Basic Math Software

Hi,

Having worked in casinos I of course have thought of lots game ideas, But one particular one I can't shake and I've decided to look at it further.
So I was wondering is there any software out there to help with the basic math and probability.

Thanks

I don't know what to say.

I'm guessing it's a stupid question then, but thanks.

I can work out the basic probability for each event, I know the odds that I feel should be offered I'm just trying to see how combining all the events and there probability fit with odds.

I'm looking for a starting point of sorts, this site was recommended, I guessing I didn't explain myself to well and probably still haven't, but again rsactuary i'd just like to say thanks.

I think most of the math guys use the same thing: Excel.

I don't mean to sound like a smart-ass, but what kind of answer did you expect from such a vague question?

Quote: P4R4GON

Hi,

Having worked in casinos I of course have thought of lots game ideas, But one particular one I can't shake and I've decided to look at it further.
So I was wondering is there any software out there to help with the basic math and probability.

Thanks

I'm not a math guy but I try to be a nice guy. Welcome to the forum!

Probably something along the lines of your answer. To be honest I never considered Excel, more fool me, I use it for so many other things and only really simple math.

I think I'm just a bit duanted at working out the odds for the main bet to my game, and was looking for an easier way.

1BB - Thanks

Maybe you need to look into some of Excel's more obscure functions.

One that gets used and mentioned here a lot is Combin (combinatorial).
For example:
=combin(52,5)/4 is the 1 to x odds of dealing a Royal Flush in stud poker (divide by 4 since you don't care about the suit).
Fact (factorial) could also be used:
=fact(52)/fact(47)/fact(5)/4

Does that help get you started with basic math?

I don't quite understand what you're asking. IT SEEMS to me, like you're unsure of how to do the math or when to use which formula. If that is the case, then the answer is (kind of) simple: study up! Get a book on statistics or look stuff up online. Lots of good stuff on YouTube believe it or not (Khan Academy is awesome with about any subject, mostly math related).

Or just ask here if you're not sure. Lots of math people can figure weird stuff out.

If you understand the math and how to work it out, then Excel is probably the easiest to use and learn. It's pretty confusing sometimes (I'm definitely no master at it)....but it comes in great when you want to do weird math stuff. Hell, the Wizard generated a blackjack basic strategy table only using Excel!!! Look up the formulas/functions and whatnot that you can use in Excel, like DJTB mentioned.

MATLAB is coded similarly to java, so if you know java then that's an option. Mathematica for abstract math, which you probably won't be doing.

Excel is simple and easy, stick with that if you don't know java, or know java and don't want to learn MATLAB.

Those are the three math based programs I used in engineering and personally would be comfortable considering if I were in your shoes.

Quote: ahiromu

Excel is simple and easy.

Unless you know VBA, Excel is worthless for all but the easiest games. Most of my analysis is done in C or C++. Some in Java and some in VBA. I sometimes export data into CSV files and complete the analysis in Excel. The only native Excel (without VBA) work I do is creating PARS for slots.

Hi, P4, and welcome to the forum!

I would suggest you read back in the Game Inventor's Corner (this one) and the Math forum particularly; there's years of archives discussing the sort of things you're trying to understand.

There are also several people who do provide professional services on gaming math who are active here; CrystalMath, CRMousseau, Miplet, and MathExtremist come to mind, all in the US. charliepatrick is in the UK. (These are the people I've spoken to - and recommend - about various math questions on my game designs.) There are others, (including Wizard and teliot who don't work with private inventors any more), you may notice in those threads.

And, yes, Khan Academy is a great resource!

Good luck, and don't be afraid to ask specific math questions here; the guys like a challenge from time to time. :)

Quote: P4R4GON

So I was wondering is there any software out there to help with the basic math and probability.

Thanks

i like this one
https://www.mathsisfun.com/

click the DATA button
lots of fun there is

and have fun

You can do the prob and stats course at Khan Academy for free:

https://www.khanacademy.org/math/probability

You can do a intro to stats class for free at Udacity:

https://www.udacity.com/course/intro-to-statistics--st101

Of course you can take a intro to stats course at your local community college.

