How to Figure Them Out
This Article is inspired by a recently resurrected thread.
The more recent posts of this thread tend to ask some Basic questions about slot Progressives, so I am going to use this Article to attempt to impart some general information.
Slot, Video Keno and Video Poker Progressives are often capable of presenting Advantage Play opportunities that, I would argue, the casino is not going to particularly frown upon because Progressives generally go up by a fixed percentage of coin-in. As a result, the casino will always (in the long-run) generate revenue that is reflective of the hold of the Base Game less the Progressive meter move.
Imagine that you have a 98.45% game of 9/5 Jacks or Better that has a Progressive whereby 0.5% of all monies bet are added to the Royal Flush Progressive: What that means is, regardless of where the meter on that Royal Flush is at any particular time, that machine will hold 1.05% of all monies bet for the casino in the long-run. While it is true that Advantage Players will only play this game if certain conditions are met, it is (or should be) largely irrelevant to the casino who is playing the machines.
There will be some people who will disagree with me by stating that the casinos actually DO care whether or not an Advantage Player will only play them positively, because the casino would prefer non-AP's who usually play it negatively to hit the Progressive as they will, "Give the money back," by way of playing a negative expectation game later on. Many of the people who disagree with me might cite the fact that some casinos will toss out Ultimate X vultures as an example, however, I personally believe that most casinos aren't inclined to get too uptight about who is or is not playing a positive Video Poker Progressive. If they were so inclined, then they should simply not have the Progressive, or have it, but on a horrendously bad paytable.
In this sense, Slot Progressives work much the same way. However, unlike Video Poker, the return of almost all slot machines cannot be readily known and there is no tool (such as the WizardofOdds Return Calculator for Video Poker) by which an individual can determine the precise return of a slot game based on the Progressive Meter(s).
With that being said, there are a number of distinctions that can be made with respect to Slot Progressives, how easily a positive, 'Jump in point,' can be determined and indeed, whether or not it is even worth determining.
I have already written extensively about Must-Hit slot machines in this Article.
As well as in others, so I would encourage anyone looking for information about Must-Hit slots to look for Articles in which they are mentioned. Moreover, there have been many threads on these Forums dedicated, in part if not in whole, to Must-Hit slot machines and pages on the WoO site to be found concerning that subject. I may write more about the subject in the future, particularly if there are any significant changes to the nature of these machines, but I believe the culmination of information that can be found on all of the above-referenced sources on these sites will be sufficient and sufficiently recent.
Capped v. Uncapped Progressives
The distinction between capped and uncapped Progressives is an important one because an uncapped Progressive, theoretically, can always be positive at some point and a game with a Capped Progressive might always be negative even when the Progressive is, "Capped out." With an Uncapped Progressive, the Progressive Meter continues to move upward the proscribed amount until the result that awards the Progressive (whether it be a function of Bonus Games, a Scatter Pay or a Top Line hit) is achieved. At this point, the Progressive will pay and reset to what is known as its, "Base Amount."
Capped Progressives are different because, when the Progressive Meter reaches a certain point, it either stops moving and returns to its Base Amount after it hits, or alternatively, any monies that would otherwise be added to the Capped Progressive over and above the maximum possible award simply, "Roll Over," and are added to the Base Amount after the Progressive is hit.
An example of such Capped Progressives, with rollover, was discussed by former Forum Member MickeyCrimm in this thread.
Essentially, in the State of Montana, there is a State Law that results in a jackpot cap of $800 for anything, so in the above thread MickeyCrimm discussed a Keno game that had a Roll Over Progressive that gets added to the Base Amount after the 5/5 result is hit on the Video Keno game he referenced.
Another example of a Capped Progressive actually does not invoke a pay for any particular kind of hit at all, but rather, it invokes Free Games. On the slot machine title, 'Three Kings,' there is a Progressive with respect to each of three levels of Bonus Games by which a player can win whatever number of Bonus Games correlates to the Progressive in question. Interestingly, MickeyCrimm did an empirical study of some of these machines and determined the one he was looking at in particular can NEVER go positive, even when all Bonus Games are maxed out. I will say this: If MickeyCrimm does an Empirical on something, you can get out your deposit slip and take that directly to the bank.
In my personal experience, I have observed the Three Kings game, but was never personally inclined to do an Empirical on it. Aside from that, I do not believe that I can recall encountering any slot machines (other than Must-Hits) that have a Capped progressive, so that's not something I can really speak to other than to cite MickeyCrimm's findings.
The reason I say, 'Other than Must-Hits,' is because, yes, Must-Hits are technically a capped Progressive. The only difference is that they are guaranteed to hit if they reach the cap whereas the other machines in question are not.
If you ever do encounter a Capped Progressive on a slot machine that is not a Must-Hit, then my advice is to be wary and do an Empirical (or just don't play if you're not willing to do an Empirical) and DO NOT assume that a Progressive having Capped is an inherently positive situation. To wit, one could theoretically Cap a Progressive for just that reason; so that it can literally not ever go positive. If it is a Capped Progressive on a Video Poker game, then use Wizard's return calculator, and if it is on a Video Keno game, feel free to shoot me a PM. Keno Math is pretty easy.
The remainder of this Article is going to address Uncapped Progressives because there is really not much more that can be said about Capped Progressives without invoking specific situations.
Are There Bonus Games, and How Do They Operate?
Perhaps the most important thing that I would want to know with respect to an Uncapped Progressive is whether or not the machine in question has Bonus Games, and if so, how do those Bonus Games operate? For example, if there is a slot machine with Bonus Games that operate on an entirely separate reel strip, (or perhaps that play a different game entirely) then I will say that is going to be difficult, if not impossible, to do an Empirical on because you are likely not going to get enough plays in on the Bonus Games to approximate the average value of said Bonus Games based on symbol frequencies.
