Thanks Harry,
I am sorry for "muddying the waters" with my mistype in the first
line It is a good thing I repeated a little at the end of the post.
The other two cards were the Q diamonds and K hearts in the first
hand.
You made a good guess and I understand your answer. It has
reinforced the idea to think about the possible value of my
discards. Your detail explanation is the real value of your answer
to my post. In other words, instead of just memorizing hands, I
should look for and try to understand this type of logical hand
analysis. However, in this case I must just memorize the correct
hold with the EV difference being so small.
Bob
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...>
wrote:
futrend wrote:
> I do not understand what is the difference between these two
Hands in NSUD
> Hand 1: 2,4,5, & K of Diamonds & K Hearts. ER is 5.050879
holding
> 2,4, & 5 and the ER is 5.076276 holding the 2 only
>
> Hand 2: 2,4,5, & 10 of Spades & Q Diamonds. ER is 5.050879
holding
> 2,4, & 5 and the ER is 5.023387 holding the 2 only
>
>
> Confused... am I mising something obvious? There is no gap
between
> the King and Queeen in Hand 1 and one gap between the Ten and
Queen
> in Hand 2. Can that be the difference?
Hey, Bob 
Ok, from the full message text I'm going to assume that the Kh in
the first hand should actually be Qh. The gaps involved between KQ
vs TQ are exactly what the difference in the lone duck holds. The
question is, how many straights are available on the draw for each
hand in question.
Then you toss a single gap couple of cards, you reduce the potential
number of straights by one more than when tossing a 2-gapped couple
of cards (I'm inclined to say "pair" rather than "couple", but that
becomes ambiguous 
In the case of the T/Q discards, straights involving 6-T through T-A
are reduced in number (5 in total).
Now, the Q/K couple is considered to be 2-gapped. Because the
available straights on the upper end are capped by the A, there are
the same number of possible straights to be formed that include both
cards as there is a "non-capped" 2 gapped couple -- e.g. 7/T. In
either case, there are 3 possible straights that include both cards
(beginning with 5 through 7 for 7/T, and 8 through T for Q/K) ...
apologies if this isn't stated in the most straight forward manner.
At any rate, for Q/K discards, straights involving 8-Q through T-A
are reduced in number (just 3) Because the number of potential
straight possibilities when you hold just the deuce are greater when
you discard Q/K than T/Q, this deuce hold with Q/K discard has the
greater EV.
Writing on the fly, I hope this is at least slightly clearer than
mud
ยทยทยท
- Harry