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Math can play some very nasty tricks on the unsuspecting human. It can do quite a number even on those of us who are pretty good.

It is these “tricks” that can so easily distract a player, causing him to believe all sorts of outlandish things – like the machines are rigged. This, in turn, can cause a player to wonder why he should follow any strategy based on math if the games are rigged.

Really, the question you should ask is: If the games are rigged, why would you want to play them at all?

In a manner of speaking, the games are rigged. For the most part, they are designed with a mathematical advantage to the house. Since this is completely legal, I have no idea why a casino would want to rig them any further.

Why would a casino put in a 98% video poker and then “rig” it so it only pays 95%? They could just as easily drop a couple of pays and voila! It is now a 95% machine.

At a locals casino this might cause some players to stay away. On the Strip and in a lot of other areas where casinos exist, most players won’t even notice.

So, we’re going to have to go with the notion that the games are not rigged in that way. They play according to natural probabilities that would exist if we used a standard 52-card deck and dealt the cards physically right in front of us.

If we start with this as an assumption, everything one needs to know about the game can be laid out in front of us. Every single probability is known. It can be computed with certainty. But that does not mean the average person knows what to do with it.

I was playing video poker this week and admittedly getting rather frustrated with the number of Razgus I was getting. A Razgu is the worst “playable” hand in that it requires you discard all five cards and draw five new ones.

In a Jacks or Better machine it should occur about 3.25% of the time – or about 1 in 31 hands. But, what does this really mean? It doesn’t mean every 31st hand is going to be a Razgu.

In the very short run, the odds of any one hand being a Razgu is 1 in 31. Thus, the odds of back-to-back Razgus is about 1 in 950. Three in a row, roughly 1 in 29,241. Have you ever had three in a row? If you’re a regular player, you may have logged hundreds of thousands of hands, so figure a 1 in 29,000 chance it’s going to happen.

Of course, there are many other possibilities that could be affecting this. The first is your memory. What if it wasn’t three in a row, but three out of four hands? In between two of these Razgus, you were dealt a low pair. Then we are talking about 1 in 7,555. Not nearly as long odds as three in a row.

Then there is the question of whether or not you are properly recognizing some of the lower playable hands. A single high card is better than a Razgu. Any imaginable 3-card Double Inside Straight Flush (with no High Cards) is better than a Razgu.

If you misplay some of these hands as Razgus, then you are increasing the probability of a Razgu, which increases the probability of getting multiple in a row. If your own strategy causes you to play 4% of the hands as a Razgu (instead of 3.25%), then the odds of three in a row decreases all the way down 1 in 15,625. This shaves it almost in half!

Looking over a slightly longer time frame, some of you may be surprised to get some other statistics. Using the standard strategy, which results in a Razgu 3.25% of the time, you will get one or more Razgus in a 20 hand stretch 48% of the time.

Even though the hand “on average” occurs 1 in 31 times, you’ll get 2 in 20 hands more than 11%. You’ll get three, more than 2% of the time. Even at 6 in 20, you are still talking 1 in 35,000. These are long odds, but not astronomical. When considering how many players are playing at any point in time, you realize it is happening to at least one of them constantly.

Why does any of this matter? As frustrating as these situations are, you have to realize they are part of the normal swings. About 51% of the time, you won’t get any Razgus in 20 hands. When these streaks are happening (and longer), you probably don’t even notice.

Get dealt three Razgus out of five hands (and remember it as 3 out of 3 or 3 out of 4) and it immediately makes your brain start wondering if there is something wrong with the machine. Almost assuredly there is not.

You have to accept it all and not let the machine play a trick on you right before your very eyes!

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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 Email: [email protected]

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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