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by Frank Kneeland

Frank Kneeland was the manager of the largest progressive video poker team in Las Vegas, and has authored a book about his adventures entitled, "The Secret World of Video Poker Progressives". You can get the book as well as some extra info about Kneeland on his website In addition, there you'll find the show archive for his radio show on pro-gambling, "Gambling with an Edge" that he co-hosted with Bob Dancer for six months.

Sometimes you can't be certain, but you can be absolutely sure just how uncertain you are.

~FK 2012

Welcome to the third and final part of my series of articles on doubt in the fairness and randomness of video poker machines. It is not my intention to suggest that machines are unfair, nor is it my intention to assure you that they are fair. So many people worry about such things that I feel that a detailed description on how to prove it to yourself is in order. I've always been an advocate of skepticism when warranted; when your money is on the line and others could profit from deception, skepticism seems the prudent course.

In Part I, "The Death of Doubt" I recounted the method I used when I was a progressive team manager to remove my own personal doubts. It involved brute force; a massive sample that would be impossible for individuals today to implement. Last month in Part 2, "Doubt Hunting" I went over the industry standard equation, Chi Squared, used to test the randomness of machines. Most importantly, we discussed what the equation tells you, and that it can't be used on old data. Understanding these two issues is paramount for correct implementation of confidence testing, so I highly recommend reading part II before you read this. Part I can be skipped without issue because, as I already stated, you aren't going to be doing it the way I did it.

To make it easy to do this at home (in a casino), I've created a spreadsheet utility that incorporates the Chi Squared test, and makes record keeping easy. Instructions for downloading it are included at the end of this article. The following subheadings explain the three tests included in the utility.

Three Paths to the Same Destination

If you are concerned that video poker machines are not random and fair there are three fundamental types of data that you can easily track for the purpose of confidence testing. The task may have the additional benefit of adding enjoyment to your VP play since many people like to keep track of what hands they hit. Though each data type is similar in conclusion, they are very different from the point of view of what you track, how you track it, and how long it will take to accumulate the data. They are also dissimilar in the amount of effort required and how visible they make you to casino personnel. One can track all the cards one is dealt and all one's draws. One can track dealt hands and the paying combinations one makes. Alternatively, a person can track the times they hold certain cards and the times they make the hands they were drawing to. Two of these methods work independently of strategy; the third does not. By far, the quickest way to discern meaningful information about randomness from VP play is by tracking all dealt cards and all drawn cards. This method is also the most labor intensive, boring, and visible, but we'll go over this one first as it is the quickest and most accurate.

The All Cards Test (Time to complete: One very long very boring day)

Unlike most things in politics, this test is exactly what it sounds like. When you are dealt a hand, you record all five dealt cards on a sheet of paper (don't use a computer or cell phone). I like using a simple note pad with a column for each rank of each suit, and then one simply makes a hash mark for each card when it comes up. After you record the dealt cards, you hold whatever you want and draw, recording all the drawn cards as well in a separate but connected reckoning. Since a deck contains 52 cards, it works best to record sets of 104 hands in this manner, which renders an exact expected average of 10 occurrences for each card per set. In the utility, I've created an entry field for 12 sets of 104 hands, for a total of 1248 hands. Because each hand represents 5-10 trials and the cycle length of getting any single card is 1 in 52, this method is surprisingly effective and fast, but it's also the most obvious and labor intensive. In a casino with 'heat,' it would be ill advised and nigh impossible to do without being noticed. Only you can decide if it is bad to be noticed.

Unfortunately, what gives the method its strength is also is biggest weakness. Since you aren't tracking made hands, true skeptics will never believe the results of any test that ignores how they are doing (money-wise) on the machine. The test could show that all the cards are coming with perfect 1 in 52 frequency, but if the user hadn't gotten as many four of a kinds and they felt they were due, or if they were losing, they would most likely disbelieve the results. There's no mathematical basis to disbelieve the data based on results, but I guarantee you there will be naysayers of this method for that reason.

