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
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.