extreme example points up a basic online poker games
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 notwant 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.
World Series of Poker Champion Phil Hellmuth is famous
for his late tournament arrivals. He buys in the day
before and has sometimes arrived as much as three
hours late, finding his starting stack has shrunk
to 65 percent of its starting size.
Hellmuth insists the late arrivals are due to his
desire to get enough sleep. "The chips I lose
are much less important than being well-rested,"
he says. His practice is so consistent, though, that
most opponents believe he could arrive on time if
he really wanted to and that the late arrivals are
a psychological ploy designed to intimidate opponents.
By arriving so (ate, Hellmuth is, in effect, announcing,
"I don't need as many starting chips as you do
to beat you." Once a wag criticized a late-starting
tournament by saying "This tournament started
so late, Phil Hellmuth was on time."
The rest isn't worthless, of course, but it's hard
to put a price on psychological dominance. Beginners
are well-advised not to try this one.