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Randy Fromm's

Slot Tech Magazine

EditorRandy Fromm

Technical WritersJames Borg, Jason Czito,Vic Fortenbach, DianaGruber, Henry Kollar, ChuckLentine, Craig Nelson,Kevin Noble, Pat Porath

Slot Tech Magazine is publishedmonthly bySlot Tech Magazine1944 Falmouth Dr.El Cajon, CA 92020-2827tel.619.838.7111 fax.619.593.6132e-mail [email protected] the website at slot-techs.com

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Slot Tech Magazine-EditorialPage 4-An Epic PrinterPage 11-Training With My Homeboys in El CajonPage 14-Quick & Simple Repairs #97Page 17-Training at Apache Casino, Lawton, OklahomaPage 18-The Mathematical Configuration of Paylines

Randy Fromm

PublisherPublisherPublisherPublisherPublisherSlot Tech MagazineSlot Tech MagazineSlot Tech MagazineSlot Tech MagazineSlot Tech Magazine

Dear Friends,

I’d like to comment on the “Women in Gaming” award/recognition/seminar programs that are popping up all over in the trade journalsand at gaming seminars. At a time in Western Society, when we’retrying so desperately to EQUALIZE our population and recognizeeveryone as simply a fellow citizen and/or human being (withoutregard to race, nationality, religion, blah, blah, blah) why would youwant to single out women as a group of people for a “special award?” Ithink it’s insulting. It’s as if you are saying to them “You’re not goodenough to compete in the broad arena of the casino industry sohere’s a unique award that’s based primarily upon yourchromosomes. Secondarily, we’ll consider your qualifications andyour performance.” That’s bullshit. Women in gaming are exactly thesame as men in gaming. There is ZERO difference.

I realize that Hollywood has their “Best Actor” and “Best Actress”Academy Awards but these awards also reflect old, twentieth-centurythinking (established in 1928). Female thespians now refer tothemselves as “actors” (rather than “actress”) in a effort to moveaway from the distinction of gender in the workplace. And guesswhat, it’s not even legal to advertise “Girl Wanted” for employment sowhy is it acceptable to advertise “girl wanted” (or “woman wanted” or“female wanted”) because you want to hand out some sort of awardbut only to a female applicant? Just who is stroking what and why?

Why stop there? Why not extend this whole awards scheme to othergroups of people working in the casino industry? Let’s see . . . Howabout BMI? Surely those with a high Body Mass Index deservespecial recognition. It must be just as challenging to be a largeperson working in a casino as it is to be a female. How about peopleof color? How about Jews? When I was a boy, my father received the“Ner Tamid” award from the Boy Scouts, a special award that wasonly given to a Jew. He never did anything “Jewish” while inscouting, he just happened to be an awesome scout leader and aJew. Nobody else was even considered for the award as he was theonly Jewish scout leader. That’s not an award I’d be interested inaccepting. I’d have turned it down with thanks but without gratitudefor the consideration.

So, I put it to you: If you’re the type that looks for personalrecognition with the ephemera of award certificates, pins, plaques,medals and statuettes that go along with it (Look up. Do you have an“I love ME” wall in your office or shop, covered with diplomas and/orcertificates of completion? If so, I’m talkin’ to YOU) would you ratherhave these awards based solely upon your personal achievements inthe broad arena of competition or would your rather be given ahelping-hand by the elimination of your competition through somesort of non-meritorious selection process? I can easily imagine a“Slot Tech of the Year” award (I wish there was one). I can’t imaginea “Male Slot Tech of the Year” award or a “Female Slot Tech of theYear” award. I can’t imagine who would want it. TechFest 28

Las Vegas, NevadaNovember 12-14, 2013

Venue TBA

June 2013Slot Tech Magazine

Slot Tech Feature Article

To a slot attendant, aprinter is just part of aslot machine. They fill

it with paper, feed the paperinto the slot and fix any mi-nor paper jams that mightoccur. Occasionally, the slotattendants want us techni-cians to refill the printer ink.

