THE GOOD AND BAD CARDS
One
approach to poker is to raise when you have a very good
hand and fold when you have a very bad hand. But what happens
when you follow that approach? Let's say you have three
aces rolled up on your first three cards in seven-card stud.
That's the best possible hand you could have at that point.
You put in a raise, and everybody folds. You have won a
very small pot with a hand that potentially could have won
a huge pot
The
Cost of Giving Your Hand Away
This
extreme example points up a basic poker dilemma. You want
to make the most of your hands by maximizing your gains
and minimizing your losses, yet what are you costing yourself
when you play in such a way that your opponents should know
what you have? The answer to this question is contained
in the Fundamental Theorem of Online Poker Games, which states that every
time opponents play a hand differently from the way they
would have if they could see all your cards, you gain; and
every time they play a hand the same way they would have
played it if they could see all your cards, you lose.
The Fundamental Theorem indicates that when you play in
a way that lets your opponents know what you have, you may
be costing yourself substantially. If opponents know exactly
what you have, they will never make a mistake except on
very close mathematical decisions. The more your play gives
away what you have, the less likely it is that your opponents
will make a mistake. Yet you want them to make mistakes.
Creating mistakes is, in a sense, the whole objective of
the games. Clearly you might not want to raise immediately
with three aces rolled up because you don't want your opponents
to know what a strong hand you have. You want to win more
money from them on later betting rounds. At the same time,
never raising with a big hand could be a mistake too.
An interesting example of such a mistake came up toward
the end of the 1977 World Series of Online Poker Games in a hand between
two world-class players, Doyle Brunson from Longworth, Texas,
and Bones Berland from Gardena, California. The games was
no-limit hold 'em. Brunson had about $20,000 in front of
him, and Berland, about $50,000. Before the flop Berland
raised in early position, a hefty raise, and Brunson called
him with two queens. The flop came J,5,2. Again Berland
made a pretty good bet, and Brunson called him. On fourth
street came another small card, and Bones made a gigantic
bet, just about enough to put Doyle all-in. Doyle thought
and thought and thought, and finally he pushed in his money
and called.
Many people thought Brunson played incorrectly in calling
with two queens. Berland was not about to bluff in this
situation. These critics felt there was a great chance that
Berland had two aces or two kings, and there were other
hands he could have had that Doyle's two queens couldn't
beat. Given the way he played it, the only hand Bones might
possibly have that Brunson could beat was an ace, jack -
the top pair on board with an ace kicker.
When Bones turned over his cards in the showdown, he had
precisely ace, jack. Brunson won the hand with two queens
and went on to win the world championship of poker that
year. You asked Doyle afterward about his risky call. "Well,"
he said, "Bones couldn't have two aces or two kings
because he never raised in early position with these hands
before the flop. He would just call, hoping to reraise,
you know, on a slow play."
Here was a case, then, where a top player was given information
because another top player played properly but with too
much consistency. In no-limit hold 'em it is generally correct
to slow play in early position with two aces or two kings.
However, when Berland always played those pairs the same
way, as he supposedly did, the information he gave away
was much more costly than the money he figured to gain by
playing the aces and kings properly every time.
To illustrate further the cost of giving away your hand,
suppose you are playing head-up razz with no ante, no forced
bet, and all the time in the world. You have decided, therefore,
to play super-super-tight, folding everything except A,2,3
on your first three cards. With no ante it would seem you're
a cinch to end up a winner, but the fact is a good player
will slaughter you. He'll soon know you are playing only
A,2,3, and he'll play his cards accordingly. He'll start
off with slightly worse hands than yours, like three-card
Ss and three-card 6s, but he'll wind up beating you on later
plays since he'll know exactly what you have. He'll know
when you pair up and when you don't, and he'll never make
a mistake. On the other hand, though you start out with
the better hand, you will make mistakes because you won't
know what your opponent has. Thus, while in general it is
correct to play very tight when there is no ante and no
forced bet, by playing only A,2,3 in razz, you are giving
away so much information that you don't stand a chance against
a good opponent.
