Ask the Slot Expert: Where have all the deuces gone?

Robin, the Boy Wonder, picked up the parchment he found on the casino floor.

"Holy video poker, Batman. The Riddler left another one of his diabolical riddles."

"Read it, Robin," said the Caped Crusader.

"When is playing NSU Deuces like playing 9/6 Jacks or Better?" said Robin. "This is a tough one, Batman."

"I think I know the answer, old chum. Playing NSU is like playing 9/6 Jacks or Better when you don't get your share of sets of deuces."

Last year I went a little over three months between hitting sets of deuces. The fact that the casinos were closed most of that time had a lot to do with that gap. I never thought I'd leave that record in the dust with the casinos open and my playing regularly again, but not nearly as much as I did pre-pandemic (and pre-slot club downgrades!)

Jean Scott once told me that one of the reasons she likes NSU Deuces Wild over 9/6 Jacks is that hitting a set of deuces can help you recover from a couple of bad sessions or even one terrible session. Jacks or Better doesn't have a comparable hand. The next best thing to a royal in 9/6 Jacks is a straight flush, but it pays only a quarter of what four deuces pay and it hits about half as frequently. She said that sometimes your only hope of getting out of a hole is to hit a royal.

Three-of-a-kind, the lowest-paying hand in NSU, doesn't hit as frequently as a high pair, the lowest-paying hand, in Jacks or Better. You need to hit your share of Wild Royals and five-of-kinds to make up for the less frequent pushes. Many times a flurry of premium hands (Wild Royals, five-of-a-kinds and straight flushes) near the end of my session has turned that session from loser to nearly breakeven.

Over the past few months, not only have I not been getting my share of deuces, I also haven't been getting my share of premium hands. It seems like I used to have a pretty good chance of breaking even for a session. Small win, small loss, sometimes sizable win or sizable loss. But it wasn't loss, loss, loss, loss...loss the way it's been the past few months.

Let's take a look at my diary.

February 24, 2020. A double header. A royal and a set of deuces.

July 14. 2021. I get a set of deuces. It's been 90,000 hands since my last royal. I should have hit two royals in that number of hands, on the average, but at least I've had 17 sets of deuces, which is about the number expected.

August 12. About 5500 hands played since last set. That's about 5400 hands between sets, on the average, but it's not unusual to go one cycle without getting a set.

August 27. Over 10,000 hands since last set. Two cycles, no deuces, not unusual.

October 10. Over 15,000 hands since last set. The probability of an event not happening in three cycles is 0.05.

October 20. Over 20,000 hands without a set of deuces. The probability of an event not happening in four cycles is 0.018.

November 7. Almost 25,000 hands since my last deuces. The probability of an event not happening in five cycles is 0.007. But I did win a consolation prize. I was dealt a 4-card royal in hearts. I was hoping for a deuce to score a nice dirty royal. I didn't really want to get my first W-2G of the year. I hit draw and got the king I needed to complete the royal. Okay, I'll take it. Especially since it's been 19 months and over 100,000 hands since my last royal.

November 14. Over 31,000 hands since four twos have graced my screen at one time. This is getting ridiculous. I sometimes check that I see deuces in all four suits while playing. It's hard to believe that I've sometimes hit three sets of deuces in a session of 2000 hands. The probability of an event not happening in six cycles is 0.003.

November 21. Finally, after four months and about 35,000 hands, I was dealt three deuces and the fourth was not hiding in some other machine when I hit Deal. The probability of an event not happening in seven cycles is 0.0009. Have to remember that extremely unlikely is not the same thing as impossible.

Based on the 1.1 million hands I've played and the average hit frequency of royals and deuces, I estimate that NSU owes me eight royals and eight sets of deuces. I wish I could expect that the game will make up for that shortfall in the next million hands, but that's not what is most likely to happen.

The most likely thing to happen is the most likely thing to happen. The most likely thing to happen over the next million hands is that I'll hit royals about once every 43,478 hands and deuces once every 5347 hands, on the average.

Right now, I figure that I've gotten a royal once every 63,000 hands and deuces once every 5500 hands. What will my stats be if I just hit these hands with the expected frequency in the next million hands?

My average number of hands between royals drops to about 52,000. It's still above the expected average number of hands between hits, but it's much closer.

My average number of hands between deuces drops to about 5400. That's very close to the expected number.

If the hands continue to hit with the expected frequency for another million hands, the hands between hits stats would get even closer to the expected number. The machines don't have to do anything to make up for my shortfall so far. All they have to do is do what they're likely to do.

One of the Gambler's Fallacies is that an event is more likely to occur in the future because it hasn't occurred as frequently as it should have in the past. How else is a machine going to "make its numbers?"

How many times have you thought, "This machine hasn't been paying. It's got to start paying soon. It's due." Or, "I haven't had a bonus in a long time. It must hit soon."

How many players have lost more than they should have because they thought that a big hit must be coming soon?

The opposite situation is not a problem, though.

No one ever got into trouble leaving a machine that they think will turn cold.

Here are the latest Covid data. There is a difference in the hospitalization data for US versus NV. The CDC reports total number of Covid hospital admissions. Nevada reports current hospitalizations, not admissions.

All data comes from the CDC (https://www.cdc.gov/covid-data-tracker/#cases_totalcases, https://covid.cdc.gov/covid-data-tracker/#new-hospital-admissions), except for Nevada current hospitalizations (https://nvhealthresponse.nv.gov/).