins, how does using a calculated average of the number of free games and RTP affect the detailed breakdown analysis of the bonus?

If the bonus has no maximum number of free spins, the calculated average is just the way to go, as it it the convergent geometric series in Equation 27.
If it does have a maximum number of free spins (as seems to be the case for most land-based machines but barely ever online), that series truncates at the maximum number of re-triggers. Slightly more complex when the number of additional spins are themselves selected from a probability distribution, but it's the same principle. What exactly do you mean by breakdown in this context? Each spin has the same detailed table in terms of how much each win category contributes to the return, regardless of how many spins that have been awarded at the end of the day, so I suppose the short answer to your question would be "not at all".

L

[StatFreak]

Leo, welcome to the forum, and thank you for answering my questions.

My asking about the breakdown of detail might have been rooted in the past, where PAR sheets were required to detail exactly how many of each particular outcome would occur for every permutation, which clearly doesn't apply to these newer games.

An example which comes to mind is the bonus round in a Gamemaker game which can start with as few as two and as many as five special symbols in the window (one on each reel), from left to right. They lock and the rest spin, with extra spins awarded for each successive locked reel and winners paid for each spin. It ends with all five locked or after the spins run out. The PAR had many pages that detailed every possible outcome.

Regulators are slow to change but I should have realized that they would have to accept calculated average payouts for open ended bonus rounds.

It seems to me that it would still be possible to calculate the standard deviation for a given number of trials in order to offer a volatility index table in the PAR sheets, even with these open ended games. Am I wrong? If I'm right, why would the PAR sheets TZtech was discussing in our old thread fail to offer this information?

[StatFreak]

Thanks Robert. I had forgotten about that old thread TZTech mentioned and am also interested in hearing what Leo has to say about it -- in particular: whether it's possible to offer viable (from the casino's perspective regarding risk) high volatility themes in games with very long cycles and how to address the casinos concerns, why many of these games seem to have incomplete PAR sheet data, and if there is a solution to the problem.
...

I'm still curious about your opinion regarding the viability of high volatility games with very long cycles that cannot be achieved in the lifetime of the machines on the casino floor.

TZtech related that casinos are uneasy about such games, even though the top prize odds aren't nearly as long as a full cycle of combinations (usually better than 17 million to one.) The current lineup of games suggests that most, if not all, are being designed as low volatility games. (Possibly to address these concerns?) Does that mean that as these very long cycle machines take over the gaming floor that players will see the end of higher volatility themes?

[StatFreak]

P.S. Leo, I found your blog. That will keep me busy for a while.     Cool.


SF

[StatFreak]

Your blog article, "Line Up," addresses the volatility issue somewhat. However, more and more games require the player to play all lines, with bets in multiples of the number of lines plus any bonus purchase. Even with those that don't, I am forced to wonder how many players looking for more volatility would ever consider betting fewer lines on the same game to achieve their desired game flow? Many gamblers don't even understand how lines affect volatility.

[Leo]

...I am forced to wonder how many players looking for more volatility would ever consider betting fewer lines on the same game to achieve their desired game flow? Many gamblers don't even understand how lines affect volatility.

Hi StatFreak, nice to know that you found my blog!

Players do, to a great extent, play the maximum number of available lines, and, as you say, most players would not even be aware that they can actually affect the volatility themselves. It is therefore important from a game designer's perspective, which is what the blog post is meant to emphasize, to adapt the maximum number of lines to the desired playing experience.

L

[StatFreak]

Hi StatFreak, nice to know that you found my blog!

Players do, to a great extent, play the maximum number of available lines, and, as you say, most players would not even be aware that they can actually affect the volatility themselves. It is therefore important from a game designer's perspective, which is what the blog post is meant to emphasize, to adapt the maximum number of lines to the desired playing experience.

L

That brings us back to my previous question. How do you assuage the fears of casino executives that a high volatility game (say, at max bet, max lines) with several hundred million or a billion plus combinations isn't going to adversely affect their bottom line during its relatively short life in their establishment?

I have never seen a 5-reel, gazillion line machine with anywhere near the volatility of, say 5-times pay 3-reel cm, let alone 10 times pay 3-reel cm. There are players who are looking for that level of volatility (or something closer to it than to the current lineup of 5-reelers.) What happens when all the 3-reelers are gone and we're left with 5-reelers with 30+ lines with forced bets of multiples of 30+ (all lines must be played)? That is certainly where we seem to be headed, at least in Nevada.

It's almost impossible to find one of these machines that let the player bet only one line. And in those cases, the only bet is one coin because subsequent coins are forced to other lines and must be distributed evenly.



Or are we training a new generation of gamblers to accept and expect these low volatility themes where they win almost every spin but win less than they actually bet with occasional medium level pays and virtually no large pays? I guess that's a philosophical question and not a math question, but the game mathematicians are certainly in a position to steer or influence the trends.

[TZtech]

Leo

Welcome to NLG and thanks for taking the time to reply. will be checking out Your blog as soon as I get a gap.


Robert

Posted your link on www.slottechforum.com which has a wider user base of active Slot techs.

[mohican]

Thank you Robert.  Good reading materials.