Faith keeps many doubts in her pay. If I could not doubt, I should not believe. ~Henry David Thoreau

After two decades as a pro gambler, it's really hard to think back to the time when I was brand new and green around the gills. As with most distant memories, what seem to predominate my recollections are emotions. What emotions? Well, fear and doubt mostly. I wasn't sure video poker machines were truly random. I wasn't sure that math was all there was to gambling. I wasn't sure of many other things, other than how much I was unsure. I seem to recall waking up insecure and going to bed perplexed with nothing but quandary, guesswork, and doubt in between. Most of all, I remember the doubt, lots and lots of doubt. My daily fair was a double order of doubt, topped with doubting sauce and an extra portion of doubtfulness on the side. So when did my doubt die, and what killed it? Good questions!

I was very fortunate, when during only my third year of gambling, I was handed the reigns of the largest progressive video poker team in the world, which was tantamount to declaring open season on my doubt and handing me a semi-automatic shotgun for the hunt. Had I not been thrust into such a unique situation, I might well still harbor reservations to this day. My dubiousness has undoubtedly departed, and now it seems my obligation is to impart the road that led me to the blessed state of moderate certainty that I now enjoy.

In this month's column, I'll detail what staunched my own incredulity and misgivings about the fair randomness of video poker machines in Nevada. Since you, dear reader, will likely not have a huge team from which to gather statistical samples, in my article in next month’s issue of BJI, I’ll discuss what you alone can do to kill your incertitude (if you have any) and gain a bit of confidence (if you need any). I will also be publishing a do-it-yourself-home-test for randomness that you can use.

Included in my tasks as manager of a large progressive team, it was my doubly dull duty to do paperwork and record keeping. To understand how we data mined our records to reveal the rather boring truth concealed within them, first, you need to understand how we kept records. Each team player kept a log card with the time of their buy-ins and the progressive meter amount when they bought in. The standard buy in amount was $100, and they logged this as well. By knowing how fast the meter progression was, we could very easily reverse engineer the total number of hands played from when we sat down to when the meter hit. Since we typically had all the seats, simple division determined calculating jackpot frequency.

Playing a progressive strategy that's designed for high royals on Jacks or Better machines, the math predicts that you should get one royal flush about every 32,500 hands. When looking at our records, over the course of three years it turned out that we had not gotten exactly one Royal for every 32,500 hands ... actually, we did slightly better, at just over 32,000 hands for each royal. As you might imagine, finding out that the reality was better than predicted went a long way toward assuaging our concerns. We can only hope that if a casino or gaming company was bold enough go against gaming commission rules to gaff their machines, they would at least do it in the house's favor. Though statistically insignificant, what we found in our records was in the players' favor.

Now, it seems a good idea to state how big our sample was. When I came on as manager, we had roughly 48 players, which expanded to the high 60's over the course of a few months, because of an employee hiring drive and training program that my mother and I started. If you include all the progressives around town at that time, and the ones in neighboring cities, on a good day we had as many as four progressive royal plays. It was rare not to have at least one ongoing play somewhere in town at all hours of the day and night. It was a 24/7 business. Even though it varied from year to year, a good solid average number of hands for our entire team were in the neighborhood of twenty million hands played per year. I only had access to the records during my stay as manager and those left to me by the former manager, which covered about two years. This was still a sample of more than 50-million hands. Essentially, if we are talking the size of VP hand samples, "Mine is bigger than yours." Moreover, these were real hands, not simulated ones.

Obviously, progressive jackpot frequency isn't the only thing a dastardly casino might choose to alter to increase their ill-gotten gains. They could manipulate the base return by decreasing the frequency of any of the lower payoffs. You'd still get just as many jackpots as you expected, but your cost would always run too high. Yes, we looked at this as well. And what did we find? 'Bout what you'd expect. Graphing the results of many plays, we found the familiar and beautiful bell curve shifted just slightly left of expected return with perfect play. Since we expect people to play less than perfectly, left of perfect was exactly what we expected. However, there was one anomaly...

For some reason, which at first remained a mystery, our results were too consistent. You're probably thinking, "Huh, why is he complaining about that?" We'll it's simple, really. True, fair randomness is far more chaotic than we'd like to admit to ourselves, so when things go too closely to plan, something is clearly amiss. When looking at our results, they were too clustered around expectancy, giving our bell curve a mountain peak appearance. Team players were not having as many gargantuan losses as expected, nor were they having as many humongous wins as would be predicted. Our accountant, Dave, came up with the reason why our big losses were truncated, and once I tell you, you'll think, "Of course, that's obvious". Well it wasn't to us, and for several months, it had us stumped.

Our players didn't like losing, so when they were down, they slowed their play, which had the effect of decreasing the maximum they were able to lose in a shift. Forlorn and downtrodden players simply played slower. Kinda a no-brainer once you think about it. Inversely, if players were doing well, they sped up their play, increasing their hand speed. Since they were playing on negative expectancy machines (not including the Jackpot), this tended to make their results fall closer to mean. However, that still doesn't explain the lack of huge wins.

Sadly, we explained this anomaly as well, and it turned out to be an artifice of human nature, as well ... the darker part of it; namely, "dishonesty." It seems that some players felt it was easier to hide theft by taking the top off a large win than it was to increase an already large loss further. I guess they figured that no one would expect someone handing in a $1,000 machine win would be stealing. Of course, mathematics easily revealed the deception, once we knew what to look for. After meticulously going through our records, I flagged several players with suspicious results and had them watched by a special player in charge of security. This special player kept duplicate records of the players seated next to them, so we could double check what was turned in. In two weeks, I fired over ten people for stealing. In the process, I found out I'm no Donald Trump because the least favorite part of my whole job was letting people go.

What were my ultimate conclusions about honesty and randomness in the video poker world? It was this:

As an individual, you aren't going to have multi-million trial samples to work with to put your own doubt to the scythe; and if one is going to be sure of something like this, personal experience is by far the best route. In next month's article, I'll cover mathematical formulas and record keeping techniques that you will be able to use to quell your doubts that a video poker machine is gaffed.

NOTE: Our team played only in Nevada regulated areas. I have no direct knowledge of machine fairness outside of Nevada. My tenure as team manger was in the early 90's; consequently, my information is two decades old. I don’t have any information from direct observation and large-scale samples that's more recent.