Deconstructing Jackpot Party
What has always help me back is that the slot makers don't show you the entire reel strips. You can only see three frames at a time. However, it occurred to me that if I played enough I could piece together the entire reel strips, enabling me to do an exact analysis. So that is what I did.
Please be the first to preview my new page Deconstructing Jackpot Party. As always, I welcome comments, questions, and corrections before I announce this on my Odds site.
video? Isn't it against their rules?
Also, it's just semantics, but now days, most slot machines use EEPROM or Flash, but in the end, it's all read only memory. :)
Quote: WizardAs far as I know, until now there has never been a published example of an actual video slot machine.
Actually, Kevin A. Harrigan at U. of Waterloo has published several studies on par sheets from the standpoint of the psychology of addiction. For example, PAR Sheets, probabilities, and slot machine play: Implications for problem and non-problem gambling.
Quote:What has always help me back is that the slot makers don't show you the entire reel strips. You can only see three frames at a time. However, it occurred to me that if I played enough I could piece together the entire reel strips, enabling me to do an exact analysis. So that is what I did.
That methodology is not necessarily correct. A slot machine reel containing [A, B, C, A, C, B, C, B] contains the following three-symbol strings:
ABC
BCA
CAC
ACB
CBC
BCB
CBA
BAB
Each string occurs once. However, a reel containing [A, B, C, A, C, B, C, B, C, B] contains the same three-symbol strings, but CBC and BCB occur twice each. Unless you've done a frequency analysis, you won't know enough to be able to assume that each three-symbol combination is equally likely.
Agreed! Looks like it was a lot of work.Quote: AcesAndEightsCool article!
Quote: EvenBobThe Wynn let you sit there and record all that video? Isn't it against their rules?
They never said I couldn't. I've never seen any rule posted addressing that.
Quote: MathExtremistUnless you've done a frequency analysis, you won't know enough to be able to assume that each three-symbol combination is equally likely.
That is betting rather nit picky. With 10 different symbols there would be 1,000 ways to arrange three of them. It doesn't seem likely that they would have the same closed loop more than once. Furthermore, the way I did it, the bottom lines is consistent with Strip norms for penny slots. However, to help alleviate your concern, here is how often each 3-symbol pattern occurred, based on the hypothetical order on my Odds site.
| Position | Reel 1 | Reel 2 | Reel 3 | Reel 4 | Reel 5 |
|---|---|---|---|---|---|
| 1 | 10 | 13 | 9 | 5 | 8 |
| 2 | 8 | 5 | 6 | 7 | 7 |
| 3 | 4 | 7 | 10 | 5 | 8 |
| 4 | 5 | 4 | 6 | 10 | 9 |
| 5 | 4 | 8 | 9 | 5 | 7 |
| 6 | 5 | 12 | 9 | 10 | 10 |
| 7 | 7 | 15 | 6 | 10 | 6 |
| 8 | 9 | 6 | 6 | 12 | 10 |
| 9 | 11 | 3 | 5 | 3 | 4 |
| 10 | 13 | 6 | 7 | 12 | 6 |
| 11 | 11 | 7 | 7 | 3 | 12 |
| 12 | 8 | 8 | 10 | 5 | 16 |
| 13 | 14 | 6 | 10 | 7 | 9 |
| 14 | 7 | 12 | 8 | 7 | 3 |
| 15 | 5 | 6 | 13 | 7 | 8 |
| 16 | 10 | 6 | 7 | 9 | 10 |
| 17 | 10 | 14 | 12 | 9 | 7 |
| 18 | 10 | 6 | 11 | 5 | 12 |
| 19 | 5 | 6 | 12 | 8 | 5 |
| 20 | 9 | 8 | 10 | 10 | 5 |
| 21 | 9 | 3 | 12 | 5 | 13 |
| 22 | 8 | 10 | 6 | 6 | 11 |
| 23 | 9 | 7 | 6 | 5 | 5 |
| 24 | 5 | 2 | 5 | 7 | 5 |
| 25 | 9 | 8 | 7 | 9 | 9 |
| 26 | 7 | 7 | 3 | 8 | 7 |
| 27 | 7 | 6 | |||
| 28 | 15 | 5 | |||
| 29 | 0 | 10 | 12 | ||
| Total | 212 | 227 | 212 | 212 | 212 |
Finally, there are the p value of a chi-squared test for each reel, assuming a uniform distribution.