I'm not saying that it is impossible to do so, anything regarding doing an Empirical study is possible, I'm simply stating that it is extremely unlikely that undertaking such a challenge is going to be worth ($$$) your time.
On the other hand, a dying beast is slot machines that DO have Bonus games, but the Bonus Games operate on the same reel strips. Furthermore, there are multiple Video Keno games out there that may have Bonus Games and Progressives, and though the paytables or drawing rules may be different, the Keno game is going to be relatively easy to analyze. With respect to the slot machines, however, it is not all black and white like it is with Video Poker (Wizard has already done the work) or Video Keno, (easy combinatorics) and thousands of spins of Empirical data and symbol frequencies are going to need to be gathered before you can even begin feeling at all confident in the results. More like tens of thousands for High Variance Multi-Line games, which brings us to:
Single-Line, Three-Line or Multi-Line?
When determining whether or not you want to attempt an Empirical study of a slot machine to determine whether or not an Uncapped Progressive can be positive, it is also important to look at how much work is going to need to be put into it before you can be reasonably confident about your results.
The easiest machines to analyze, based on symbol frequency, are Single-Line slot machine games, (Triple Diamond is a good example) but such games are rapidly going extinct. There are some hangers-on among the older titles, but new titles for single-line games very rarely, if ever, hit casino floors and old titles can barely keep players interested. In addition to that, many of the new Multi-Line games (but not all or even half) allow a player to play One Line at One (or more) units Per Line, so effectively, they allow for single-line games.
If you do find a Single-Line game that you would like to attempt to analyze, then all you need to do is determine symbol frequency on the main line over thousands of spins. How many thousands, you may ask? Maybe it will only be three thousand, but then, maybe it could be as many as ten thousand, maybe more...
You will reach a point that you can be reasonably confident in the return when both of these criteria are met:
A.) It is not a ridiculous percentage. (Ex. 106%, off-the-top)
B.) If you add another thousand or fifteen-hundred spins to your sample and recalculate, your results change by less than a percentage point. While it is true that this could simply be a coincidence and you may have just gotten positively or negatively skewed reel frequencies over two relatively large samples, it's not terribly likely, and you can repeat the exercise of adding 1,000-1,500 again if you like.
There are also a myriad of statistical analyses that can be used to gauge Confidence Intervals for your set of results, and while I may write an Article about those at a later time, they are outside of the purview of this Article.
With respect to Triple Line games, essentially the same Rules apply as with Single-Line and, "What's good for one line is good for every other line," so you can just add up the appearances of symbols over many thousand spins, and if it is a Triple-Line game, make sure that you multiply the number of spins you have taken by three when analyzing your results.
This concept can also be used for Multi-Line Games, but Multi-Line games usually operate on a Bonus Games that is a different set of Reels, or sometimes, that has almost nothing whatsoever to do with the Base Game! In cases such as those, I would advise that it is not worth your time UNLESS you have a ton of casinos within very close proximity with a ton of these machines, in which case, it PROBABLY isn't worth your time.
There are even more bizarre types of machines out there that do not have, "Lines," in the traditional sense at all, or that have 780, (or whatever) "Ways," that results can take place. Some slot games also have bizarre sets of Rules such as one of the newer lines of Quick Hits machines in which the Progressives can be won at any bet level ($1, $2 or $3 on the specific ones to which I refer) but you have, "Improved Odds," of hitting the Bonus by betting more. Since you don't know how much you are costing yourself by NOT betting more vs. how much you gain by attacking the Progressive with smaller bets, there is really no easy way to even know whether or not the Progressive puts you at an Advantage, even IF you can somehow figure out the Progressive frequency on this game that operates on THREE different sets of reel strips with FIFTEEN stops at once!!!
I usually do not like to be pessimistic when it comes to Advantage Play, and I genuinely think that Slots can be fun to figure out sometimes, but many of these machines are far too complicated to be worth anyone's time (except for the manufacturers') to attempt to analyze Empirically. In some cases, I'm not even sure if it is practically possible.
Furthermore, it's a Catch-22 because you do not know what percentage value a higher amount Progressive is going to add until you have already completed the analysis. Imagine putting all of that work into something just to find that the target Progressive needs to go something like twenty cycles without hitting to be positive: TIP: Regardless of how frequent or infrequent a Progressive result is, it is almost never going to go twenty cycles without hitting.
As a result, you might find yourself doing all of that work, and rest assured, it is a lot more work than it used to be, just to find out that the target Progressive will almost never bring the machine positive. Also, when it does bring the machine positive (if you can even get on it) your Expected Profit might only be a few bucks.
If you can somehow garner access to PAR Sheets for a specific title, then that is obviously the only pragmatic way to do this. Otherwise, I would recommend only doing Empirical analyses of Progressives on relatively simple games in which the Bonus Games (if applicable) do not operate on separate reel strips. Even then, you might not get many plays (i.e. much $$$ value) as a result.
I'm not going to go as far as to suggest that attempting to analyze Progressives is not a legitimate form of Advantage Play, indeed it can be if you can do it correctly, but it really is much more of a hobbyist type thing on these newer machines.
The biggest takeaway from this Article should be to never make assumptions, though, just because a certain Progressive on Machine A is $747.22 and on Machine B is $1,682.34 (assume same title) does not mean that Machine B is necessarily at an advantage: It just means that, all else equal, Machine B is better than Machine A. They may both be at an advantage, or neither may be at an Advantage. You simply do not know, and it is becoming increasingly difficult and decreasingly valuable to attempt to figure it out.