Playing at normal speed one could get through 1248 hands in a couple hours. Obviously if you are taking notes for every hand, it will take longer (one could use a partner to record the data to speed things up), but even going slowly this is still something one could do in a single day. This test works independently of strategy and is effective for any game type.

Strategy Dependent Test (Time to complete: Several months to your entire lifetime.)

By far the most common type of records people keep is made hands. We've all seen people that pause and record whenever they make a 4K, SF, or Royal. This test utilizes made hand data, but it is vital to understand that the hands you make and the frequency of those hands is totally dependent on what strategy you play. The utility has the frequencies for various hands, straight on up to Royal Flush, hard-coded for the most popular game types built in. However, if you don't play perfect strategy your results will be inaccurate. For instance: On 5-7-T Double Bonus Poker, it is not correct to hold a pair of aces over two pair. That having been said, many do it anyway. If you choose to deviate from correct strategy or if you simply make an error, it will throw the test off and give you incorrect results. How inaccurate the test results are, depends on how inaccurately you play.

Due to dependence on playing correct strategy, this test is the most error prone. It is also the least labor intensive (least number of data entries), simplest to implement, and something you can do for the entirety of your gaming experience. Because it's something you can do over years of play, it retains a measure of accuracy due to potential sample size. You'll need at least several months of data for the test to render meaningful results. This is the slowest of the three methods.

Lastly, this test requires the absolutely accurate tracking of the total number of hands you play, which is assisted in the utility by tracking your slot club points and the number of points per hand (or hands per point). If you were to miscalculate how many hands you played in a session even once, it would throw the test off by an unacceptable margin, so again this test tends to be the most error prone. If you never make a mistake calculating your hands played and you play near perfect strategy, the test works just fine. Just don't overestimate your chances of never making a mistake. To err is, after all, human.

Strategy Independent Test (Time to complete: Several days to a few weeks.)

One way to eliminate the effects of strategy errors on confidence testing is to track the times you draw to certain hands and record the times you make the hands you are drawing to. In other words, rather than simply recording how many flushes you get, you record how many times you are dealt 4 to a flush, draw to it, and make it. This is not only faster than the strategy dependent method, since it samples more things (holds as well as draws) and it is less error prone. The primary disadvantage is that you'll be pausing far more often, since you'll be recording holds like 2-pair, 3K, 4FL, 4ST, etc., as well as whether or not you draw the paying ST, FL, FH, 4K, SF, or Royal after making such holds. This method still requires tracking total hands as it tracks dealt made hands, but it is far less error prone and completely ignores what strategy you choose to play and how accurately you play it. Its major benefit is that it will engender meaningful confidence in a reasonable amount of time. Most likely, it is not something you'll want to do for your entire career. You'll just whip it out when intense doubt of a particular machine rears its ugly head. Remember to toss out the data that made you suspicious in the first place.

Unlike the strategy dependent method, you will not be recording ALL made hands. You'll only be recording the times you made certain hands drawing to certain holds. Example: You'll record some of the four of a kinds you get, but not all of them. Specifically, you'll record only the ones you are dealt and the ones you get drawing to three of a kind. If you hold a lone ace and make four aces, you won't bother recording it (for this test).

It is, of course, possible to use this test in conjunction with the Strategy Dependent Test as well, as long as you don't confuse the data entry between the two methods.


There is absolutely no reason why you can't use the Strategy Dependent Test all the time, incorporating it into your daily lifetime record keeping and use the other two tests only when you become really suspicious of a certain machine and would like to test it quickly and more vigorously. In fact, this is exactly what I recommend. Each test has its strengths and weaknesses, time vs. accuracy, visibility vs. stealth, fun vs. drudgery, etc., and no one test is right for every situation. I know several players who enjoy tracking their play in this manner and they assure me it adds to their enjoyment of the game. If it doesn't add to your enjoyment, don't do it.

You can download the utility entitled The Confidence Quantifier direct from my homepage and it comes in Microsoft Excel format and OpenOffice format (which is a free download here: for the app).

The Strategy Dependent part of the Utility can also be used for tax records.

(Please note: The Confidence Quantifier only works on video poker and is ineffective for validating political campaign promises)

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