Reel p-value
1 63.57%
2 1.11%
3 69.16%
4 58.70%
5 28.00%
Quote: EvenBobThe Wynn let you sit there and record all that
video? Isn't it against their rules?
The Wiz didn't ask a pit boss, so couldn't read them of his lips...
Quote: WizardWith 10 different symbols there would be 1,000 ways to arrange three of them. It doesn't seem likely that they would have the same closed loop more than once. Furthermore, the way I did it, the bottom lines is consistent with Strip norms for penny slots. I could post the results of my 212 recorded spins, which I think would be within statistical norms of how I laid out the reel strips.
Many of the games I do have the same three symbols more than once. If there is a wide disparity between the frequency of top and bottom symbols, it's almost inevitable.
Of your 212 spins, did you see each of the 26 combinations of 3 symbols on the first reel roughly an equal number of times? Or was one or more roughly twice as frequent as another?
Quote: MathExtremistOf your 212 spins, did you see each of the 26 combinations of 3 symbols on the first reel roughly an equal number of times? Or was one or more roughly twice as frequent as another?
See my amended reply above.
I never saw any rule posted saying I could not use my brain when playing Blackjack, but that doesn't stop Dan Lubin from calling me a cheater . LOL
Quote: WizardThey never said I couldn't. I've never seen any rule posted addressing that.
Good point.
One time a customer required we include photos of every item offered. Only 250 or so items <sigh>. So a coworker and I trekked to the nearby Walmart, where security promptly infomred us we couldn't take pictures. We wound up taking cell phone pics (ca. 2006 with an economy phone, not very good quality), buying some items we needed to open, and downloading tons of pics from the web. Oh, there was no rule posted forbidding photography,as there is for example at Costco.
Namely, how do we know that each of the positions on each reel have equal probability? For example, reel #1 has 26 symbols, but the RNG doesn't necessarily have to pick a number from 1 to 26 to choose the final position of this reel. It could just as easily pick a number between 1 and 1,000 (or some other arbitrarily large value), and apply some sort of weighting to each of the 26 positions.
There are several ways a different EPROM could change the house edge. The simplest way is to adjust the pay table. Another way is to change the layout of the symbols on each reel. Yet another way would keep the symbols on each reel the same, but change the weighting assigned to each of the possible outcomes for each reel.
I think more research is necessary to get the real answers. I'd be curious to observe thousands (perhaps millions) of spins and see the distribution of the possible outcomes for each of the individual reels (e.g. if I do 26,000 spins, do I get each possible outcome for reel #1 roughly 1,000 times)? I'd also be curious to observe another machine, which is very likely to have a higher return (e.g. pick the same game with a 5-cent or 10-cent denomination at an off-strip casino), and see if each of the reels uses the exact same set of symbols. If the sequence of symbols is consistent across several machines at multiple denominations and locations, I would further assert that the machine assigns a weighting to each of the possible outcomes for each reel.
Quote: CowPieDonWhile this article was an interesting read, and the calculated return is consistent with what we might expect for a penny slot at a high end casino, I am skeptical of some of the assumptions made.
Namely, how do we know that each of the positions on each reel have equal probability? For example, reel #1 has 26 symbols, but the RNG doesn't necessarily have to pick a number from 1 to 26 to choose the final position of this reel. It could just as easily pick a number between 1 and 1,000 (or some other arbitrarily large value), and apply some sort of weighting to each of the 26 positions.
There are several ways a different EPROM could change the house edge. The simplest way is to adjust the pay table. Another way is to change the layout of the symbols on each reel. Yet another way would keep the symbols on each reel the same, but change the weighting assigned to each of the possible outcomes for each reel.
I think more research is necessary to get the real answers. I'd be curious to observe thousands (perhaps millions) of spins and see the distribution of the possible outcomes for each of the individual reels (e.g. if I do 26,000 spins, do I get each possible outcome for reel #1 roughly 1,000 times)? I'd also be curious to observe another machine, which is very likely to have a higher return (e.g. pick the same game with a 5-cent or 10-cent denomination at an off-strip casino), and see if each of the reels uses the exact same set of symbols. If the sequence of symbols is consistent across several machines at multiple denominations and locations, I would further assert that the machine assigns a weighting to each of the possible outcomes for each reel.
Multiline slot games use equally-weighted reels. Otherwise the RTP would be different for each payline, and that's a very difficult computation to support. It's not impossible to do, but it's not practical. The way to change the RTP of a video slot is to change the reel strips, not to keep them the same and weight them.
