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 corrects 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.