An Epic PrinterBy Vic Fortenbach

To a slot machine technician,the printer is much more. Infact, the Epic 950 printer,manufactured by TransactTechnologies is no newcomerto the gaming world. Trans-act Technologies first gamingprinter was the Ithaca 750printer followed by the Ithaca850 and now the Epic 950printer. The Ithaca 750 isover 10 years old and a work-horse of a printer. We stillhave over 30 Ithaca 750printers working and trouble

free on our casino floor.While the Epic 950 printeris the newest printer, its re-liability and trouble free op-eration is matched with theIthaca 750 printer. The fea-tures of the Epic 950 printerinclude two stepper motorsinstead of just one to movethe ticket paper through theprinter. If the second steepermotor is not turning, the pa-per ticket will never be pre-sented to the player. Nomore long tails of blank tick-

Slot Tech MagazineJune 2013


ets on the floor, from a run-away printer due to a sensormalfunction. Four papersensors instead of the nor-mal three. A ticket burst fea-ture that actually separatesthe printed ticket at the per-foration inside the printerbefore presenting it to thecasino guest.

For visual troubleshooting,the printer’s keypad has afeed button and four LED in-dicators. These LED indica-tors are not your standardLEDs. They work together togive the slot technician anedge toward troubleshootingthe printer. Normally, aprinter LED will illuminate toindicate a problem such asthe fault LED it lights for aprinter fault. Not on the Epic950 printer. A printer headtemperature error will lightthe ready LED AND theblink the fault LED. This isLED indication to the ex-treme! There are ten differ-ent on/off indications andthree different blinking LEDspeeds possible with thesefour LEDs and the front be-zel. The printer status tablelists all of the troubleshoot-ing LED combinations.

Overall, the Epic 950 printeris trouble free, but whenthere is a problem, usually ablast of compressed air orusing a cotton swab gets theprinter and the slot machineback on line. Troubleshoot-ing the Epic 950 printer onthe casino floor is easy andcan be completed by usingjust your eyes and some ba-sic printer knowledge. Actualpart replacement should becompleted on the bench andcan be completed with just a#2 Phillips screwdriver andsome needle nosed pliers.

Inside the Epic 950 printer

are three optical sensorsthat detect the ticket paperas its various points. The sen-sors are named in order ofpaper travel, Top Of Form(TOF), ticket burst and tickettaken sensors. The first sen-sor encountered by the pa-per is the TOF sensor. Thissensor is located just insidethe lip of the paper-in slot onthe top of the printer. TheTOF sensor detects the blackindex mark on the ticket pa-pers right edge. A bad TOFsensor can be isolated whenthe paper is not drawn intothe printer after being in-serted into the paper slot onthe top of the printer. Thefeed button can be pushedto draw the paper into theprinter but because the badTOF sensor does not “see”

the black index mark, themotor will continue to run,bunching up the paper in-side the printer. When theindex mark is detected by aworking TOF sensor, the firststepper motor, called theticket feed motor is activated.The rubber rollers connectedto this motor grab the paperand as the motor turns, mov-ing the paper through theprinter to line up the paper’sblack index mark with theTOF sensor.

The second sensor next inline is the ticket burst sen-sor. This burst sensor is lo-cated behind the silver platein the inside middle of theprinter. This plate can beeasily seen by lifting up theblue hinged top cover. This


silver metal plate has a sharppoint on the bottom edge to“burst” or separate the paperat its perforation. Once thepaper edge has crossed overthe burst sensor, the secondticket transport motor startsto rotate at a speed a bit fasterthan the feed motor andgrabs the paper. This in-creases the tension on themoving paper to burst orseparate the ticket paper atits perforation. Once the pa-per has been separated, thesecond motor continues toturn and an additional set ofrollers grabs the paper andmoves it through the printerto the third sensor, the“ticket taken sensor” and outto the guest.

A telltale sign that the burstsensor is bad (or the ticketpaper has been inserted in-correctly) is that the paperdoes not stop and alsobunches up inside theprinter like a bad TOF sen-sor. The bunching up of thepaper is not a blockage in thepaper path but rather causedby the second stepper motorsince is not turning due to abad burst sensor.

Once the ticket taken sen-sor is blocked by the ticketpaper, the printer’s controlboard turns off the transportmotor. The paper snout (thebezel) of the Epic 950 printerhas been designed to be justlong enough so that a casinoguest cannot pull on the pa-per until all of the printinghas been completed and theticket has been burst at itsperforation. As the paper ispresented to the guest, theprinter’s blue bezel willflash, drawing attention tothe ticket in waiting. Whenthis sensor fails, the printer’sfront bezel will continually

flash, even though there isno paper blocking this sen-sor.