Regardless of your choice, whenever you encounter a new topic or concept after you get it right according to the book, ask yourself how it can be applied in a casino setting.

Welcome to the forum P4R4GON! Those ideas that continue to haunt you are the ones that demand you take some action, so I wish you well; joining here is a step in the right direction.

Am I right in assuming that you're in the early stage of wanting to verify the mathematical feasibility of your idea? And that even if you could figure out how to do the math, you wouldn't feel comfortable with the accuracy of the results? If the answer to both is "yes," then it sounds like you need to investigate the cost of getting a professional mathematical opinion ... and a complete analysis if you get a 'green light' on the viability of your game. Of course, the cost would vary depending on the mathematician and complexity of the project. But you will eventually need this anyway if you decide to go forward with the game.

Most, if not all, of the math professionals who specialize in the casino industry are members on this site. Just say "HELP!" and you'll get some names and recommendations. There are others here who are very good at casino game mathematics and happy to help by answering specific questions, but they can't help much beyond that if they don't know the rules of the game, and you need to take steps to protect your idea before publicly disclosing the rules (a simple Non-disclosure Agreement works as a general rule for private disclosres).

My experience with the professional mathematicians that I've worked with makes me comfortable getting math advice and reports on new unprotected concepts without an NDA, confidentiality being understood without any formality.

Eliot is right about Excel. The basic rule of thumb for me is if the game involves cards and a player or dealer decision point, it probably requires custom software. There are some smaller strategy card games I've been able to do in Excel, but I also have several Excel sheets over 30Mb. Most of the new strategy games I do require software.

There is no such thing as a basic math package that will let you plug in the details of your new casino game and spit out the odds. Those will be new calculations that nobody's ever done before, so they have to happen for the first time somehow either in Excel, some other stats package, or as custom software. If the math isn't being done for the first time, then you're not really the first person to work on the game...

So what kind of game have you developed? If it's dice, roulette, or a non-strategy card game, there's a good chance someone here will run the numbers in Excel for you (for free, because there are a lot of helpful people here).

Quote: MathExtremist

So what kind of game have you developed?
If it's dice, roulette, or a non-strategy card game, there's a good chance

i hope it is a dice game
and how good?
over/under 50%

Quote: MathExtremist

someone here will run the numbers in Excel for you (for free, because there are a lot of helpful people here).

i say not just
because there are a lot of helpful people here
many just love to do math, because it is fun!

go figure!
and not just this figure
362436

Quote: P4R4GON

I'm guessing it's a stupid question then, but thanks.

I can work out the basic probability for each event, I know the odds that I feel should be offered I'm just trying to see how combining all the events and there probability fit with odds.

I'm looking for a starting point of sorts, this site was recommended, I guessing I didn't explain myself to well and probably still haven't, but again rsactuary i'd just like to say thanks.

Before looking for a math expert, you should just PLAY THE GAME many hundreds or thousands of times on your kitchen table and register the win/loss/push results or other stats. The exercise could give you the bulk of numbers U need. Many a game could have a converged result within hundreds / thousands of hands. If you can play 60 hands per hours, this initial work will only take a couple of days. Prove of concepts.

Feel free to PM me the game. I can sign a NDA if you want.

Quote: miplet

Feel free to PM me the game. I can sign a NDA if you want.

And Mips is an excellence resource for early number crunching on game concepts. I have used him several times as he is cost effective when you just aren't sure if he game really works.....Mips will let you know for less than having a full blown math report completed.

CMousseau is who I have used and recommend if you have a game that passes the initial analysis and want to get a report you can provide during marketing. I have also been very pleased with his work.

Good luck and as BBB suggested, you should read/buy this book before spending too much time & $$ Contemporary Casino Table Game Design.

Quote: mustangsally

i hope it is a dice game
and how good?
over/under 50%
i say not just
because there are a lot of helpful people here
many just love to do math, because it is fun!

go figure!
and not just this figure
362436

362436, that's almost as special as Pi...

Quote: P4R4GON

Hi,

Having worked in casinos I of course have thought of lots game ideas, But one particular one I can't shake and I've decided to look at it further.
So I was wondering is there any software out there to help with the basic math and probability.

