Mom, Where Do Royals Come From?

            In last week's column I discussed Four of a Kinds and the probabilities of drawing one from a Pair vs. drawing one from Trips.  It's interesting stuff, but not necessarily overly useful.  We very rarely throw away a Pair to go for Quads.  If you have a 4-Card Flush, a 3-Card Royal or the rare - J-Q-K-A you would do so.  But not a lot of thought needs to go into playing Pairs.

            Royals fall into a similar category to Quads.  We do NOT get most of our Royals from a 4-Card Royal.  Of course, once we have a 4-Card Royal, it offers us a much better chance than if we had a 3-Card Royal.  But 3-Card Royals are so much more common than 4-Card Royals that we find that this is the most common way a Player will hit a Royal.   In similar vain, we find that we are about 20 times more likely to be dealt a Royal on the Deal than we are to Draw one from a Razgu.  But, most Razgus will involve throwing away 5 cards that could not have made up any part of a Royal (the exception being Razgus that have a 10).  So, the probability of getting a Royal from a Razgu is actually higher than getting one on a deal.  But only 4% of our hands our Razgus, and 100% of our hands have an initial deal, so the initial deal is actually the more likely way a Player will get one.

            Unlike Pairs and Trips strategy, partial Royal Flush strategy is not so clean.  I think it is fairly obvious that if you are dealt a Royal, you keep it.  The same is true if you are dealt a 4-Card Royal.  Even if the hands is also a Flush or a Straight, you go for the big prize.  Next up is a 3-Card Royal Flush.  You need to pay a bit more attention to this hand.  If you have a Flush or a Straight, you keep it.  If you have a 4-Card Flush or 4-Card Straight, you still go for the Royal.  But if you have a 4-Card Straight Flush (Inside or Outside), you go for the 4-Card Straight Flush.   Do not forget that your odds of hitting the Royal is still 1081 to 1.  An 800 payout still leaves us with an expected value of 0.80 before we account for all the other possible winners.  It is a powerful incentive, but it is not all powerful!

            Now it gets really messy as we move to the 2-Card Royal.  Many 2-Card Royals are effectively ignored.  If you have a 4-Card Straight that includes a 2-Card Royal, most likely you are playing the 4-Card Straight.  I can't cover all of the combinations in my column today.  But, 2-Card Royals are broken down into 4 possiblities.  JQ, JK, QK is one.  JA, QA, KA is the second,  10J, 10Q, 10K is the third.  The last is 10A.  This last one is not even considered playable in jacks or better.   Aces are not as powerful as J, Q or K because they make the Straight 'Inside' and limit the possibilities.  10's are weaker yet because they don't count as High Cards. 

            The critical part of the strategy is that if you have 3 High Cards and TWO of them are suited, you keep that 2-Card Royal.  While the possibilities of the Royal plays a part in this decision (but it's a 16,000+ to 1 longshot), it is also the added possibilities of drawing a Flush that helps to create this situation.  When my father, Lenny Frome, first analyzed video poker, I think this was one of the larger surprises that he discovered.  Before this, if dealt any 3 High Cards he was holding that over any two suited High Cards.  This turned out to be the incorrect play.  The only time we play 3 High Cards is if they are JQK and all three are of different suits.

            No one ever refers to holding a single High Card as a 1-Card Royal, but that is essentially what it is.  Of course, since our strategy teaches us to NOT hold a 10-A suited, it is possible that if you had one of these and properly played just the Ace that you would have given up any chance of getting the Royal.  But at 178K to 1, the impact of the Royal has nearly vanished.  We really don't hold the 1 High Card because we hope to get a Royal.  We hold it because it is preferable to throwing all five cards (albeit barely) and we mostly hope to pull a High Pair and get out of there even.   But, the 1 High Card will occur just over 15% of the time and as a result, we can expect to get about 4% of our Royals this way.

            Last and least is the Razgu.  You've been dealt 5 cards below a Jack.  You don't have a 4-Card Straight, a 3-Card Straight Flush or a Pair.  You throw all five cards and hope for the best.  Less than 1% of our Royals will come this way.  This is mostly because Razgus are relatively rare themselves. 

            So, the next time you're playing make sure that you properly identify your partial Royals and play them correctly.  You might just be surprised where your next Royal comes from.