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