The Fundamental Theorem of Poker is
believed to have been first articulated by David
Sklansky. In essence, the theorem expresses the basic
notion that poker is a game of decision-making but is
played while having only partial information.
In poker, it is critical that a
player master the art of being able to play his hand in
the very same way that he would have played his hand had
he been able to see the cards in the hands of his
opponents. The Fundamental Theorem of Poker stresses
that each time that you would have played your hand
differently than the way you did play it if you had only
been able to see your opponent?s cards, then your
opponent likely won.
Each decision in poker can be
analyzed in terms of the concept of a mathematical
concept known as expected value. Expected value is the
term used to express the average payoff of a decision if
that decision is replicated a large number of times. So
for poker, we state that the correct decision to make in
a given game situation would always be the very decision
that provides the largest expected value. Of course, if
you could truly see all of your opponents' cards during
a game, you would undoubtedly be able to make the
correct decision and be able to do so with absolute
mathematical certainty. The Fundamental Theorem of poker
is essentially based upon a players ability not to
deviate from these correct decisions.
In attempting to explain the
Fundamental theorem, let us look at a hand from a game
of holdem. Suppose you are playing limit holdem and have
been dealt a pair of eights, the eight of hearts and the
8 of spades, prior to the flop. For sake of argument,
suppose you call, and everyone folds but the big blind
who instead checks.
Suppose we proceed to the flop, which
comes up all diamonds, a King, a Queen and a 10. The big
blind then bets. According to the fundamental theorem,
you are now about to make a decision based upon
incomplete information. In this example, the decision
most players would insist is the correct decision would
be to fold. The reason is that there are too many
additional turn and river cards that could kill your
hand. The big blind may not have an A or a K (though he
of course could), and with three cards to a flush and
two cards to a straight on the flop, he could easily be
in position for a straight or even a flush draw. You
essentially can only hope to draw another eight and
given the bet of the big blind, even that might not hold
up.
However, what if you knew that the
big blind was actually holding a four of hearts and a
seven of clubs. That is to say, suppose you knew the big
blind was merely bluffing. In this case with two eights,
poker players would say that you should raise, even
though the big blind would still have the option to
call. Again in accordance with the fundamental theorem,
if you had folded you would have been playing your hand
differently than you would have had you been able to see
your opponent?s cards, it would be deemed that in
essence you would have made a mistake. This, even though
given the incomplete information you have, the most
logical choice would have been to fold.
This simple example also reveals one
of the most important aspects of poker strategy.
Ultimately, the most important goal in poker is to
induce an opponent into making a mistake. In the example
with the big-blind, the semi-bluff employed was an
attempt to get you to fold, hoping you would make a
mistake. The big blind also had an out if you called or
raised, so he was in great position to employ the bluff
but it would have been a big mistake for you to have
folded.
What makes the game of poker so
extraordinary of course is the fact that you are often
sitting around the table with a number of players. At
times, several opponents can make a series of incorrect
decisions, but it is the "collective decision" of all
your opponents that ultimately matters. Though several
players might have erred, their collective efforts might
actually work against you as an individual player.
The Fundamental theorem of poker may
be expressed simply and be written as if it is an axiom,
but the proper application of this theorem in the face
of the countless circumstances that a poker player may
encounter when playing requires substantial poker
knowledge, skill, and game experience.