On our Bally Alpha ma-chines, the printer bezel ap-pears to be flashing withouta ticket in waiting. At first wethought it to be a bad sen-sor but in fact it was just dustblocking this sensor. How-ever, because this sensor ismounted horizontally, with adepressed area where thephototransistor and the plas-tic of the sensor meet, dirtaccumulates in this area. Asimple blowing with com-pressed air will usually dis-lodge the dirt.

The Epic 950 printer has a

bank of eight dip switches,but only switches 2, 7 and 8have useful functions. Dipswitch number 2 controls thebest feature of any printer,the ability to turn off the “pa-per low” candle light soft tiltfunction on the slot ma-chine. This feature can beused if the casino’s ticketpaper is not reflectiveenough to trigger the paperlow sensor on the printer.Pretty cool huh?

Dip switch #7 has two func-tions. On a Bally Alpha slotmachine with an operatingsystem of 3.17 or higher, thisswitch must be on to avoidany printer COMM errors.This switch also activates the


smart suite features of thebench test utility whenbench testing this printer.Dip switch number 8 acti-vates the two color printingoption. Of course, you willhave to have unique two colorthermal paper to use thisfunction.

As I mentioned previously,the Epic 950 printer has twostepper motors. These step-per motors are identical tothe motors used in position-ing the reels on a slot ma-chine, only smaller-muchsmaller. These motors areboth physically the same andcan be interchanged. Thereis one very minor difference.On the printer’s controlboard, the motors connectinto different receptacles,one is white and the other iswhite with a black sharpiemark. When you replace amotor, mark the plug of themotor accordingly so thenext technician that has toreplace a motor won’t getfrustrated when the motorthat presents the ticket runswhen the paper is insertedinto the printer.

While most printers have sta-tus LEDs, the Epic 950printer goes a step farther byflashing two or more theLEDs to better guide thetechnician to the problem.The four status LEDs on theprinter do give the slot tech-nician a starting point as towhat the problem may be.

The printer has been outfit-ted with a LED panel systemthat provides the conditionof the printer by using solidor blinking status LEDs tocommunicate status infor-mation. The following tablelists the different LED statesfor specific conditions.

With any printer, a visual inspection and a light cleaningto remove paper fibers from the sensors is often all that isrequired to keep the printer functioning.

Vic Fortenbach Vic Fortenbach Vic Fortenbach Vic Fortenbach Vic [email protected]@[email protected]@[email protected]

For schematic diagrams, servicemanuals, software, etc., visit theSlot Technical FTP Server atslot-tech.com

username=Slot Techpassword=kxkvi8


Slot Tech EventTraining With My Homeboys

I am fortunate to live in SouthernCalifornia, in San Diego County. Wehave great climate, clean and sandy

beaches, the Taylor Guitar factory is here,we have breweries, we have Sea World, wehave an extraordinary zoo and we have adozen casinos. My friends at nearbySycuan Casino requested training forsome new slot techs and offered me theclassroom space if I wanted to inviteanyone else to the event (three folks fromBear River Casino joined us). Naturally, Ijumped at the chance to hold a classwithout having to fly across the country todo it. I actually got to return home everynight to be with my beloved dogs wife. -rfrfrfrfrf

Attending the class from Sycuan Casino were AdelaCorrea (arguably “homegirl rather than homeboy), KevinKing, Joseph Semaia, and Louis Carrion. Attending fromBear River Casino were Miguel Trujillo, Aaron Pepetoneand Jai Kibby.

Miguel Trujillo and Aaron Pepetone (Bear River Casino)work on the digital lab project.


Slot Tech Feature Article

Quick & SimpleRepairs #97

By Pat Porath

IGT AVP Bar Top Game, Black LCDIGT AVP Bar Top Game, Black LCDIGT AVP Bar Top Game, Black LCDIGT AVP Bar Top Game, Black LCDIGT AVP Bar Top Game, Black LCD

While making a round on thegaming floor I came across an IGTAVP multi-game bar top that had

a totally black LCD. When taking a look atthe inside, even the LCD power LED wastotally black. Could it be a loose LCDpower cord, a bad game power supply, badLCD power supply, a loose connectionsomewhere?

At first I wasn’t sure where to start but hadto start somewhere. The 120 vac powercord to the LCD was unplugged for a fewseconds, then plugged back in whilelooking at the power LED on the LCD.Absolutely no sign of power at all! Thelight didn’t even flicker for a half second,even though the rest of the game did havepower (the bill acceptor bezel was lit, theprinter bezel was lit and the interior gamelight was on).

