Following is an in-depth look at the three different sets of the hand with probabilities, analysis, and grading for each. Keep in
mind that while many numbers are put forth here, it is far from a complete predictive picture. The goal of this particular article is to
introduce the concept of array sorting and organization.
The array of unknown cards for each set has been sorted into 5 potential draw ranges that feed the three rows:
Front Primary & Secondary Draw(s)
Front-Middle Merged Draw
Middle Primary & Secondary Draw(s)
Middle-Back Merged Draw
Back Primary & Secondary Draw(s)
SET A: X / 73 / 665 -- *ARRAY SORT 12 / 28 / 21 -- **6TH STREET EVENT 26% / 60% / 45%
What the *ARRAY SORT numbers represent are the number of outs in the draw ranges that improve each row.
In this set, the front row has
a draw range of 12 outs feeding it (QQQQ KKKK AAAA), the middle row 28, and the back row 21. The **6TH STREET EVENT
percentages reflect what will happen on 6th street once the first five cards have been set and the draws have been organized into these particular
ranges. For instance,
of the 12 cards set aside for the front row draw, you will pull one of those cards from the deck 26% of the time. The middle
row has 28 outs that improve it (this event will occur 60% of the time), and the back row has 21 outs feeding it and will occur
45% of the time on the 6th street pull.
Front row draw card arrives on 6th street: 26%
Middle row draw card arrives on 6th street: 60%
Back row draw card arrives on 6th street: 45%
62% chance to two-pair+ back row from array subset 66555
44% chance to pair the 7 or 3
34% chance any 8, 9, 10 or J arrives on 6th street
27% chance to two-pair+ middle
20% chance to boat back row
13% chance to runner-runner AA, KK, or any random live pair
7% chance to runner-runner 7's or 3's to make middle row trips
IF live subset 55666 hits on 6th street (a 12% chance), THEN probability to boat upgraded to 55%.
IF live 8, 9, 10, or J comes on 6th street (a 34% chance) and is placed in the back row, THEN probability to two-pair+ back row
upgraded to 82%.
the four Fantasyland-qualifying Queens are the primary draw for the front (making Aces and Kings a natural draw for the middle),
the A's and K's are arranged to be flexibly set into either the front or middle row, thus
giving the front row 12, not 4, cards as its principal improvement draw range. If a K were to arrive on 6th street, it would be set in
the middle. But if a K arrives, say, on 10th street, and there is a strong
case in the middle for support of a K-high or paired-K front, it could be comfortably set there, and any other live K's left in the
array could slide from the front-middle merged draw into the front row's primary draw or secondary draw.
Also a justification for flexibility is the fact that a K-high or A-high front row is often winning in HU play.
The 37 middle makes 3's and 7's the primary improvement draw, with 2's and 4's the secondary draw. The row is also fed by the KKKK AAAA
front-middle merged draw range, as well as all diamonds and a potential pair such as 88-JJ (which would borrow an out from the back row draw);
i.e. if a diamond J arrived on 6th street, it would go
in the middle. This would keep the flush draw alive while simultaneously allowing the J to pair at a 45% probability if live. This card
would be considered a 'flex' card as it provides multiple options to improve the row going forward.
Pairing the 3's does not give the middle row
much strength; however the addition of 2's and 4's to the middle row secondary draw allows the possibility of a 3344 or 3322 two-pair row
that can be supported by a back row 6655 or 6665 (either of which is 62% likely to occur over the course of the hand). This is one way to
keep your Fantasyland ambitions alive.
In the unlikely event (7%) of the specific two-pair 7733, any pair 88-JJ in the back row adds support to keep the middle unfouled.
A naked pair of 7's would land in the center of middle-row strength. This is an important strategic point. With the opponent
always setting stray Q's in front, and often bolstering front row scoring chances with J's or 10's, you can see that the 7's land squarely
in the middle of a pair v. pair battle:
[2 3 4 5 6 7 8 9 10 K A]
Additionally, a pair of 7's is unlikely to cause
a foul because of the initial back row
improvement probability, as well as the additional secondary and merged draws feeding the back row.
The chance of runner-runner cards that make 333 or 777 is only 7%. In fact, you are nearly twice as likely to runner-runner a pair of Kings or
Aces than to catch trip 7's or 3's. The potential middle row flush draw is left open in this set, a long-term EV consideration.
The back row's primary draw is non-diamond 5's and 6's, with secondary draw support from non-diamond 8's through J's, and merged draw
support from the diamonds 56 8910J. As mentioned above, chances
to two-pair+ drawing any 5's and 6's are 62%, with the probability of catching a full house at 20%.
And, of course, a full house would be necessary to support a middle-row flush. While the flush/boat scenario is unlikely, it has a higher
probability than boat/boat.
Planning for the 'elephants' 8-J range to come as outlined in Part I: if a live non-diamond 8-J (i.e. the 9 of clubs)
comes on 6th street, it can be placed in the back row, which then becomes an 82% favorite to two pair or better.
Then the corresponding diamond pair card (9d)
will be more likely to be set in the back row if it comes. If, on the other hand, the 6 of clubs comes on 6th street, the back
row is now improved to 55% to make the full house, allowing
the middle row to be more safely drawn to the flush or other strength.
The 8-J of diamonds then would add no value to the back row, so they would be reserved
at that point for upper row setting. However starting with the 56 8910J of diamonds merged is important as they add value to both the middle
and back row draws.
Coming Soon: Part III - Other Set Analyses and Grades