Not
only was your opponent able to clock your pattern of bluffing
whenever you had a drawing hand that did not materialize,
but your results were never a function of your own actions.
Instead, the results you achieved were wholly dependent on
your opponent’s decision.
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GAME THEORY WITHOUT GAMES
By: Lou Krieger©
Game theory has long been applicable to poker. I first encountered
it in Nesmith C. Ankeny’s "Poker Strategy: Winning
With Game Theory," published in 1981. David Sklansky
also discussed game theory two years later in his seminal
work, "Winning Poker."
Despite its name, game theory is not really about such leisure-time
diversions as Monopoly, Parcheesi, Scrabble, and Trivial Pursuit.
It’s a branch of mathematics that deals with decision-making
and has applicability in fields as diverse as economics, political
science, operations research, military science, and poker
æ where the idea is to optimize a decision rather than
to maximize or minimize any one of a multitude of possible
choices.
Suppose you’re heads-up in a poker game after all the cards
have been dealt, and you know nothing about your opponent. You’ve
never played against him before and haven’t been able to
pick up even the slightest inkling of a tell. In fact, why don’t
we just assume you’re playing against the Invisible Man.
You don’t have much of a hand – nothing more, actually,
than a busted flush æ and the only way you can win is
by bluffing successfully. To complete this set-up, let’s
assume your opponent knows with absolute certainty that you
were on a flush draw. Although he cannot beat a flush, his hand
is strong enough to beat any busted flush.
Here’s where game theory comes into play. Suppose you
decide to bet every flush draw — whether you make it
or not. What do you think would happen? A cautious opponent
would throw his hand away most of the time, and you’d
win the pot whenever he did. But if your adversary were a
decent player, he’d begin to suspect you of larceny and
would call with increasing regularity.
Once he pegs you as a habitual bluffer, he will call every
time you come out betting. Now the situation has reversed
itself. Rather than winning each time you came out betting,
you’d lose much of the time. Only your legitimate hands
would win, and your opponent would win a pot that now includes
one additional bet whenever you bluffed.
Suppose you took the opposite tack, never bluffed, and bet
only when you made a legitimate hand. Just as he did when
you bluffed too often, your opponent would soon get wise to
you. Once he gloms on to the fact that you never bluff, he
would adjust his strategy accordingly by folding when you
bet and showing down the best whenever you checked.
Do you see what’s happening here? Not only was your opponent
able to clock your pattern of bluffing whenever you had a
drawing hand that did not materialize, but your results were
never a function of your own actions. Instead, the results
you achieved were wholly dependent on your opponent’s
decision. You were no longer in charge. Your playing strategy
allowed the locus of control to pass to your opponent, who,
by virtue of his calling or folding decisions, was the one
who determined how much you won or lost.
It’s pretty clear from all of this that you can’t
be a one-dimensional player, and you don’t have to know
about an arcane branch of mathematics called game theory to
tell you that. Even if you only bluffed once in a blue moon,
or refrained from bluffing just this once æ no matter
how much you’d really like to steal that pot æ
you’d establish opportunities for your opponent to make
errors by forcing him to make a decision about the legitimacy
of your hand. If you always bluff, or never bluff, your opponent
is relieved of this responsibility and freed from the chance
of making a mistake. If he knows you bluff all the time or
perhaps realizes that you never bluff at all æ either
way it makes no difference æ his strategy is as easy
as it is obvious, and he will maximize his winnings as a result.
But when you veer away from polar extremes, your opponent
is put to the test: Do you or don’t you have the goods?
And you know what, whenever you give your opponent a chance
to make mistakes, some mistakes will be made. He will, I will,
and every player who’s ever lived will make errors in
judgment. In poker, no one makes the right decision all the
time; it’s a game of incomplete information, and in the
absence of absolute certainty, wrong decisions will be made.
Game theory gives one the wherewithal to optimize decision
making, thus guaranteeing that by bluffing with a certain
frequency it will not matter how your opponent responds. Game
theory allows you to control the outcome of your actions and
optimize æ while neither maximizing nor minimizing æ
the results you achieve.
Here’s how to bluff using game theory. Make sure the
odds against your bluff are equal to the odds your opponent
is getting from the pot. Confusing? Not really. Suppose your
bet creates a situation where your opponent will be getting
4:1 odds from the pot. That’s easy to imagine. The pot
contains $300, and by calling your $100 bet, your opponent
stands to win $400 if he shows down the best hand.
Now, let’s say any one of eight available cards would
have given you the winning hand. If you bluff whenever two
predetermined cards come up in addition to the eight you need,
you are bluffing at a frequency that precludes your opponent
from taking advantage of your bluffing proclivities æ
regardless of what he chooses to do.
How easy is that to pull off? You can trigger your bluff versus
not-bluff decision by randomizing it with cards. Suppose you
are looking for either a seven or a queen to complete your
hand. Any one of those eight cards will do; it doesn’t
matter which one pops out of the deck. Now suppose you tell
yourself that you will come out bluffing if your last card
is a red deuce instead of the hoped-for seven or queen. Now
you’ve given yourself two bluffing cards æ randomly
selected, and that’s critically important æ as
well as eight winning cards in the 4-to-1 ratio of winning
cards to your opponent’s pot odds, thus optimizing your
results.
But there is a rub. It’s tough to make these kinds of calculations
in the heat of battle. Most players don’t do this sort
of thing; trust me. Nevertheless, you can work out common drawing
situations in advance, just like we did here, and you don’t
even have to be absolutely precise. Oh, sure, it’s stylish
to be right on the money, mathematically speaking. As long as
you realize that to play winning poker you have to allow yourself
the opportunity to make mistakes at the polar extremes –
neither habitually bluffing nor always checking, nor always
calling your opponent’s wager or folding every time he
bets æ to avoid making more costly mistakes in the middle.
When all is said and done, you’re not even going to use
game theory all that often at the table. And the more you
play, and the better able you are to read your opponent æ
putting him on a hand, as it were, and picking up tells æ
the less you’ll have to rely on game theory. After all,
you usually won’t be playing against the Invisible Man.
Even if you play on line, where your opponents actually are
invisible, you can discover tells and read them for hands
based on their proclivities for checking versus betting and
calling versus folding.
While game theory is pretty cool stuff, and we all owe a debt
of gratitude to Ankeny and Sklansky for presenting it so cogently,
its greatest value probably lies in assisting us to learn
how often to bluff for value as well as how frequently to
fold or try to snap off your opponent’s bluff.
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