What about a good old fashioned powercycle of the game? During the rebootprocess, I did hear typical “IGT AVP”startup sounds; the bill acceptor cyclednormally too. All the while still no sign oflife from the LCD. It was original. What the. . .? How can these power supply boardsbe different? The exterior of both LCDslooked exactly the same to me. Now howcan I repair the game?

When taking a closer look at the powersupply board on the original bad unit, one

of the capacitors was domed. In addition,the bottom plug was starting to come outof it. No doubt a bad cap. So off to the techshop I went with intentions of replacing afew caps. The obvious bad cap was removedalong with two others that were in thearea. If one of them was bad, maybe theother two were starting to go bad as well.


All three caps werereplaced with the samevalue and the LCD was putback together. Now it wasready for testing (withfingers crossed because Iam not a bench tech and Idon’t solder very oftenanymore). Game power wasturned on and bingo! Themonitor lit up perfectly. Thegame booted up and wasworking again. Simply andeasily replacing threecapacitors on the powersupply board of the LCDrepaired the game. Note:Capacitors replaced wereC813, C814, and C815.

IGT AVP 3.0 “PeripheralIGT AVP 3.0 “PeripheralIGT AVP 3.0 “PeripheralIGT AVP 3.0 “PeripheralIGT AVP 3.0 “Peripheraltilt”tilt”tilt”tilt”tilt”

I received a call for a“Peripheral tilt” on an IGTAVP 3.0 game. On thescreen, it showed“PERIPHERAL TILT, getstatus poll failure, Digitechsystem. Not exactly surewhat everything meant, Idid know that a touchscreen was a “peripheraldevice” and “Digitechsystem” was the brand oftouch screen controller.Connections were checkedon the main screen, suchas video, power and such.Everything looked nice andsnug, also, nothingappeared to be pinched inthe door frame area. So thegame was power cycled tosee if the error reappeared.After boot up all of theerrors cleared. It looked likea simple reboot did thetrick this time.

WMS Bluebird Dim BellyWMS Bluebird Dim BellyWMS Bluebird Dim BellyWMS Bluebird Dim BellyWMS Bluebird Dim BellyLightLightLightLightLight

A co-worker was telling meabout a WMS Bluebirdgame in which the bellylight, a T6-6 wattfluorescent tube, wouldonly last a few days then itwould need replacing. Weknow that under normalcircumstances, fluorescenttubes can last for years.When looking at the bellyglass, it was quite a bitdimmer than the game nextdoor. Another bulb was putin for the heck of it, and

the same thing. It was kindof dim. The ballast wasexamined but it was, infact, rated the correctwattage. We have had thegames for a few years or so,maybe the ballast wasgoing bad. It wasdisconnected andreconnected only to havethe same result. A spareballast was installed, alsomaking sure it was rated foran output of 6 watts. Whenpower was applied the bulblit up beautifully. Theoriginal ballast was startingto go bad.


Editor’s Note: Editor’s Note: Editor’s Note: Editor’s Note: Editor’s Note: Thisillustrates the importanceof tracking machinerepairs. It’s as simple asmaintaining the “MEAL”book (Machine Entry AndLog)-sort of an odd name-that should be in each andevery machine. There areonly two components to thesystem: The lamp and theballast. If the MEAL bookshows multiple lampreplacements, let’s notwaste any more of thecasino’s money on lamps.This is one of the placesthat competent slot techsreally “shine.” A good techmakes a point of beingaware of EVERYTHING thatpertains to the “normal”operation of the casino (notjust the machinesthemselves) from atechnical standpoint. Weirdsh*t calls for YOURintervention to make thingsright because nobody else

knows what the Hell isgoing on.

