I would say the strategy to calculate the strategy came to me in an
epiphany but I don't have a good understanding of what that word
means. The word brainstorm comes to mind. When I left the Vegas
Club I returned to my hotel room, pulled out my pocket calculator,
grabbed a notepad out of my luggage, threw them on the table, then
sat down and....stared at the wall....then I stared at the wall some
more....then I started talking to myself....pretty soon it became a
full flown conversation. With it's thin walls anyone coming down the
hallway of the third floor of the Golden Gate would have gotten an
earful of the insane ravings of a video poker lunatic:
"Do the RF4's first"
"No do the hands that don't pertain to the DTUW feature."
"You can't do that, stupid! If you can't figure out the royal cards
and straight flush cards it ain't gonna do you any good."
"The SF4's are no brainers."
"So,what? What about the SF3's? What are you gonna do there, brain
surgeon."
"I don't know. I'll figure something out."
"The ER of the RF3's must reflect the ER of the RF4's."
"I think I'll do the RF4's and SF4's first just to get into the right
frame of mind."
"Hands that pertain to...."
"Wait a minute! What did you just say?"
"I didn't! You cut me off."
"No, before that."
"You're so smart. You tell me."
"If you don't tell me what you said I'm gonna knock that big lump off
your shoulders!"
"Okay! Okay! Uh, the ER of the RF3 has to have an accounting for the
ER of the RF4?"
"THAT'S IT!! YOU CRACKED IT!!! You're not as dumb as you look."
"I did?"
"Yeah, now leave me alone. I have strategy to write."
"Where's my tip?"
"Oh, you wanna tip? Bet the farm on Pappy's Dancer in the fifth.
Now, beat it!"
So, after a fashion, I fashioned a strategy to calculate the
strategy.
CALCULATING THE STRATEGY
The ER of the RF3 must have an accounting for the ER of the RF4.
That creates a whole new category (with sub-categories)for a hand
that can be made. So here we go. We'll use the AKT for the
example. There's no SF possibility to clutter up the mind.
What can we make on the draw with the AKT?
Category 1: RF
This is a no brainer. There is only one combination that makes a
royal returning 800 bets.
Category 2: FL
C(10,2) then subtract 1 because one of those combinations makes an
RF. So 44 flush combinations return 220 bets.
Category 3: ST
4 Queens X 4 Jacks. Then subtact 1 because one of those combinations
makes an RF. So 15 combinations return 60 bets.
Category 4: 3K
There are 3 pairs of Aces, 3 pairs of Kings, 3 pairs of Tens left in
the deck. C(3,2) times 3. So 9 combinations return 27 bets
Category 5: 2P
Any one of 3 Aces X 3 Kings, any one of 3 Aces X 3 Tens, any one of 3
Kings X 3 Tens. So 27 combinations return 27 bets.
Category 6: HP
First their are 6 pairs of Queens left in the deck C(4,2). Likewise
for the Jacks. Now, in order to make a pair of Aces we would have to
catch one Ace with a sidecard that is not an Ace, King or a Ten.
Catching on Ace leaves 46 cards in the deck, so we subtract 2 Aces, 3
Kings, and 3 Tens leaving 38 sidecards. Like wise for making a pair
of Kings. So 6 X 38 plus 12 is 240 combinations returning 240
bets.
Now, at this point, if we were just playing 6/5 DB, the ER of the
hand would be the total of the bets returned (1374)divided by the
cycle C(47,2) or 1081 for an ER of 1.271. But we have another
category to add.
Category 7: RF4
Sub-Category A: RF4 (AKQT)
In order to make an RF 4 this way we have to catch the Queen with a
card that does not make the hand a paying hand. Catching the Queen
leaves 46 cards in the deck. So we eliminate 9 flush cards (includes
the royal card), 3 Queens, 3 Offsuit Jacks, 3 Aces, and 3 Kings.
That totals to 21 cards. 46 minus 21 means there are 25 combinations
that would make the hand a non-paying AKQT. So 25 combinations X 41
(the ER of this particular RF4-which I showed in a prior post) totals
to 1025 bets.
Sub-Category B: RF4 (AKJT)
The math for this sub-category is exactly the same as sub-category A.
So this one also totals to 1025 bets.
So we take the total bets of Category 7 (2050 bets) and add them to
the total bets of the first 6 categories (1374) for a grand total of
3424. Dividing 3424 by the cycle C(47,2) for an ER of 3.167. I used
the same process for RF2's, RF1's, SF3's, and SF2's (SF2's do make
the strategy chart).
I spent two very long days writing the strategy, then fell into bed
and dreamt tremulous dreams of DTUW. The next morning I showered,
shaved, got dressed and went down to the San Francisco Grill for some
steak and eggs. While finishing breakfast I thought "I think I'll
just step on over to the Vegas Club and play a little DTUW." So, with
strategy in pocket and chest puffed out, I walked on over, plopped
down in the seat, punched up the Game Selection Screen...THE GAME WAS
GONE!!! "SON OF A...." "How long did I spend writing that
strategy? 35 hours? AND THEY TOOK THE GAME OFF? Why, those dirty @!
#$%&*!@#$%!@#'s
I searched Vegas high and low. But to no avail (I learned later that
the game was still Speedway). Then the little guy on my shoulder
whispered "Go north, young man."