Quote: CowPieDonNamely, how do we know that each of the positions on each reel have equal probability? For example, reel #1 has 26 symbols, but the RNG doesn't necessarily have to pick a number from 1 to 26 to choose the final position of this reel. It could just as easily pick a number between 1 and 1,000 (or some other arbitrarily large value), and apply some sort of weighting to each of the 26 positions.
If the stops were not equally weighted then each payline would have a different return. While what you say is possible, and consistent with many conspiracy theorists on the forum, there is no upside to doing it that way. A box full of PARS sheets in my office also indicate the stops are equally weighted.
Quote: CowPieDonThere are several ways a different EPROM could change the house edge. The simplest way is to adjust the pay table. Another way is to change the layout of the symbols on each reel. Yet another way would keep the symbols on each reel the same, but change the weighting assigned to each of the possible outcomes for each reel.
I've never seen a slot machine to change the pay table according to the EPROM. I agree the EPROMS do vary the reel strips. I'm only make a statement about the one machine I saw that Wynn. At the bottom I indicate that what I observed is not indicative of all Jackpot Party machines.
Quote: CowPieDonI think more research is necessary to get the real answers. I'd be curious to observe thousands (perhaps millions) of spins and see the distribution of the possible outcomes for each of the individual reels (e.g. if I do 26,000 spins, do I get each possible outcome for reel #1 roughly 1,000 times)?
I disagree. Regarding the 26,000 spins you must have me confused with somebody who has that kind of time.
GREAT Work as always, Wizard!
http://www.nj.gov/oag/ge/docs/Financials/MGR2011/201112revenue.pdf
Quote: WizardA box full of PARS sheets in my office also indicate the stops are equally weighted.
On the other hand...
What's to say that there isn't a duplication of the 8 stops between the identical sequences, or the 21 stops the other way. That would skew your results.Quote: WoO PageA tricky part was that in reel 2 one sequence (blue 7-plum-orange) appears in two separate places.
Reel 2 should say 29.Quote: WoO PageReel 1: 26
Reel 2: 28
Reel 3: 26
Reel 4: 29
Reel 5: 26
Bottom line, what does it all mean?
Is there any way to use this analysis, and determine of a particular Jackpot Party machine has this 86% return, or even if it has a better return?
Quote: DJTeddyBearWhat's to say that there isn't a duplication of the 8 stops between the identical sequences, or the 21 stops the other way. That would skew your results.
While that is possible, and I may really be sitting in a pod somewhere and just dreaming I'm writing this, there is no upside to doing that. Slot makers like to keep things simple. I can't see any reason why they would duplicate a long sequence of symbols. The upside to not doing that is that players see more different patterns.
Quote: DJTeddyBearReel 2 should say 29.
No, it shouldn't. I said there were 28 distinct patterns in reel 2. Later I state one of them appears twice, so 29 total stops.
Quote: DJTeddyBearBottom line, what does it all mean? Is there any way to use this analysis, and determine of a particular Jackpot Party machine has this 86% return, or even if it has a better return?
If I had the reel stripping to all their EPROMs then I could do that. I did back in 2001/2002 when I did my Las Vegas slot machine survey.
However, that wasn't the point of all this. That is what I stated the purpose of the study in the summary. It is not to tell the public that a particular machine at the Wynn pays 86%. This was supposed to be an exercise in slot machine design, to show how they work.
Quote: BozGREAT Work as always, Wizard!
Quote: FinsRuleVery cool Wizard. Thank you so much.
Thank you! :-)
Quote: MathExtremistIf you got the machine number and/or location, you might be able to get the Wynn slot staff to confirm or deny that the game was set to 86.1% on the day in question.
I would lay 50 to 1 they wouldn't answer the question. Why would they admit to such a low return?
Quote: dwheatleyI think the analysis is really neat. Thanks again Wizard. I bet the reel puzzle was more fun than you made it sound.
Thank you! Yes, it was fun connecting the different pieces together. It took some trial and error because many two-symbol patterns repeat, so it often wasn't obvious which symbol came next. Reel 2 was definitely the hardest with the repeating pattern.
"For example, in the game chose the numbers 10,7,7,3,21 for reels 1 to 5 respectively, and mapped them to the position on the reels on the top row on the screen, then the screen would like this:"
The word "look" should be the 2nd to last word. And the 3rd word - "in" should be taken out or changed to "if" in that sentence.