Thanks

As you can see, you don't seem to be able to just go buy something that will solve your problems. Interesting I say. At least you got more polite responses than I did when posing a similar question a couple of months ago. I would think that some savvy software company would 'sell' a powerful simulation program to all of us 'inspired' gamblers ( after all, there is a whole new crop every year)) One that doesn't require counting cards. If you find one, or figure out how to do it yourself on ExCell, pls let me know. And the best of luck to you!

Quote: TwoFeathersATL

I would think that some savvy software company would 'sell' a powerful simulation program to all of us 'inspired' gamblers ( after all, there is a whole new crop every year)) One that doesn't require counting cards.

There already are companies that have apps designed to allow gamblers to simulate a variety of scenarios. But they are only for games that already exist.

Writing a simulator to handle a variety of situations when you don't even know the rules is impossible and would have a very small customer base. That's why it doesn't exist.

Quote: P4R4GON

I'm guessing it's a stupid question then, but thanks.

I can work out the basic probability for each event, I know the odds that I feel should be offered I'm just trying to see how combining all the events and there probability fit with odds.

I'm looking for a starting point of sorts, this site was recommended, I guessing I didn't explain myself to well and probably still haven't, but again rsactuary i'd just like to say thanks.

It depends on what you mean by "combining all the events". Are the events related somehow - for example, if you are at "position A", there is a probability p of getting to position B1, and (1-p) of getting to B2, and if you are at B2, there is a probability q of getting back to position A?

This sort of thing ends up being more of a math problem than something you need to simulate, although there are some cases where you might want to simulate it first if the math is rather hard. (Also, it doesn't hurt to simulate it just to be sure that you did the math right.)
Personally, I use Microsoft Visual C# for my simulations; you can download a free version (Visual C# Express) from Microsoft.

However, just because you know how to write code doesn't mean that calculating things will be easy. There's a saying in computer science along the lines of, "The hard part of programming isn't writing the code, but figuring out what code to write in the first place." You can "dumb down" a language all you want coughCOBOLwheeze, but it doesn't make programming any easier.

P4R4GON -- I forgot that I made a video to explain gaming math, "A Brief Tutorial on Combinatorial Analysis."

Maybe it will help:

http://apheat.net/2013/03/13/video-a-brief-tutorial-on-combinatorial-analysis/

Quote: TwoFeathersATL

As you can see, you don't seem to be able to just go buy something that will solve your problems. Interesting I say. At least you got more polite responses than I did when posing a similar question a couple of months ago. I would think that some savvy software company would 'sell' a powerful simulation program to all of us 'inspired' gamblers ( after all, there is a whole new crop every year)) One that doesn't require counting cards. If you find one, or figure out how to do it yourself on ExCell, pls let me know. And the best of luck to you!

I think it's possible to get pretty close, that is, to expose the primitive elements to card games in a way that a non-mathematician can put them together in a lot interesting and novel patterns. I've been working on it on and off for a couple of years, but it's still a ways off. Roughly speaking, there will be a front end for both BJ-like and poker-like games where you can produce a demo and then a backend that can wrap those same rules up to perform the math. How long it takes depends on whether my second project catches traction.

Quote: DJTeddyBear

Writing a simulator to handle a variety of situations when you don't even know the rules is impossible and would have a very small customer base. That's why it doesn't exist.

Do you need a large customer base? If you offer it as a service and dramatically reduce the cost to get math done... You could still charge $1k instead of several(many?) times that and do ok, though it seems like the long term strategy would be to get bought out by Shufflemaster.

edit: I'd be very interested if anyone would want to take a stab at the value of such a program if it were flexible enough to cover 70% of the BJ/poker-like games reviewed on WOO

I think there are a range of tools available depending on how complicated the question is.

For a simple side-bet (e.g. 3-card Pair+ or one based on a collection of initial cards ) an excel spreadsheet will do the business, but you need to evaluate all the possibilities (e.g. Trips .... Pair) or run through all the perms.

Excel can also be used for Blackjack (infinite deck), but you need a bigger tool for finite decks (i.e. composition analysis). Similarly if you want to analyse complicated poker games (personally I've not tried this).

