Getting Ugly

For the past few weeks, I've been slowly walking through the strategy table for full-pay jacks or better video poker.  I'm about 2/3 of the way though and what's left is well, just not pretty.  The expected values of the rest of the table are below 0.60.  This means you can expect, on average, a return of only 60% of your wager.  But, as I've explained the past few weeks, learning to play the ugly hands is at least as important as learning how to play the good hands.  It is also probably more difficult to learn these hands as there are a lot of subtle nuances and a great deal of overlap.  For example, one of the hands from last week was the 2-Card Royal with no Aces or 10's.  This week's top hand is a 4-Card Inside Straight with 4 High Cards, which is really a 4 High Card hand.  There is only one way this occurs -  J Q K A.  But, if we compare this to the 2-Card Royal we realize that if TWO of the J/Q/K are suited, we actually go that route instead of the 4-Card Inside Straight.

Let's take a look at the next few entries and see what we can learn from them:

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

{C}{C}·       {C}{C}2-Card Royal with an Ace, but no 10

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

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

{C}{C}·       {C}{C}3-Card Inside Straight Flush with 0 High Cards

{C}{C}·       {C}{C}3 High Cards

Okay, so we've already covered a critical point of these hands above.  Adding to the complexity however is the 2nd rule down when compared with the 1st.  IF the 2 suited cards are an Ace and either the Jack, Queen or King, THEN we keep the 4-Card Straight!

Next up is the 3-Card Double Inside Straight Flush with 1 High Card.  So, a suited 8-9-Q would cover this.  This can't overlap with our 2-Card Royals, but can overlap with a 4-Card Inside Straight (8-9-Q suited with a Jack off-suit).  This would make it a 4-Card Inside Straight with 2 High Cards.   You'll note that the 4-Card Inside Straight with 3 High Cards is below the 3-Card Double Inside Straight with 1 High Card, so surely the 2 High Card version is even lower.  In reality, we won't find it on this strategy table at all as a 4-Card Inside Straight with 2 or less High Cards is NOT a playable hand in full-pay jacks or better.  In this case we would keep the 3-Card Straight Flush over the 4-Card Straight.

The next hand is the 3-Card Inside Straight Flush with 0 High Cards (i.e. 5-7-8 suited).  If we have a 6 off-suit this would be a 4-Card Straight with 0 High Cards which is much higher in the table and thus would be played as the 4-Card Straight.  If we have a 4 off-suit, then it is a 4-Card Inside Straight with 0 High Cards.  If the 2 High Card version is not playable then for sure neither is the 0 High Card Version.  We would play the 3-Card Straight Flush.

The 3 High Card hand is a critical hand to learn about.  It is frequently misplayed.  There are four possible High Cards - Jack, Queen, King and Ace.  However, 3 High Cards is a bit of a misnomer.  In order for the hand to be 3 High Cards, it MUST be J-Q-K.  If we have J-Q-A we would discard the Ace unless the Ace matches in suit to one of the other two then it would play as a 2-Card Royal.  In similar fashion, we would ONLY play J-Q-K if the three are of different suits.  Otherwise we would again have a 2-Card Royal (V3) and would play the hand that way.  The 2-Card Royals are frequently overlooked when there is a 3rd High Card, but this is simply not the right way to play the hand.

There are only 5 more hands on our strategy table and I will cover them next week.   These five hands all have expected value below 0.50.  Unfortunately, they account for about 1/3 of all hands dealt - so they are critical to learn.