Aristocrat Verve-No COMAristocrat Verve-No COMAristocrat Verve-No COMAristocrat Verve-No COMAristocrat Verve-No COM

We were doing an install ofa bank of four, AristocratVerve “Superman” (similarmodel game as “Tarzan”).When there is a yellowborder around the OasisSentinel III, there is aGAME TO SENTINALcommunication error.When a red border appearson the Oasis display, it maybe a SENTINAL TO SYSTEMerror, such as a fiberconverter down orsomething like that. Withthis game (yellow border)options were looked at suchas SPC board address set to1. Connections werechecked next, the interfacecable from the Sentinel tothe SPC board wasconnected and all threecables were connected at

the SPC board (interfacecable from Sentinel, power,and interface cable fromgame). The Sentinel wasrebooted (along with theSPC board) but neitherhelped. The “slot mast IDnumber” was doublechecked, which wascorrect. As the SPC boardwas examined moreclosely, the problem wasfound. Somehow theinterface cable FROM theSentinel was plugged inbackwards! After it was puton correctly COM wasestablished.

Bally Alpha 2 LockingBally Alpha 2 LockingBally Alpha 2 LockingBally Alpha 2 LockingBally Alpha 2 LockingUp For Hand PayUp For Hand PayUp For Hand PayUp For Hand PayUp For Hand Pays

I received a call about aBally Alpha 2 “U Spin”game that locked up forthree small hand pays.Instead of printing a ticket,it went into jackpot handpay mode. To make sure


the game did have aproblem, two small-amounttickets were used fortesting. Sure enough, afterthe nine-cent ticket wasinserted and the cash outbutton pressed, it didindeed lock up for a handpay. The main door wasopened up and closed tosee if the Oasis Sentinel IIresponded with acorresponding door signalon the display. Since it didread a door OPEN andCLOSED properly, I knew Ihad game TO Sentinelcommunication. Maybe theSentinel and or gameneeded to be rebooted?Very shortly after aSentinel power cycle, thecorrect DPU numberappeared on the Oasisdisplay. This indicated goodcommunication FROM theSentinel TO the OasisSystem. Game options werechecked such as “validationenhanced,” “Ithaca 950printer” was selected, “SASPrimary” was selected forcommunication, and so on.Everything looked good asfar as I could see. Eventhree test tickets wereprinted from the game.What was left? Well, aboutthe only thing that I couldcome up with (after givingthe game an evil stare) wasto look at all of the OasisGlobal settings. A bit deepinto selections was anoption set “TICKETS NO.” Itis suppose to be set“TICKETS OK” so I set itaccordingly. Once again aticket was inserted to see ifit would print instead of thegame locking up. YES! A

cash out ticket did print. Itwas inserted once again,and it printedagain…finally! Onlybecause an Oasis Globaloption was set incorrectly,the game would not printout a ticket.

Bally CinevisionBally CinevisionBally CinevisionBally CinevisionBally CinevisionWouldn’t Cash OutWouldn’t Cash OutWouldn’t Cash OutWouldn’t Cash OutWouldn’t Cash OutCreditsCreditsCreditsCreditsCredits

After opening up the doorand removing both theplastic and metal cover, itwas obviously a bad microswitch in the cash outbutton. While the customerwas waiting for her creditsto cash out, I quickly lookedto see if I had a microswitch in my tool pouch.Which I did not, I only hadone of the bill acceptor doortype that wouldn’t work.Swapping connectors withthe service button, Ithought it would cash outthe credits. The gamedoesn’t know whichphysical button is whichand only a “working” switch

would work. The connectorsreached and it would haveworked except the darnservice button was verysticky and did not workeither. So much for thatplan, get the game to printa ticket for the customer,then replace the badswitch. I called the slotattendant back over to thegame to have a cash paydone so the customer couldget her money faster thanme running to our shop,then replacing the parts.Two spare micro switcheswere retrieved from theshop and installed into thegame. The service buttonwas cleaned up a bit, nowboth the cash button andservice button worked,verified by “button test” indiagnostics. Since I was inthe area of “buttondiagnostics,” the rest of theplayer buttons were testedtoo. Now ALL of the playerbuttons tested A-OK.

- Pat Porath - Pat Porath - Pat Porath - Pat Porath - Pat [email protected]@[email protected]@[email protected]


Slot Tech Event

Training at Apache CasinoLawton, Oklahoma

Oklahoma was making the news big time in thefirst weeks of June, 2013. Tornadoesslammed into the state with the fury that

always accompanies them. The week before I wasscheduled to train at the Apache Casino Hotel inLawton, Oklahoma, I received an e-mail from a friend, begging me toreconsider. Actually, it was really justtwo words: Don’t go!

