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| The
Basic of Poker Games |
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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