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POKER
BASIC THEORY
There is
a Fundamental Theorem of Algebra and a Fundamental
Theorem of Calculus. So it's about time to introduce
the Fundamental Theorem of Poker. Poker, like all card
games, is game of incomplete information, which distinguishes
it from board games like chess, backgammon, and checkers,
where you can always see what your opponent is doing.
If everybody's cards were showing at all times, there
would always be a precise, mathematically correct play
for each player. Any player who deviated from his correct
play would be reducing his mathematical expectation
and increasing the expectation of his opponents.
Of course, if all cards were exposed at all times, there wouldn't
be game of poker. The art of poker is filling the gaps in the incomplete
information provided by your opponent's betting and the exposed
cards in open-handed games, and at the same time preventing your
opponents from discovering any more than what you want them to
know about your hand.
That leads us to the Fundamental Theorem of Poker:
Every time you play a hand differently from the way you would have
played it if you could see all your opponents' cards, they gain;
and every time you play your hand the same way you would have played
it if you could see all their cards, they lose. Conversely, every
time opponents play their hands differently from the way they would
have if they could see all your cards, you gain; and every time
they play their hands the same way they would have played if they
could see all your cards, you lose.
The Fundamental Theorem applies universally when a hand has been
reduced to a contest between you and a single opponent. It nearly
always applies to multi-way pots as well, but there are rare exceptions,
which we will discuss at the end of this page.
What does the Fundamental Theorem mean? Realize that if somehow
your opponent knew your hand, there would be a correct play for
him to make. If, for instance, in a draw poker games your opponent
saw that you had a pat flush before the draw, his correct play
would be to throw away a pair of aces when you bet. Calling would
be a mistake, but it is a special kind of mistake. We do not mean
your opponent played the hand badly by calling with a pair of aces;
we mean he played it differently from the way he would play it
if he could see your cards.
This flush example is very obvious. In fact, the whole theorem
is obvious, which is its beauty; yet its applications are often
not so obvious. Sometimes the amount of money in the pot makes
it correct to call, even if you could see that your opponent's
hand is better than yours. Let's look at several examples of the
Fundamental Theorem of Poker in action.
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