Royal Appearance

            Last week’s column was prompted by a reader who raised some concerns that Players who use their frequent player cards are somehow cheated by casinos.  The ‘proof’ of this is that some locals (i.e. frequent Players) don’t seem to get as many Royals as the tourists.  Previously, I had cited at least two reason for this. 

            The first is selective memory.  We tend to remember things we want to remember.  When we go through an extended cold streak, every other scream of “Royal” is burned into our brains.  I’m guessing that in the week you hit your last Royal, someone else did too that week, but it didn’t bother you one bit.  If you’ve gone a year without one, everytime someone gets one, it hits you like a ton of bricks.

            Secondly, even if you’re trying to be relatively objective about it, you also have to remember that ‘you’ are greatly outnumbered by ‘them’.  Even if there are a couple of you playing together, there are dozens if not hundreds of other people playing around you.  It is no surprise that they WILL actually get more Royals than your group will.

            There is, of course, another possibility – other people ARE actually get more Royals than you are!  So, am I buying into the whole ‘rigged’ video poker machine theory?  ABSOLUTELY NOT! 

            But, the number of Royals you get over an extended period of time is greatly influenced by the strategy you use.  So, there are two possibilities.  YOU may be using the wrong strategy which is reducing the probability of a Royal OR the other guy is using the wrong strategy which might INCREASE the probability of a Royal.

            Let’s look at these two scenarios.  The proper strategy for any particular video poker machine is one that maximizes the overall payback, not one that maximizes the probability of hitting a Royal.  What do you do when you’re dealt the following?

A♥       Q♥       10♥      5♥        5♠

            Do you hold the Low-Pair?  The 4-Card Flush?  The 3-Card Royal?

            The correct answer is the 3-Card Royal.  If you’re playing one of the other two, not only are you hurting yourself from a payback perspective, you’re lowering your chances of hitting a Royal.  By the way, the decision is not even close.  The expected value (EV) of the 3-Card Royal is 1.41.  The 4-Card Flush has an EV of 1.22 and the Low Pair a meager 0.82.

            So, if you’re not playing this hand correctly, don’t be surprised if some others around you are hitting more Royals.  Of course, they may have their own issues.  What do you do when you’re dealt the following?

A♥       Q♥       10♥      5♥        Q♠

            The correct answer is hold the High Pair with an expected value of 1.54.  Now, you may be doing this, but that ‘tourist’ behind you may not.  What is the impact of holding the 3-Card Royal.  Well, he’ll lower his overall expected payback, BUT he will increase his probability of hitting a Royal.

            The examples I used here are not the most common occurrences, so these will not make a big difference to the frequency of a Royal happening.  Far more common are the hands that include a 2-Card Royal that also include 3-Card and 4-Card Flushes and Straights.  I have little doubt that there are many novice Players who get Royal fever and just play every 2-Card Royal instead of 4-Card Straights and Flushes or 3-Card Straight Flushes.  Doing so, will make them hit more Royals than you will, but they won’t be any richer for it. 

            Under normal circumstances, for a jacks or better machine, a Royal should appear about once every 40,000 hands or so.  By altering one’s strategy it is very easy to reduce this to once every 30,000 hands or so, which is considerably more frequent.  But, it will come at a cost of lowering the payback by a significant amount too.  So, the next time you’re upset that someone else got a Royal, start worrying about how you’re playing and not what’s happening around the corner.  They may pay dearly for their Royal appearance.