But what the heck? This is thecasino business anyway so Itook a gamble on good weather (at the very least,non-tornadic weather) and flew into the cutest littleairport I’ve ever been to: Lawton, Oklahoma. Theweather “issue” was actually in Dallas, and we were90 minutes late getting in but to the credit of AmericanAirlines and Hertz, they both did a great job of gettingme to the hotel, long after the midnight hour. Whew!

Honestly, this is a nice casino with some 800+ ma-chines. It was busy as heck the entire week I wasthere for the class, which was on the subjects ofpower supply and LCD monitor repair. Although theclass was intended for slot techs without any previouselectronics training, I was really happy to see that theyhave one, really good bench tech (James) who will beable to guide the other techs through their repairs, nowthat they know the basics of electronic troubleshootingand repair. -rf

Attending the class at Apache Casino Hotel inLawton were both slot techs and gaming regula-tors. I have to give props to the gaming regulatorsas they actually paid attention and learnedelectronics!


Slot Math

In the last decade, mathematics has been takenmore and more seriously

into account in gambling,as being the essence thatgoverns the functionality ofgames of chance and theonly rigorous tool providinginformation on optimalplay, where possible.

Also in slots, there ismathematics behind thesparkling machines, andmany people will be sur-prised to find that themathematical modelsaround which a slot ma-chine is developed belongnot only to Combinatorics,Probability Theory, or Sta-tistics, but also to othermathematical domainssuch as Topology.

The design of slot

machines can be of anycomplexity with regard toboth interface and case –and the models on themarket exhibit this com-plexity. Of all physicalparts, the interface is themost important with re-spect to the mathematicalmodeling, as it shows themachine in action, its out-comes, the game rules, andhow these rules are appliedin actual practice. When wetalk about the configurationof a slot machine, we actu-ally refer only to the techni-cal component of its designthat characterizes its inter-face, in its essential ele-ments, and relations be-tween them that are indis-pensable to a rigorousmathematical model – thatis shape, topology, arrange-ment, and cardinality.There are the parameters ofthe mathematical models ofthis configuration in slotproducers’ hands thatgenerate the wide diversityof the slot games wordwide.

The configuration of aslot machine is specified bythe configuration of itsdisplay and the configura-tion of its reels. Lines andpaylines belong to theformer and in this article Iwill talk about the math-ematical configuration ofthe display.

The display of a slotmachine shows the out-comes of the reels ingroups of visible stops (vis-ible stop refers to a unitpart of a reel holding onesymbol, visible through itswindow after the spin; awindow can show one ormore stops) having a cer-tain shape and arrange-ment. It also points out theways (rules) the combina-tions of outcomes can turninto winning combinations.

The most natural andsimplest mathematicalrepresentation of the con-figuration of the display isthe Cartesian grid of inte-gers, where the grid?spoints stand for the reel

The Mathematical Configurationof Paylines - Part 1

by Catalin Barboianu


stops. Another alternative isto represent the configura-tion of the display as agraph. However, given thelimited applicability of thetheoretical results (themodel provides us only withthe number of all possiblelines of a particular type,and only few features of thelines count toward prob-ability calculus), the Carte-sian grid is preferable dueto the higher difficulty ofworking with graph theory.

The mathematicalsetting in a Cartesian gridstarts with defining thebasic terms of distancebetween two points on anaxis, the neighboring of twopoints, and the vicinity of apoint. These definitionsuses a basic discrete metri-cal topology. Then, themain notion of line in a gridis defined as a set of mini-mum tree neighboring

points. The cardinality ofthis set is called the lengthof that line (see figure 1,Examples of lines of length5 in a grid).

A line in a grid is afinite set of points that canbe connected through apath linking successivelyneighboring points of thatset. Although the line wasdefined in a sequentialmanner, which involves adirection of walkingthrough its points, we areinterested in the line onlyas a set of points, regard-less of the possible pathsthrough which its pointscan be linked. Therefore aline has a connectivityproperty, not in a continu-ous sense, but in a discreteone (through the neighbor-ing property). Although aline can be “walked” inseveral ways, this has nogeometrical or combinato-

rial interpretations, butonly topological.

The terminology usedin this model complies inbig part with the commonlanguage of slots.

The main propertiesof a line, having a geometri-cal analogue, arehorizontality (when line’spoints all have the samecoordinate on the y-axis),verticality (when line’spoints all have the samecoordinate on thex-axis), and obliquity (whenthe absolute value of thedifference of the coordi-nates of any two consecu-tive points of the line is 1on both axes). A line is saidto be broken if it is nothorizontal, vertical, or ob-lique.

