Stroll Through the Strategy Table

            This week we continue our walk through a video poker strategy table.  Specifically, the strategy table for full-pay jacks or better video poker.  Last week we left off at the 4-Card Flush which was the last of the hands with an expected value of greater than 1.0.  These are the hands that result in net wins in the long run.  The rest of the strategy table have expected values below 1.0.  This means that in the long run we will not get back our entire wager.  But, that doesn't make them any less important.  When playing video poker, playing every hand correctly is critical if you want to achieve the theoretical payback.

            It could be argued that playing the hands below 1.0 correctly is more important than playing the ones above this line correctly.  First, the hands below make up the lion's share of hands.  Second, the hands below are by far more complex than the ones above.  You don't have to worry about confusing a Two-Pair with a 4-Card Straight Flush as this is an impossibility.  But a 4-Card Straight vs. a 3-Card Straight Flush might leave you shaking your head. 

            Without further ado, here are the next batch of hands on our strategy table:

{C}{C}·       {C}{C}4-Card Straight with 3 High Cards

{C}{C}·       {C}{C}Low Pair

{C}{C}·       {C}{C}4-Card Straight with 2 High Cards

{C}{C}·       {C}{C}4-Card Straight with 1 High Card

{C}{C}·       {C}{C}3-Card Inside Straight Flush with 2 High Cards

{C}{C}·       {C}{C}3-Card Straight Flush with 1 High Card

{C}{C}·       {C}{C}4-Card Straight with 0 High Cards

            The first thing you'll probably notice is that with the exception of the Low Pair, the number of High Cards is specified.  When the inventor of video poker decided to pay on Jacks or better, he added an incredible layer of complexity to the strategy.  Simply put, in any hand without a Pair or better, any card that is a Jack or higher is worth considerably more than any other card.  The reason should be fairly obvious.  We have the opportunity to win with High Pairs.  For each High Card in the hand, we have three additional cards that we can draw that will turn our hand into a winner.  These three cards add just over 0.06 to the expected value of the hand. 

            Sometimes, this 0.06 means nothing and sometimes it means everything.  We just need to look at the first three hands to see the impact.  If you have a 4-Card Straight with 3 High Cards and a Low Pair, you keep the partial Straight.  If you have a 4-Card Straight with 2 High Cards and a Low Pair, you keep the Lower Pair.  These hands are not very common, but they illustrate the impact of the High Card.   So, if you have 10-10-J-Q-K (assuming no 3-Card Royal), then you keep the Straight.  If you have 9-10-10-J-Q then you keep the Low Pair.  Having a 9 instead of a King lowers the expected value so that it falls just below that of the Low Pair.

            If we keep moving down the chart, we find that the next entry is the 4-Card Straight with 1 High Card.  As this is adjacent to the 2 High Card version, there really is no impact in this case.  We could lump these two hands together if we want to remove 1 hand from the strategy table.  We keep them separate because there are versions of video poker where it is relevant and we want to make sure the Player doesn't get 'lazy'. 

            In between a 4-Card Straight with 1 High Card and a 4-Card Straight with 0 High Cards we find 2 other hands.  They are both variants of a 3-Card Straight Flush.  The first is an Inside Straight Flush with 2 High Cards and the second is a 3-Card Straight Flush with 1 High Card.  This can start looking more confusing than it really is.  Most of these hands CANNOT occur in a single hand.  It is not possible to have both a 3-Card Straight Flush with 1 High Card and a 3-Card Inside Straight Flush with 2 High Cards.   But, you can have a 4-Card Straight with 1 High Card with a 3-Card Straight Flush with 1 High Card.  (8C 9D 10D JD 4H).  We learn from the strategy table that the right play is the 4-Card Straight.

            One last point that I should mention.  All the 4-Card Straights to this point have been Open Straight Flushes - meaning that they can be completed on both ends.   This means that as we have completed about 60% of the strategy table, we have accounted for all Pairs and for all 4-Card Straights (Open ended) and 4-Card Flushes.  The remaining 40% of the strategy tables contains very 'not pretty' hands.  It is a mish-mosh of 3-Card Straight Flushes, Inside Straight Flushes and even Double Inside Straight Flushes, along with 2-Card Royals and hands with just High Cards.  To make matters worse, these 40% of the entries account for nearly 50% of the hands.  

            Next week, we'll continue our stroll through the strategy table.