Oh. I completely missed that. I read the page again, and see that you mentioned that as the last sentence.Quote: WizardIf I had the reel stripping to all their EPROMs then I could do that. I did back in 2001/2002 when I did my Las Vegas slot machine survey.Quote: DJTeddyBearBottom line, what does it all mean? Is there any way to use this analysis, and determine of a particular Jackpot Party machine has this 86% return, or even if it has a better return?
However, that wasn't the point of all this. That is what I stated the purpose of the study in the summary. It is not to tell the public that a particular machine at the Wynn pays 86%. This was supposed to be an exercise in slot machine design, to show how they work.
Quote: CowPieDonNamely, how do we know that each of the positions on each reel have equal probability? For example, reel #1 has 26 symbols, but the RNG doesn't necessarily have to pick a number from 1 to 26 to choose the final position of this reel. It could just as easily pick a number between 1 and 1,000 (or some other arbitrarily large value), and apply some sort of weighting to each of the 26 positions.
Quote: WizardIf the stops were not equally weighted then each payline would have a different return. While what you say is possible, and consistent with many conspiracy theorists on the forum, there is no upside to doing it that way. A box full of PARS sheets in my office also indicate the stops are equally weighted.
Thanks for the clarification. I guess I had been under the assumption that there was always unequal weighting, but I've also never seen the PARS sheets you have access to.
A couple follow-up questions:
1) Is it usually safe to assume that slot machines apply equal weighting to each stop, or should we only make this assumption on machines which have multiple paylines?
2) Tribal casinos in some states have machines which are legally classified as Video Lottery Terminals. With a VLT, the outcome is determined at the time the bet is booked, regardless of any decisions made by the player after the fact. For example, on a VLT made to look like a Video Poker game, if you're dealt J-J-J-J-4, and throw away one of the jacks, you will end up with a 3-of-a-kind or a full house, and the machine will use a bonus feature to ensure you are rewarded the original 4-of-a-kind payout. On a VLT made to look like a slot machine, I imagine that they'd have to somehow rig bonus rounds to guarantee the correct payout. If we ignore bonus rounds, do you think the analysis you did on the Wynn machine would be applicable to a VLT? In other words, do you have any information to confirm or deny the idea that each stop position has equal weighting on a VLT?
Quote: CowPieDonThanks for the clarification. I guess I had been under the assumption that there was always unequal weighting, but I've also never seen the PARS sheets you have access to.
A couple follow-up questions:
1) Is it usually safe to assume that slot machines apply equal weighting to each stop, or should we only make this assumption on machines which have multiple paylines?
2) Tribal casinos in some states have machines which are legally classified as Video Lottery Terminals. With a VLT, the outcome is determined at the time the bet is booked, regardless of any decisions made by the player after the fact. For example, on a VLT made to look like a Video Poker game, if you're dealt J-J-J-J-4, and throw away one of the jacks, you will end up with a 3-of-a-kind or a full house, and the machine will use a bonus feature to ensure you are rewarded the original 4-of-a-kind payout. On a VLT made to look like a slot machine, I imagine that they'd have to somehow rig bonus rounds to guarantee the correct payout. If we ignore bonus rounds, do you think the analysis you did on the Wynn machine would be applicable to a VLT? In other words, do you have any information to confirm or deny the idea that each stop position has equal weighting on a VLT?
Multiline video games use equally-weighted reels; single-line games almost uniformly do not (since the mid-1980s when Telnaes invented weighted reels).
Also, no, VLTs like that are merely display mechanisms for the award sent to it by the central system. The purpose of the reels + bonus round is to provide a visual representation of the predetermined award, so the reels are not spun randomly at all and the idea of "weighted vs. not" is meaningless in that context.
You're talking about a reel VLT. Don was talking about a poker VLT.
Quote: DJTeddyBearMathE -
You're talking about a reel VLT. Don was talking about a poker VLT.
I thought he mentioned reel stops. Either way, the game isn't dealt/spun randomly -- it's driven by the receipt of an award amount.
Quote: AyecarumbaVery interesting Wizard. I am curious if the construction of the reelstrips on the games with 15 paylines includes the same equal weighting. Since those games have wacky, zig-zag paylines, do they just have many more symbols on each reel, so that all the symbols on the reels can appear as a "set" (with the RNG determining at random, which "set" to display), or is each reel stop actually determined at random, and the payout analyzed at that time?
On true RNG-driven slot games, it's the latter. The game model is based on the fact that each stop on a given reel occurs with equal probability, so the game is equivalent to rolling five very large dice.
