using game theory to decide whether to bluff, you
must first determine your chances of making your hand.
You must then determine the odds your opponent is
getting on that bet. Then you must randomly bluff
in such a way that the odds against your bluffing
are identical to your opponent's pot odds.
Here's one more example. Suppose you have a 20 percent
chance of making your hand, there's $100 in the pot,
and the bet is $25. Your opponent is then getting
$125-to-$25 or 5-to-1 odds if you bet. The ratio of
your good hands to your bluffs should, therefore,
be 5-to-1. Since you have a 20 percent chance of making
your hand, you should randomly bluff 4 percent of
the time. (20 percent-to-4 percent equals 5-to-1.)
When you bluff in this fashion, you take optimum advantage
of the situation.
A good, convenient way to randomize your bluffs, as
we have seen, is to pick cards from among those you
haven't seen. If, for example, ten cards make your
hand and you need a 5-to-1 bluffing ratio, then you
should pick two additional cards to bluff with.
Here is another example. You draw one card to a spade
flush in draw poker, and your opponent draws three
cards. Therefore, the chances are enormous that your
opponent will not be able to beat a flush, only a
bluff. The pot contains $20. The bet is $10. If you
bet, your opponent is getting $30-to-$10 or 9-to-3
odds from the pot. Since nine unseen spades make your
flush, you should pick three additional cards to bluff
with, such as the two red 4s and the 4 of clubs. You
now bet with twelve cards creating a 9-to-3 ratio
between your good hands and your bluffs.
It is not always possible to use cards to arrive at
exactly the ratio you need to bluff optimally. However,
as long as you are close, you can still expect to
gain. You recall that choosing six cards to bluff
with in the draw lowball example created exactly the
right proportion vis-à-vis the pot odds my
opponent was getting; nevertheless, I still ended
up with a profit when I bluffed with five or with
seven cards whether my opponent called or folded.
Of course, the closer you are to the exact ratio,
the better, in terms of game theory.
most of the time you won't be heads up. You need to
make a judgment about your hand and how it stacks
up to all the other hands that are still active. When
this involves four, five, or six players, this judgment
can be problematic.
If there are three or four (or more) active hands
seeing the flop, it's important to bet your good hands
like top pair with a good kicker. Try to drop as many
players as you can. In accomplishing this, your position
relative to the button isn't as important as your
position relative to a likely bettor or raiser. For
example, if you are in early position in a raised
pot and a very aggressive player is on the button,
then it might be a good idea to check your strong
hands, expecting him to bet so that you can raise,
facing those players after you with two bets cold,
and putting pressure on them to fold. The more active
hands there are on the flop, the more important this
is. With few opponents, it's often right to slowplay
on the flop, waiting until the turn when the bet size
doubles before you raise. Waiting is seldom a good
idea against a large field. There's just too many
bad things that can happen on later streets if you
let a lot of opponents in cheaply on the flop.