Dealt Card #1
Nine (9) "... wearing a made-to-measure Armani suit ..." = Dressed to the
Nine[s] (This card will be held and become part of the final winning hand)
Dealt Card #2
Eight (8) "... in a terrible financial bind" = Behind the eight ball (This
card will be held and become part of the final winning hand)
Dealt Card #3
Four (4) "... living so far apart in France, Canada, and Japan") = "[being] scattered to the four winds" This card will be discarded and
will not be in the final winning hand.
(This change [from "four corners of the earth" to "scattered to the four winds"] is in recognition that "scattered to the four winds" is a better choice.
Dealt Card #4
Eleven (11) "... at the last minute ..." = The eleventh hour (This card will
be held and become part of the final winning hand)
Dealt Card #5
Four (4): "... I figured it all out" = "I put two and two together"
(two plus two equals four) This card will be discarded and
will not be in the final winning hand.
This card (a four) together with "Dealt Card #3 (also a four) make up the originally dealt pair, and I think that, in spite the prompt's
insistence that "suits ... do not matter*** ...," they both must be
discarded to completely address the point (a good one, imo) made by
hyst329 in his/her final
answer concerning having to "choose a particular [paired card] (whose suit doesn't
match to the other [member of the pair], since you're building a straight flush) to win."
By discarding both cards making up the pair, the impossible task of
definitely choosing the correct one is avoided.
***(Ignoring the existence/importance of suits is fine to a point, but when two [or more] of the same numbered cards are involved and present
in a card hand, side-by-side, it becomes [nearly] impossible for me to
visualize them as being either "suit-less" or all of the same suit, so I thought:
"Why not just discard both/all matching cards to avoid this issue?")
Card X (drawing deck):
Ten (10) "Yes! Got it! Loud and clear!" = "Ten-Four [good buddy]" in CB radio parlance. Without making it an equation and since
just the first one will suffice, that gives 10. (This card will be
drawn to replace "Dealt Card #3" and it will be part of the final
winning hand)
Card Y (drawing deck):
Seven (7) "... must have made a blunder" = "must have been confused/in a state of confusion" = "[be] at sixes and sevens."
The decision to go with
the idiom's "seven" (and not its "six") was based on how "Lucky me!"
could evoke "Lucky number
7"
or even (albeit a tad hyperbolic for this context) "Being in
seventh
heaven."
(This card will be
drawn to replace "Dealt Card #4" and it will be part of the final
winning hand)
(Taken literally, which I probably shouldn't be doing, your comment:
"Funnily enough, though, the numbers for Card Y and Z actually need to
be switched around," seems to be saying that Card Y is a "thirteen"
and Card Z is a "seven." While I could make Card Y a "thirteen" by
adding the six and the seven from the "at sixes and sevens"
expression, I really don't see a way to make Card Z a "seven" [short of > contriving something like "'Seven come eleven' minus/disposed of eleven equals seven], so I'll just leave Cards X and Z as they were for now.)
Card Z (drawing deck)
This card's number/value is actually irrelevant because it will not be drawn and it will not be part of the final winning hand. However,
its clue could at least explain why the player was seemingly
hell-bent on holding/using Dealt Card #4 (an 11, aka Jack, which is
the only available "repdigit" card, according to my analysis), in spite of this being a very
questionable move in that it required drawing (a ten) to his/her mere
beginnings of an inside straight (8,9,11) and then either a 7 or a
Queen to complete filling it from the outside (again according to my
analysis, the move was the correct one, for a 10 and a 7 were both
drawn). To the extent that knowing this card's precise value/number
is required for the purpose of knowing what the winning hand is and/or
for completely solving this puzzle, I would return to the idiom (all
the clues lead to idiomatic uses of numbers) discussed in "Card Y
(drawing deck)" (i.e., "to be at sixes and sevens"= state of
confusion/disarray), but instead of choosing between the 6 and the 7,
for this card I would add them to get thirteen (13) = King.
(Taken literally, which I probably shouldn't be doing, your comment:
"Funnily enough, though, the numbers for Card Y and Z actually need to
be switched around," seems to be saying that Card Y is a "thirteen"
and Card Z is a "seven." While I could make Card Y a "thirteen" by
adding the six and the seven from the "at sixes and sevens"
expression, I really don't see a way to make Card Z a "seven" [short of contriving something like "'Seven come eleven' minus/disposed of eleven equals seven], so I'll just leave Cards X and Z as they were for now.)
The [final winning] hand:
A Jack-high straight (flush) (7, 8, 9, 10, Jack) of whatever suit that
suits you best) (See the reasoning included above to explain why I
think this is the case)
wordplay
tag.) $\endgroup$