Quote: MathExtremistOn true RNG-driven slot games, it's the latter. The game model is based on the fact that each stop on a given reel occurs with equal probability, so the game is equivalent to rolling five very large dice.
This explains why payouts that use sequences of combinations on different reels, must begin with reels one or five, no matter how wacky the payline. Are the symbols on these two the most important for determining the frequency of each payout.
Quote: DJTeddyBearMathE -
You're talking about a reel VLT. Don was talking about a poker VLT.
I was actually interested in knowing how reel VLTs worked, but used poker to provide an example to demonstrate a specific situation where it's obvious that the outcome on a VLT is predetermined, and cannot be changed based on any playing decisions made by the player.
The fact that the result is pulled down from a central server and not randomly generated by the machine itself answered my question.
Wiz, how did you make out? Did you lose a buck or two?
Loved this breakdown, always wondered how they work. I like to consider myself strictly a blackjack player but once in a while the sucker in me gives me the urge to go put a 20 into a video machine.
On a somewhat related note I was recently in New Zealand and the slot machines in the casinos there tell you the return if you push the info button. I played a penny machine that was 88.29 and a nickel machine that was 89.74. New Zealand gives its people a lot of useful info, all cans and bottles containing alcohol have a diagram on them that say how many standard drinks the package contains as well.
One question... based on the information put together by the Wizard it appears that the odds remain the same regardless of the bet. I know there are a lot of stupid gamblers out there, but I can't tell you how many times I've heard people in casinos say "If you're going to play a machine you better at least play max bet/full coin on it.
Quote: winmonkeyspit3One question... based on the information put together by the Wizard it appears that the odds remain the same regardless of the bet. I know there are a lot of stupid gamblers out there, but I can't tell you how many times I've heard people in casinos say "If you're going to play a machine you better at least play max bet/full coin on it.
That's not typically true for video slots. It is true for older multiplier slots where the 2nd or 3rd coin had a bonused top award -- if you played 3 coins, your top award was worth more than 3x the 1-coin pay. In that case, your return is better by playing max coin.
Quote: winmonkeyspit3One question... based on the information put together by the Wizard it appears that the odds remain the same regardless of the bet. I know there are a lot of stupid gamblers out there, but I can't tell you how many times I've heard people in casinos say "If you're going to play a machine you better at least play max bet/full coin on it.
The bonus amounts in this game are dependent on how many coins are played. Your odds of hitting them however, don't appear to change.
Step Six - Summary
"I've shows..."
Should be "I've shown..."
Quote: AyecarumbaSmall spelling correction:
Step Six - Summary
"I've shows..."
Should be "I've shown..."
Looks like it's already fixed.
Man, this article, is SO FREAKING cool. It embodies the coolness that drips off this website.
I'm surprised my membership to this site was free. Freaking cool.
Quote: YoDiceRoll11Man, this article, is SO FREAKING cool. It embodies the coolness that drips off this website.
I'm surprised my membership to this site was free. Freaking cool.
Thank you! I appreciate the compliment. Now send me $5 in the mail.
Quote: s2dbakerCould you deconstruct the Batman/Joker machine for me please? I mean actually deconstruct it, take a jack-hammer to it, whatever you have to do to get my $100 back!
That wins the prize for the funniest post of the day!
Quote: CrystalMathWhen I worked at GLI, one of the things we did was to destroy old slot machines when the manufacturer didn't want them back or went out of business. One day, I saw the maintenance men getting ready to destroy a machine, so I went out to have a swing at it; a very "Office Space" moment. I have a picture somewhere because we were supposed to document the destruction.
Why didn't they sell them to a casino in second or third world country somewhere? I certainly saw some very dated American machines where I went to some of the more run-down casinos in Macau. If a slot maker went out of business, then I would hope that they should auction off their slots and use the money to pay their debtors something. People pay good money for any working slot at the Gambler's General Store.
I just thought it was cool that I got to be involved in my own "deconstruction."
Quote: AyecarumbaIs it possible that a three (or more) symbol sequence on each reel was never revealed during your session? If so, does it help the player's return? 86% seems low, even for a penny slot on the strip.
Anything is possible but I clearly observed every sequence of symbol to put together an entire strip. MathExtemist could come up with a scenario where there was a sequence I never observed, but in my professional opinion everything clicks into place that I did it right. If anyone doubts that I missed some combinations they can watch the second video to see if any turn up.
