The par sheet is simply a list of either your quickest moving items or your entire inventory with a par level associated to each item. In the example we used earlier, we said that the par for Ketel One was 4, we would record that number in our par sheet with the line that was associated with Ketel One. Ask the Slot Expert: Where can I find a PAR sheet for a slot machine? 25 April 2012 By John Robison. I would like to know where I can find the PAR sheet of a slot machine? Do you want the PAR sheet for a particular slot machine? That will be almost impossible to get. First, you have to find out which payback program a casino specified for the. Online Library Par Sheets Probabilities And Slot Machine Play Par Sheets Probabilities And Slot Machine Play When people should go to the book stores, search start by shop, shelf by shelf, it is in reality problematic. This is why we give the books compilations in this website.
If you want to know the setting of a specific machine at a casino you go to, you best bet without contacts is to hope you can catch a glimpse when the machine is opened up and being worked on by a tech or attendant.
What is it you think you will see when the door is open??
ZCore13
What is it you think you will see when the door is open??
Not too much on the inside... cash box, TITO printer, electronic parts, wiring, maybe a paper log (but definitely not the PAR sheet). But I'm more interested in that video monitor which may turn into a touchscreen of menus and data. Depending on what they're doing, the tech/attendant might end up going to the screen that literally states the theoretical and actual return of that machine.
Not too much on the inside... cash box, TITO printer, electronic parts, wiring, maybe a paper log (but definitely not the PAR sheet). But I'm more interested in that video monitor which may turn into a touchscreen of menus and data. Depending on what they're doing, the tech/attendant might end up going to the screen that literally states the theoretical and actual return of that machine.
Usually you want the door to be closed, and for an attendant to be doing something with the menus/selections. Tipping the attendant would be a major NO-NO (and probably cause loss of job). Asking the GM sometimes works.For example, sometimes machines are being checked every two weeks, and the settings are being written down.
There are usually 2+ screens which have the return.
1) Configuration screen, which may have the 'base game return, e.g. without progressives or bonus rounds or fancy features', 'fancy features return', 'overall return'. There are games which have multiple 'returns' at different bets or on different themes.
2) Coin-in, coin-out screen which have the theoretical & actual return
3) Sometimes other screens have the name of the software 'X machine - version Y, Z%'
Warning: the configuration screen may have options selected/unselected which will decrease the return of the game.
If you want to know the setting of a specific machine at a casino you go to, you best bet without contacts is to hope you can catch a glimpse when the machine is opened up and being worked on by a tech or attendant.
Here is a little not so secret secret. Almost every casino in the U.S. uses the same key to access the Attendant menus on the slot machine. It is known as the 'Gold Key' or 'Bronze Key' or the '2341 key'. These keys are not hard to obtain. If you don't have a contact to get one, just buy an old used slot machine and the key will come with it.
The slot techs usually have them. I remember watching them change all of the pay tables, for the worse no less, at MotorCity a few years ago on all of their VP.
Oh my gosh. How did you ever recover from that trauma??
ZCore13
Oh my gosh. How did you ever recover from that trauma??
ZCore13
Never did!!!
Oddly, their revenue revenue from them is down. No idea why though!?!?
Had 4 sessions on it, all profits.
Here is a little not so secret secret. Almost every casino in the U.S. uses the same key to access the Attendant menus on the slot machine. It is known as the 'Gold Key' or 'Bronze Key' or the '2341 key'. These keys are not hard to obtain. If you don't have a contact to get one, just buy an old used slot machine and the key will come with it.
Pretty sure you can get these on ebay or places like that. You probably recall the Peppermill-Reno fiasco a few years ago. Off the top of my head the casino knowingly sent an employee around to the competition to open their machines on the sly and look around. Google it, I forget the details. But I think it cost them a million buck fine.
I once found a bulletin board where guys were asking for and trading par sheets and stuff. I forget the name and I think it stopped. I myself picked up a par sheet of Super-8 Race, one version of it. Let me tellya, there's a gazillion things they can do to that one game. Now that I know the basic setup, I personally thoroughly check out a new game entering my casino and never assume that it is like the ones that it joins.
by Cătălin Bărboianu
For decades, the slots game has remained one of the most popular games of chance, despite a specific element that could limit its appeal, namely non-transparency: Players do not know the parametric configurations of the machines they play at, as this information is rarely exposed. Card players know the composition of the decks in play, roulette players know the numbers on the wheel, lottery players know the numbers from which the winning line is drawn, and so on. Slots remains the only game in which players are not aware of the essential parameters of the game, such as number of stops of the reels, number of symbols and their distribution on the reels, which makes the slot games unique in this respect.
