Royals once elusive in video poker
February 02, 2016 3:00 AM
by Elliot Frome
Expert Strategy consists of three key components: (1) Know which games to play, (2) know the right strategy for those games and (3) know what to expect.
I find the third one to be the most intriguing. When it comes to video poker, I realize I’m hardly the only source for video poker information. There are other writers and there is a variety of practice software out there.
These will all help you learn the first two. But, I think it is a combination of my math skill and the ability to explain it to the masses that help to separate me from some of these other sources. One doesn’t really need to know what to expect in order to master the first two, but learning it is what keeps the player disciplined to stick to the plan.
There are times when playing video poker that even I start to wonder if the games are rigged. I know they aren’t, but it just seems like that on some days I get more Razgus than High Pairs, when you should be getting four times as many of the latter. But, that doesn’t mean while you look at a sample of two hours of play it is going to be all that close to that amount.
I’m guessing it was in the early 1990s when my dad first showed video poker it to me. Up until that point I was mostly a blackjack player. But, even at $3-$5 a hand, blackjack required a bigger bankroll and I was getting a little bored with it. I was probably coming out to Vegas about 2-3 times a year for a week and most nights would play video poker for 2-4 hours. Over several years, my Royal Flush count was a big fat zero.
Adding insult to injury, my now ex-wife, came out to Vegas with me in those early years, and hit a Royal on her very first time playing. She won $12.50 (she played one nickel). My best guess was I had played well over 100,000 hands without hitting one. Feast or famine.
I spent two different weeks in Las Vegas over a six-week period. In that time, I hit three Royal Flushes. These were all max-coin quarters, so I won $1,000 for each. I would guesstimate playing 15,000 hands. So, how could I go over 100,000 hands without hitting one and then hit three in 15,000 hands?
This past week, I had to answer a question about a sidebet for Ultimate Texas Hold’em and a casino that was concerned the Royal was hitting too often. It had hit five times in a several week period and based on the number of hands played clearly “should not have” hit that often.
This concept could be one of the most baffling for even the industry to fully understand. If some event should occur 1 in 100,000 it does not mean if two of them occur over that period this was some sort of 10 billion-to-1 shot. And even if you get two of them over only 25,000 hands, it doesn’t mean something is broken. It means things are behaving exactly as they are supposed to.
The probability of hitting a Royal is 1 in 40,120. Calculating the probability of not hitting one in 100,000 hands requires us to take the opposite probability (40,119 out of 40,120) and multiply it by itself 100,000 times. This comes out to 8.27%. Um… this doesn’t sound so rare.
The probability of being dealt Two Pair or better in a 5-card deal is 7.73%. Even if I take it to 150,000 hands, it is still a 2.38% probability. Luck was not on my side at this point, but the game was just being itself.
Next up, is hitting three Royals over 15,000 hands. It works out to be 0.60% or 1 in 167. Given how many video poker players there are in the world, this 3 out of 15,000 has occurred countless times and all within the natural order of things. Nothing is broken or wrong about the math.
The probability of hitting 0 over this period would be 68.81%. Hitting 1 would be 25.73%. Hitting 2 would be 4.81%. That 0.60% is about the same probability as being dealt a Straight or a Flush right off the deal in a 5-card stud game. If you’ve played video poker for a few hours, you know it happens.
The last example was 5 Royal Flushes occurring in about 28,200 hands in a 7-card deal. A Royal should occur about 1 in 30,940 so having 5 over a slightly shorter cycle must mean someone is cheating!? Or maybe not. The probability of 5 over this period is 0.2181 or about 1 in 458.
I’m not sure exactly how many UTH tables there are, but if there are 1,000 of them and we looked at the last six weeks of play (or 28,200 hands) on average two would have had five Royals over that time. It’s not a lot.
I always love to cite the frequency of a number repeating three times in roulette, which for a single 0 is 1 in 1369. I’ve never seen it happen. But given there are dozens of of roulette wheels in Las Vegas, it likely happens here daily one or two times.
If a wheel has 500 spins per day and it happens twice one day it doesn’t mean the wheel needs maintenance. It means even the outliers are going to happen.
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Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Email: ElliotFrome@GamingToday.com.