Playing Tricks

            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 at math.  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 Red Rock Station, this might cause some players to stay away.  But, 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 that 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, just because it can be known does not mean that 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 that 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 that every 31st hand is going to be a Razgu.  It means over time that 1 in 31.  But what does it mean in the short run?


            In the very short run, it is very simple.  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?  You probably have once in a while.  If you're a regular player, you may have logged hundreds of thousands of hands, so a 1 in 29000 event is 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 was three out of four hands.  In between two of these Razgus, you were dealt a Low Pair.  Then we are talking about 1 in 7555.  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 15625.  This shaves it almost in half! 


            Looking over a slightly longer timeframe, some of you may be surprised to learn some other statistics.  Using the standard strategy which results in a Razgu 3.25% of the time, you will get 1 or more Razgus in a 20 hand stretch 48% of the time.  Even though the hand 'on average' occurs 1 in 31 hands, you'll get 2 in 20 hands more than 11% of the time.  You'll get 3, more than 2% of the time.  Even at 6 in 20, you are still talking a 1 in 35000+.  These are long odds, but they are not astronomical.  When you consider how many Players are playing at any point in time, you realize it is happening to at least one of them constantly.