Obviously, the lack of data regarding the parametric configuration of a machine prevents people from computing the odds of winning and other mathematical indicators, since the probability formulas hold as variables those parameters. The PAR sheets (Probability Accounting Reports), exposing these parameters of the machines and probabilities associated with the winning combinations are not publicly exposed and can be only retrieved upon request from the game producers, usually via legal intervention (for example, through FIPPA, Freedom of Information and Protection of Privacy Act).
Regarding the possible reasons of the game producers for keeping the PAR sheets far away from the public, there is a stated reason expressed by producers who declined the requests, in their appeals to the court decisions, through the fact that PAR sheets contain information considered to be trade secrets in the gaming industry and consist of mathematical formulas and equations developed by their engineers and that information significantly prejudices their competitive position. There are debates on whether such reason is justified and the opponents argue that it fails against the generality of the math formulas and equations – although the parametric details vary from game to game, the mathematical results concerning probability, expected value, and other statistical indicators are just applications of general formulas that are publicly available in mathematics and common across all slot machines, and no individual or corporate body can claim ownership of such a pattern or formula; they also claim that the competitive prejudice reason fails against the open possibility for all slot producers to configure, test, and use any parametric design for their slot machines and the producer can manipulate the game parameters, including the payout schedule, in unlimited ways, so as to obtain the desired statistical indicators for the house. Another possible reason is the hypothetical fear of losing players who face the real odds and expected values of their games, which is criticisable through the a priori expectation of the players for low and very low odds of winning induced by the experienced secrecy of PAR sheets and through the lottery example, in which lottery players continue to play against the (well known) lowest odds of winning from all games of chance due to other addictive elements that slots also hold.
Ongoing studies debate on the ethical aspects of the exposure of the mathematical facts behind games of chance and on whether the exposure should be limited to the parametric configuration, basic numerical results (such as probabilities for basic winning events and expected value) or more advanced mathematical results and their interpretations.
Mathematics has its role in this issue and its main contribution is not only another argument on the insubstantiality of the secrecy of slots PAR sheets, but a practical one: Mathematics provides players and professionals with some statistical methods for retrieving these missing data. Having these data along with the mathematical formulas, anyone can generate the PAR sheet of any slot machine.
The configuration of a reel refers to the distribution of the symbols over the stops of that reel. Denoting by t the number of stops and by p the number of distinct symbols on the reel, and denoting by the number of symbol on the reel (), then the vector is called the distribution of the symbols on the reel, also known as the weighting of a reel. Each reel has its own distribution of symbols. We can assume the same number of distinct symbols on each reel (p) through a convention: if a symbol does not appear on a reel, we could simply take its distribution on that reel as being zero. A blank is considered as a distinct symbol within the mathematical model.
The raw approximation. This method is based on the well-known result from probability theory called the Bernoulli’s Theorem, which states that in a sequence of independent experiments performed under identical conditions, the sequence of the relative frequencies of the occurrence of an event is convergent toward the probability of that event.
Applied to slots, that principle says that if N is the number of spins of a reel with t stops where we observe as an outcome a specific symbol S that is placed on c stops and n(N) is the number of occurrences of S after the N spins, then the sequence is convergent toward the probability of occurrence of S, namely P(S) = c/t.
The ratio n / N is the relative frequency of occurrence of S. It follows that for large values of N, the relative frequency of occurrence of S approximates the probability of S occurring. The higher N, the more accurate this approximation. Obviously, the number of spins N must be large enough for obtaining good approximations of the ratios , and this is the main issue of this method. As theory does not provide us with tools for choosing N for a given error range, all we have is the principle “the larger N, the better.”
As one can notice, this method of approximation based on statistical observation is subject to errors coming from idealizations and various assumptions, and the error ranges are not even quantifiable. Note that the described method provides us with approximations of the ratios (usually labeled as “hit frequency” in PAR sheets) for each reel and not the parameters of the configuration individually ( and t). However, knowing the basic probabilities is enough for any probability computation for a slot game. A more accurate approximation of the ratios and even of and t individually is still possible through statistical observation, using a method which can refine the raw estimations obtained through the previously described method. Such a method is briefly described further.