A line is called trans-versal for a finite set if it isincluded in the set andcontains two points from


two opposite margins ofthat set (like upper andlower, or left and rightmargins).

Symmetry is alsodefined in a Cartesian gridonly through means spe-cific to the discrete spacewithin which we work –symmetry of a point withrespect to another, symme-try of a point with respectto a horizontal or verticalline, and then a symmetricset.

As for more complexshapes, lines can be trian-gular, trapezoidal, stair ordouble-stair, zigzag, etc.All these types of lines aredefined through propertiesholding in the same Carte-sian grid. In figure 2 aresome examples of suchparticular lines in a grid,Horizontal, vertical, oblique,and broken lines, Triangu-lar line, Trapezoidal line,Zigzag lines, Double-stairline, Symmetric upper-lower transversal triangularline.

With these mainnotions rigorously estab-lished, we can move to themathematical object repre-senting the display of a slotmachine, namely the rect-angular grid:

A finite subset R ofthe Cartesian grid is calledrectangular grid if thereexist m horizontal lines ofthe same length n, with m,n > 1, such that R is theunion of these m lines andand:

a) the m lines aredistanced at 1 from eachother;

b) the m lines are left

or right aligned.m x n is called the

size of the rectangular gridR (which is also called an mx n-size rectangle or arectangle of m rows and ncolumns).(An equivalent definition isobtained by taking verticallines instead of horizontaland change the alignmentto up or down at conditionb).)

Figure 3 shows a rectangu-lar grid of size 3 x 5

In our mathematicalmodel, paylines are repre-

sented by particular linesin a rectangular grid (thedisplay). The paylines ofslot machines can be of anycomplexity for each slotmachine in part, but usu-ally they have particularshapes, following propertiessuch as non-self crossing,colinearity, symmetry, up-down or left-right direction,and/or crossing over thereels.

With respect to prob-ability calculus, there areonly the length of a line,the number of particularlines in a given rectangulargrid and the cardinality oftheir mutual intersectionsthat count (for complexevents involving severalpaylines), regardless ofother properties of them.

For instance, thetables give the number ofoblique lines included in anm x n-size rectangular gridand the number of trans-


versal oblique lines.In an n x n-size rect-

angular grid (a square grid),an oblique line of length nis called a diagonal. If ,there are no diagonals inan m x n -size rectangulargrid.If m = n, there are exactly 2diagonals. The diagonals ina square grid correspond tothe common geometricdiagonals of a square, pass-ing through two oppositevertices. In the Euclidianplane, any rectangle hasdiagonals, but in a Carte-sian grid, only a square gridhas diagonals (in the senseof the above definition).

The following tablesgive the number of someparticular triangular andtrapezoidal lines includedin an m x n-size rectangu-lar grid, usually present atmultiline slot machines.

Among these left-right transversal triangularlines, some of them may besymmetric (correspondingto isosceles triangles).

Table of valuesfor the number of symmet-ric left-right transversaltriangular lines in a rectan-gular grid

Table of values for thetotal number of left-righttransversal trapezoidal linesin a rectangular grid.

Continues next monthContinues next monthContinues next monthContinues next monthContinues next month

Catalin [email protected]@[email protected]@[email protected]

Subscriptions & Back IssuesWhy back issues of Slot Tech Magazine areWhy back issues of Slot Tech Magazine areWhy back issues of Slot Tech Magazine areWhy back issues of Slot Tech Magazine areWhy back issues of Slot Tech Magazine areimportant to own . . .important to own . . .important to own . . .important to own . . .important to own . . .

Slot Tech Magazine is strictly technical. As such, the magazine's contents are not timecritical. The repair information and technical data contained in past issues is just as valid

today as it was the day it was published.

Additionally, current and future articles more-or-less assume that readers are already familiarwith what has been covered in past issues. This editorial policy assures that Slot TechMagazine's contributing writers are not limited to "writing down" to the level of a novicetechnician but are free to continue to produce the most comprehensive technical articles inthe gaming industry.

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“OK. You asked and I listened. My new tech class eliminates obsolete CRTmonitor repair and the associated monitor repair lab. In just four or five days,your slot techs can learn to repair Power Supplies, LCD Monitors, TicketPrinters, Bill Validators and more. It’s easy and it’s fun.“- Randy Fromm

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