Another way, which I've been looking at recently, is running simulations. Assuming you're a competent programmer, it's relatively easy to generate millions or billions of shoes but you have to prove your random number generator and shuffling are correct; however the difficulty can come when working out a player strategy (assuming there is a decision to be made and it isn't obvious). I've found that using a basic strategy (for instance standard one for infinite decks on Blackjack) can give fairly close answers and help confirm theoretical numbers and other trends.

Quote: charliepatrick

Assuming you're a competent programmer, it's relatively easy to generate millions or billions of shoes but you have to prove your random number generator and shuffling are correct; however the difficulty can come when working out a player strategy (assuming there is a decision to be made and it isn't obvious). I've found that using a basic strategy (for instance standard one for infinite decks on Blackjack) can give fairly close answers and help confirm theoretical numbers and other trends.

What happens if you assume the other is not a programmer? Hasn't a clue where to begin, looked for off the shelf stuff, didn't find the product to fit the bill? This I see, I see too often.

Quote: TwoFeathersATL

What happens if you assume the other is not a programmer?

As Eliot says there are two ways to work out the House Edge - the first is Combinational Analysis and the second is Simulation.

The first could be done on paper if either it was a very simple side-bet or you enjoyed tapping at a calculator (I initially worked out infinite Blackjack on paper and a calculator). However if the game is more complicated then using a computer, whether excel or otherwise, is probably an easier option. In some games the player strategy has to be calculated for a range of possible hands, although for games such it becomes obvious except for a range of hands (e.g. 5-card poker: AKs). For some games, typically poker where lots of cards are used, it is nigh impossible!

The second approach requires sufficient trials to be statistically close enough to the result - for instance consider a simple Heads or Tails where the correct guess pays Evens. By definition it's a fair game so in theory has no House Edge. Suppose we ran a test of 100 tosses always calling Heads - then it is unlikely we'd get exactly 50; however if we tried it a million times, then the result is going to be much closer to 50% Heads. Just running the trials requires some form of coding and as using a built in random number generator is not really random enough (it cycles too often), one has to be created (I use the Mersenne one).

I think it's rather like asking whether you can calculate the tax return for a large company without writing your own code, buying an off-the-shelf product, or having a lot of accountancy staff; probably not.

I doubt there is a fill-in-the-gaps program as most analysis is done by experts who (I'm really guessing here) will have developed their own customized techniques and then adapt it or build new sub-routines for any new game. In my case last Easter I created a
(a) Random number generator
(b) Shuffling routine for decks (i) where suits don't matter (ii) where individual cards matter
(c) Dealing logic including remembering cards that have gone,
and plug in run the game (in my simple case using a fixed player strategy).

Others, analysing more complicated games, will have included a dynamic playing strategy that calculates the best option depending on the cards that have gone. This has to be exceedingly quick as it is done for every hand (or a clever way of remembering the decisions already made). For instance my simulations (being simple) always hit 16 vs 7. But in theory a comprehensive method has to decide on each occasion whether to hit 16 vs 7 (as sometimes it is correct to stand): to cycle through the six possibilities (Standing, Hitting getting Ace thru Five); for each of these work through all the permutations of hands the dealer can make and working out the chances of winning. That needs programming.


I haven't yet worked out how to run proper code using my PC (I use HTML scripting), so I imagine there are books for setting up the environment to run (compiled?) code and a manual on C++ or similar. Thus I'd be interested sometime, probably next Easter!

Quote: socks

Do you need a large customer base? If you offer it as a service and dramatically reduce the cost to get math done... You could still charge $1k instead of several(many?) times that and do ok, though it seems like the long term strategy would be to get bought out by Shufflemaster.

edit: I'd be very interested if anyone would want to take a stab at the value of such a program if it were flexible enough to cover 70% of the BJ/poker-like games reviewed on WOO

No, SHFL/Bally/SciGames would never need to buy a 3rd party software analyzer for arbitrary poker games. They already have their own resources. That'd be like trying to sell a video poker calculator to IGT. They've already got one, and even if yours worked better they still have no need of it. Numbers are numbers.

