Puzzles JOSH FELDMAN
I’VE ALWAYS HAD A LOVE/HATE RELATIONSHIP with the game
of poker. Sure, I love playing the game of poker, and although plenty of
actuaries are far better at the game than me, I’d like to think I’m not a
fish at the table. The hate part comes because there isn’t a good place
to legally play the game. For years, we here in America could play online (somewhat) legally, but aside from a few select states, those days
are long gone. That means that to play the game, I have to make a trek
to the local casino. And I HATE casinos.
Everything about the casino experience
rubs me the wrong way. The awful player
rewards cards that encourage problem
gambling, the “promotions” that have
such terrible odds that they make
Powerball jackpots seem attainable,
the architectural designs that have
no straight lines and make it impossible to find exits, the stench
from the smoke that manages
to seep into the nonsmoking
areas—the list goes on and on.
Even the best casino out there
would be considered slimy by
any rational standard.
Luckily, with the game of
poker you aren’t playing against
the house, but other players. In theory, this should decrease the amount
of sleaze emanating from the card room.
But my local casino somehow turned the
game of poker into an ugly affair.
It all started a few years ago when the
casino started awarding a jackpot to any
who played the game of Texas Hold ’em
and got a straight flush. For those who
don’t know, Hold ’em uses the standard
52-card playing deck. Each player gets
two individual cards, and five additional
cards get shared by everyone at the table.
A straight flush is when five of those seven
cards are of the same suit and in a continu-
ous sequence. the ace can be high or low, so
ace, two, three, four, five of the same suit is
a straight flush, as is ten, jack, queen, king,
ace. It doesn’t matter how many of the five
cards are from the shared community cards
or from your two individual cards. The key
point is that of the seven cards dealt, five
must result in a straight flush.
After a few weeks, the local casino
wanted to make it tougher to win the
jackpot so they put in a new rule where
in order to win the jackpot, the highest
card of the straight flush needed to be a
nine or better. Unfortunately, a few weeks
later the seven, eight, nine, ten and jack
of diamonds got dealt as the five shared
community cards, so everyone at the table
won the jackpot. Fair to say, the casino
was not happy.
To prevent the above situation, the
casino changed the rules one more time.
Now, not only do you need a nine or higher
straight flush, but to win the jackpot, both
of your individual cards must be used to
make the straight flush.
All was well until the following hand
occurred involving my friend named
The Empire. The Empire’s two individual cards were the six and seven of clubs.
Miraculously, the first three community
cards turned out to be the eight, nine and
ten of clubs. My friend thought he won the
jackpot, but controversy occurred when
the final community card was the jack
of clubs. The casino claimed that
because The Empire’s best hand (the
seven, eight, nine, ten, and jack
of clubs) only contained one of
The Empire’s individual cards, he
was not entitled to the jackpot.
The Empire understandably got
livid and demanded the jackpot,
as two of his individual cards,
along with three of the shared
cards, resulted in a straight flush.
While this decision created
plenty of bad blood between the
casino and the local poker community,
on the positive side, it did help inspire
this issue’s puzzles:
1. What is the probability of being able to
form a straight flush after getting dealt
2. How does this probability change if the
highest card of the straight flush must
be nine or higher?
3. Using the casino’s interpretation, what is
the probability of a nine or better straight
flush where your two individual cards
must be used to create the highest possible
4. Using The Empire’s interpretation, what
is the probability of winning the jackpot,
given that your two individual cards must
be used to create a straight flush, even if
it isn’t the best possible straight flush? IST