Denominator-match method. Denote by the number of occurrences of symbols to respectively after N spins of a reel. There is a slight correlation between the recorded values for various large numbers of spins N. Based upon this correlation, we can refine the estimation of the ratios obtained through the previous method and also find estimations for and t, by recognizing a numerical pattern across some sequences of fractions representing the ratios between possible values for and t.
The denominator-match method is based on the numerical analysis of the fractions and on a five-step algorithm, which I describe very briefly in this article and is explained at large in my last book The Mathematics of Slots: Configurations, Combinations, Probabilities:
We write each fraction as a chain of equal fractions, having numerators from 1 upward and denominators not necessarily integers, for every i from 1 to p. Across the p chains of equal fractions obtained, we choose that of the minimal length (let m be the minimal length). Then, across the p chains of equal fractions, we extract m sequences of fractions (one fraction from each equality chain), having the denominators the nearest to the denominators from the minimal equality chain respectively. From the m sequences of fractions obtained, we choose one sequence of p fractions by applying progressively the following filtering criteria: having denominators as close to each other as possible, having the highest number of instances of the same denominator, and the repeating denominator with the largest share being an integer. As final step, we adjust the numerators of the final sequence of fractions, through an approximation algorithm that leads to one denominator for all the fractions, being the sum of the numerators, as it is the relation between t and numbers .
This method provides us with the most probable number of stops t and associated symbol distribution of a reel in a certain probability field; the error range of this approximation is quantifiable in terms of probability.
Regarding the practical application of the methods through statistical observation, it is obviously an arduous task, since we have to watch and record spins in numbers of thousands.
Any information acquired on t besides the presented statistical methods of estimation is useful with respect to the accuracy of the approximations because it can give a clue as to how high we should choose N for avoiding irrelevant results (for example, if t = 100, we intuit that choosing N = 1,000 or lower would not be high enough for relevant results). Besides the methods based on statistical observation, there exists a method of estimating t through physical measurements, applicable to some particular types of slot machines. This method exploits the information given by the appearance of the reel on the display. As we know, only a small part of the reel (either physical or virtual) is visible on the display and this part can be seen as one or several adjacent stops (usually 3, up to 5). So we can view from 1 up to 5 consecutive stops of the reel. If the appearance of this part of the reel is three-dimensional (which is possible for both physical and virtual reels), by measuring some parameters of this image, we can deduce an estimation for the number of stops of that reel (t). Basically, the apparent lengths of the visible stops give full information on the curvature of the reel, which then leads to an estimation of the entire number of stops, since the number of visible stops per the circular length of the visible reel is proportional to the total number of stops per the circular length of the entire reel. This method can be applied only to reels showing at least two consecutive stops on the display in three-dimensional view. The method cannot be applied to virtual reels showing several consecutive stops in flat image. As in the case of the previous method through statistical observation, there are issues with the practical application of the method through physical measurements. There might be technical issues regarding acquiring the proper position for measurement or placing the measurement tool on the surface of the machine. Also for this method, an alternative would be for the observer to take photos and make the measurements on the photos. Of course, the slot machine operator might not allow the direct measurement and/or taking photos.
An applied mathematics unit using the denominator-match method applied on statistical records for retrieving the missing parametric configurations of the existent slot machines and generating their attached probability results is in project.
Par Sheet Slot Machine Definition Economics
With regard to problem gambling, past empirical studies found that facing the odds does not change much gamblers’ behavior toward a decrease, however a clear conclusion is not drawn yet. As regard to the slots game itself, the odds and other mathematical facts do count as information in a trivial strategic sense: It is as if someone asks you to bet you can jump from a high place and land on your feet; of course, it is an advantage for you to know in advance the height from which you will jump or measure it before you bet, as you might decline the bet or propose another one for a certain measurement, and this means decision.
Author’s bio:
Igt Par Sheet
Catalin Barboianu is a Romanian gaming mathematician, author of eight books on mathematics of gambling, published in several languages and listed in the official bibliographies for students at several gaming institutes around the globe. He maintains a website dedicated to probability theory and its applications for the non-mathematician at http://probability.infarom.ro and militates for the public exposure of the mathematical facts of games of chance.