There's a fellow named Robert Muir who sells a slot machine calculator, mainly for rapid prototyping. That's useful for small game studios to get their math in line before actually locking things down. Naturally, it can't handle brand-new features. If you want to do a wild symbol that explodes and turns into three other symbols, the code for that feature isn't in there. So he does a lot of feature requests.

The big difference between slots and poker is that there are no predetermined odds for slots. The reels can contain whatever the game designer wants. But a poker game is almost surely going to use a standard 52-card deck, perhaps with a joker. You'll never see a "poker" game where the deck of cards includes only three aces but also has an eagle and a buffalo.

So I don't know how you'd estimate the value of such a program because I don't know who the market would be. Doing a bunch of custom code up front in the hopes that maybe you'll get some clients later in a market that's declining, that doesn't seem like a good business plan.

Quote: MathExtremist

So I don't know how you'd estimate the value of such a program because I don't know who the market would be. Doing a bunch of custom code up front in the hopes that maybe you'll get some clients later in a market that's declining, that doesn't seem like a good business plan.

Yes, my plan was bad. If I knew then, what I knew now... both in terms of the projects difficulty and the potential market. I saw an edge (which I still have confidence in) in the tools I was working with, and I ignored other parts of the equation.

That said, I never knew where to get off the project, and at his point, I have huge pieces of it done. Please don't say "sunk costs", I know, really, but lots of it are done. As a proof of concept, after replicating the MStud math last year (easy for an experienced mathematician, I know), I took my solution apart and re-expressed it in a very compact but flexible map based data structure. Then I wrote code to rewrap this data structure and produce the MStud result. I haven't filled out all the options to this data structure, but a number of optimized pieces are written. There is some speed loss, but it seems like most poker-likes are easy to break up and send to different computers, and I think pai-gow will be easy enough to do on a GPU.

Quote: MathExtremist

No, SHFL/Bally/SciGames would never need to buy a 3rd party software analyzer for arbitrary poker games. They already have their own resources. That'd be like trying to sell a video poker calculator to IGT. They've already got one, and even if yours worked better they still have no need of it. Numbers are numbers.

Are you saying they have internal tools that allows non-mathematicians to do the work for a large number of their table games? I certainly believe that's possible, but I wouldn't assume it to be the case.

Granted, they may not need it, as in, external pressure may not exist to force the issue through internal politics, depending on how things are organized internally. But, on some level, every corporation needs efficiency as it relates to costs/profits.

How many mathematicians does shuffle employ? I think I've read (here) that it's around 100. Replacing a small number of those mathematicians with half as many smart-ish high school grads should be worth a lot.

Quote: MathExtremist

There's a fellow named Robert Muir who sells a slot machine calculator, mainly for rapid prototyping. That's useful for small game studios to get their math in line before actually locking things down. Naturally, it can't handle brand-new features. If you want to do a wild symbol that explodes and turns into three other symbols, the code for that feature isn't in there. So he does a lot of feature requests.

The big difference between slots and poker is that there are no predetermined odds for slots. The reels can contain whatever the game designer wants. But a poker game is almost surely going to use a standard 52-card deck, perhaps with a joker. You'll never see a "poker" game where the deck of cards includes only three aces but also has an eagle and a buffalo.

I've seen his site, and I had figured that feature requests would be a necessary part of my business model, especially early on.

I've worked on the BJ side more recently, and I'm allowing the user to create new rules to an extent, things like "triple down when hand total=7", "bonus if triple-downed and 2 7's are drawn" (ie "7"/7/7), or "allow 3 way split when three consecutive cards". This will be done from drop down menus containing data and operations. Obviously the math on the 3-way split is hard unless you limit it to one split, but that's going to be the case anyway. Poker-likes could have similar rules, like 3 card poker where if you get a run of cards, you can split your hand.

Having easily accessible tools to allow indie's to rapidly prototype, publish demos, and test the math on such games may create additional demand there, as well, I think.

So, yes, I should've cronfronted some big questions early on. I'm not spending much time on this atm, but my inclination is to continue with the project unless someone can say some combination of... "I know SHFL employs 10 mathematicians", "I know SHFL has advanced/flexible GUI tools to do this sort of thing" And/or "The size of the non-SHFL market is $XX" where XX is a shockingly depressing #.

