I like playing this one bartop machine at a casino I visit once or twice a week. I only play this machine when the bar is not open. I don't want to take up a position when the bar is open because I order only the occasional water or Coke, though sometimes some rum does sneak into my soft drink.
The chairs at this bar are normal height, not tall. Instead of climbing up onto them, you sink down into them. The machine's screen is at a good angle and there is no glare on it. The buttons aren't as responsive as the buttons on most slant-top machines, perhaps as a result of having more drinks spilled on them, but they work reliably. The best part about playing this machine, though, is that the bar and its attached lounge are less smoky than other areas of the casino because few, if any, people are there when the bar is closed. After picking up something for breakfast at the snack bar, I park myself at this machine to play NSU Deuces.
NSU is a moderately volatile game. Not as volatile as the [Double | Triple] Bonus Poker variations, but more volatile than Jacks or Better. Jacks or Better doesn't have the 1,000-coin mini-jackpot for getting four deuces, which has to get funded by fewer or less generous payouts lower in the pay table. I'm used to usually losing a little, sometimes a lot, but many times being able to break even and, of course, sometimes winning and, on rare occasions, winning big playing NSU.
I've played this machine almost exclusively the past few weeks and my results are miserable. The machine seemed to have only one setting — lose big. Breaking even and winning were not on the menu.
Each session followed the same script. Put money in machine. Watch credit meter go to $0. Repeat. Every time the machine gave me a straight flush, five-of-a-kind, or dirty royal, it immediately took it back. It's as if it were saying, "Oops! Didn't mean to give you a good hand."
Did I mention that this is a higher-denomination machine than I usually play? Adding insult to injury, I didn't even earn many slot club points because the machine gave me so little play for my money.
I keep track of the number of hands I play, the number of deuces (hands with four deuces, that is) and royals I hit, and my win/loss for each NSU session. I figure that I've played 14,130 hands on that machine without getting four deuces once. It was so bad I even verified that I was seeing a deuce in each suit at the beginning of one session. It became a challenge to keep playing that machine until it gave me my deuces.
Worse, my deuce drought spread to other machines in other casinos. I was owed 10 sets of deuces to bring my deuce frequency up to the expected number.
I think I figured out what was causing my lack of deuces. I had a severe case of Deuce Cooties.
Every time I was dealt a deuce, it got infected with my Deuce Cooties. One infected deuce wasn't strong enough to repel a second deuce. And two infected deuces weren't strong enough to drive away a third deuce. But three infected deuces were so strong that the fourth deuce couldn't break out of the deck and into my hand.
There's no known cure for Deuce Cooties. The only treatment is to keep playing. Increasing the sample size diminishes its effect.
I've written a few times in the past months that it's not unusual to play more than the expected number of hands between hitting premium hands. I have a vague recollection that another writer wrote an article about this subject 10 or more years ago and that the analysis used the Poisson Distribution. I also have a vague recollection of the Poisson Distribution from my college Statistics class, something about the number of blueberries in a muffin.
After brushing up on the Poisson Distribution, I discovered that it is applicable to both blueberries and royals and deuces and other independent events that occur at a constant rate. Searching for video poker articles that mentioned the distribution, I found What does royal flush cycle mean? by Henry Tamburin on this site.
Poisson did all of the heavy lifting for us and calculated the probabilities of seeing 0, 1, 2, etc. occurrences of an event in a cycle. What's a cycle? Technically speaking, it's the Mean Waiting Time between occurrences of an event. We say that you hit a royal roughly once every 40,000 hands, so on average you have to wait (play) 40,000 hands between hitting royals. The cycle is 40,000.
Four deuces occur about every 5000 hands on NSU, so the cycle for deuces is 5000.
Following are the probabilities for hitting, 0, 1, 2, 3, 4 and 5 sets of deuces in one cycle:
0 - 0.368
1 - 0.368
2 - 0.184
3 - 0.061
4 - 0.015
5 - 0.003
About one-third of the time, we'll hit one set of deuces in a cycle. Somewhat depressingly, we'll hit no sets of deuces in one cycle with the same probability.
There is some good news in the numbers. If the probability of hitting no deuces in a cycle is 0.368, then the probability of hitting 1 or more sets of deuces is 0.632. So we're more likely to hit one or more sets of deuces in a cycle than none.
What about the probability of hitting no deuces in two cycles? If the probability of hitting no deuces in one cycle is 0.368, then the probability of no deuces in two cycles is (0.368)(0.368), or 0.135. In three cycles, the probability drops to 0.049. About 1 out of 20 of our blocks of 15,000 hands will be deuce-free.
The same probabilities apply for royal flushes, straight flushes, five-of-a-kinds, and any other event that occurs once per cycle.
So I've gone almost three cycles on that darn bartop machine without a set of deuces. With a 4.9% chance of occurring, it's far from frequent and also far from being a once-in-a-lifetime occurrence.
Last week the machine finally starting showing me some love. It didn't give me deuces or a royal, but it let me play for a long time without having to feed the meter and I quit when I was $5 ahead.
I was looking forward to another good day on the machine today. Getting the deuces it owed me would have been nice, but I would have been happy with breaking even. Breaking even is the next best thing to winning.
The machine started off treating me nicely. But then My. Hyde resurfaced and the machine went back to its old playbook.
It's tempting to think that there's something wrong with that machine for denying me my deuces for so long, but Poisson showed that it's not that unusual to go one, two or three cycles without hitting deuces.
