A Chicago
Tribune article once looked at pitching performance in
terms of probability theory. The article sought to determine
the probability of nohitting a team of all 250 hitters. In
that case, the probability of an out for each player
is .75.
Use
the multiplication rule to compute the probablity of
three outs in a single inning:
.75
x .75 x .75 for one inning = .422
Use the
rule again to compute the probablity of three outs each
inning:for all nine innings:
 (.42)*(.42)*(.42)*(.42)*(.42)*(.42)*(.42)*(.42)*(.42)
= .0004
Since 1900, a
nohitter has been pitched 7.5 times for every 10,000 games
 about the same as the probability of pitching a nohitter
against a team of .235 hitters. Some "lucky" nohitters,
explainable by chance?
 Dick
Fowler (his only win in 1945 was a
nohitter)
 Virgil
Trucks (pitched 2 nohitters in 1952 in only 5
wins)
 Bobo
Holloman (pitched a nohitter in his 1st majorleague
start 1953 and won only 3 games the rest of the
season)

Poker
originated in the Louisiana territory around the year 1800.
Ever since, this addictive card game has occupied the time
and teased the minds of generations of gamblers. It has also
attracted the attention of mathematicians and
statisticians.
The standard
game and its many variants involve a curious mixture of luck
and skill. Given a deck of 52 cards, there are 2,598,960
ways to select a subset of five cards. So, the probability
of getting any one hand is 1 in 2,598,960.
One of the
first things a novice player learns is the relative value of
different sets of five cards. At the top of the heap is the
straight flush, which consists of any sequence of five cards
of the same suit. There are 40 ways of getting such a hand,
so the probability of being dealt a straight flush is
40/2,598,960, or .000015.
The next most
valuable type of hand is four of a kind, and so on. The
table below lists the number of possible ways that different
types of hands can arise and their probability of
occurrence.
Rankings of Poker Hands and Their
Frequencies of Occurrence:

Hand

No. of Ways

Probability

Straight flush

40

.000015

Four of a kind

624

.000240

Full house

3,744

.001441

Flush

5,108

.001965

Straight

10,200

.003925

Three of a kind

54,912

.021129

Two pair

123,552

.047539

One pair

1,098,240

.422569

The rules of
poker specify that a straight flush beats four of a kind,
which tops a full house, which bests a flush, and so on
through a straight, three of kind, two pair, and one pair.
Whatever your hand, you can still bet and bluff your way
into winning the pot, but the ranking (and value) of the
hands truly reflects the probabilities of obtaining various
combinations by random selections of five cards from a
deck.
Many people,
however, play a livelier version of poker. They salt the
deck with wild cards  deuces, jokers, oneeyed jacks, or
whatever. The presence of wild cards brings a new element
into the game, allowing a player to use such a card to stand
for any card of the player's choosing. It increases the
chances of drawing more valuable hands.
It also
potentially alters the ranking of different hands. One can
even draw a five of a kind, which typically goes to the top
of the rankings. Just how much wild cards alter the game is
recounted in an article in the current issue of
Chance, written by mathematician John Emert and
statistician Dale Umbach of Ball State University in Muncie,
Ind. They analyze wildcard poker and conclude, "When wild
cards are allowed, there is no ranking of the hands that can
be formed for which more valuable hands occur less
frequently."
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