Quote: socks

There is some speed loss, but it seems like most poker-likes are easy to break up and send to different computers, and I think pai-gow will be easy enough to do on a GPU.

This is the part I haven't taught myself yet, either farming out to EC2 or GPGPU programming. On the other hand, I've only really ever needed to do that once, that is, going beyond what a single CPU can handle. I've got a VP project I'll be working on this summer that may require that, so it'll be time to put on the new-tech hat again. (It's not standard video poker, the odds change dynamically on the draw depending on your hold cards.)

Quote:

Are you saying they have internal tools that allows non-mathematicians to do the work for a large number of their table games? I certainly believe that's possible, but I wouldn't assume it to be the case.

No, what I'm really saying is that they don't have such a large enough number of table games that it would matter. Think about how many different slot games are produced every year and contrast that with how many table games come out. As market leader, SHFL knows that if they have a new hit, it's likely going to replace one of their other products. So they're cannibalizing. The last thing they want to do is flood the market with more products that don't meaningfully increase their market share. That's just not good business. If you want to do some market research, look into the # of proprietary table games in NV casinos over the past few years. You can get the stats from gaming.nv.gov. Right now there are about 300 "other" games and that includes UTH and MStud (but not BJ side bets).

Quote:

How many mathematicians does shuffle employ? I think I've read (here) that it's around 100. Replacing a small number of those mathematicians with half as many smart-ish high school grads should be worth a lot.

I'm pretty sure IGT doesn't even employ 100 mathematicians. They don't have that many studios. In my consulting practice, I probably average over a dozen slot games a year for various clients, and that's not even half of my billable hours. If IGT had 100 full-time slot mathematicians they'd be cranking out thousands of games per year (which they don't). With SHFL, I'm pretty sure they have just two or three people who work on their stuff. Even if it takes someone two months full-time to do a game (does it take you two months?), that's six per year with just one game designer. SHFL doesn't really produce six totally new games/year. Plus, a lot of what they do produce is repurposed from one game to another, things like 5-card poker side bets. For that you just use a spreadsheet and you're done in an hour or less.

Quote:

Having easily accessible tools to allow indie's to rapidly prototype, publish demos, and test the math on such games may create additional demand there, as well, I think.

Sure, but remember who you're dealing with in that market. Most independent game inventors have little or no funding for things like lawyers or mathematicians. I get a lot of emails from inventors who basically say "I just invented cool new game X, all my friends like it and I know it'll be the next big thing in casinos. I want you to do the math for a percentage of the billions we're going to make, okay?" If I had accepted every single one of those generous offers, I'd have no revenues and a nice fat percentage of $0 billion.

Quote:

So, yes, I should've cronfronted some big questions early on. I'm not spending much time on this atm, but my inclination is to continue with the project unless someone can say some combination of... "I know SHFL employs 10 mathematicians", "I know SHFL has advanced/flexible GUI tools to do this sort of thing" And/or "The size of the non-SHFL market is $XX" where XX is a shockingly depressing #.

I don't know whether I've done that or not, but don't look just at the market size, look at the piece of the market you're likely to capture with your technology. What would you sell or license your software for? What would you do afterwards? (This is precisely why I've never turned my slot-designing tools into a commercial software package. I'd sell it once and then poof, no more clients.)

You can look at SHFL's financials to see the total size of their PTG market, unless that's all been swallowed up by Bally and then SciGames in the financials. I haven't looked lately.

Thanks for the thoughtful feedback. I'll definitely put some thought into things before spending a lot more time on it.

Quote: MathExtremist

What would you sell or license your software for? What would you do afterwards? (This is precisely why I've never turned my slot-designing tools into a commercial software package. I'd sell it once and then poof, no more clients.)

The initial plan was to offer the backend(the math parts) as a service, not a packaged product. Indie developers, or potentially APs, could design and publish(or not) games with a free(?) front end, and then, those who wanted would pay for a math run, to find the value and best strategy could do so afterwards. Of course, this also eliminates the communication needs between mathematician and client. Maybe this would attract big names as clients of the service or, the hope was, that maybe a big name would see enough value to just buy the business at some point.

As for what then, I have a number of other interests, outside gaming, I'd pursue.