is rarely correct to try to bluff out two or more
people when all the cards are out; your chances of
success decrease geometrically with each additional
player in the pot. Paradoxically you might have a
profitable bluffing opportunity against each of two
opponents individually, but not against both of them
as a group. Suppose, for example, you are heads-up
on the end in a $10-$20 games. There is $80 in the
pot, and you think you can get away with a bluff one
out of three times. Clearly this is an extremely profitable
bluffing situation. Once you will win $80, and twice
you will lose $20 for a net profit of $40 or an average
profit of $13.33 per bet.
Now suppose you are in the identical situation except
that you are up against two players instead of one.
We'll assume each player has put $40 in the pot to
expand it to $120, and you think, as in the former
case, that each opponent will fold one time out of
three. You are now getting 6-to-1 instead of 4-to-1
from the pot. Nevertheless, an attempt at a bluff
is no longer profitable because the probability that
both of your opponents will fold is 1/3 X '/2, which
equals 1/9. In other words, eight times out of nine
one or the other of your opponents will call on average.
So you stand to lose $20 eight times for a total of
$160 and to win $120 once. Your net loss is $40 or
$4.44 per bet. Thus, opposing each individual player
by himself results in a profitable bluffing situation,
but if they're both in against you, you have gone
from a profitable situation to an unprofitable one.
(It should be pointed out that in most bluffing situations
against more than one player the probabilities that
each player will fold are not independent. The player
in the middle will frequently fold a hand that he
would call with if he was last, and sometimes the
player who is last will call with a hand he would
have folded without hesitation had he been in the
middle, expecting the player behind him to call. Nevertheless,
the general principle still holds that it is usually
more profitable to try to bluff one player out of
a pot containing 2X dollars than to bluff two players
out of a pot containing 3X dollars.)
An Ace high flush draw also gives you a few ways to
win. The Ace is key for two reasons: you can win by
pairing the Ace and if you make a flush, you'll have
an Ace high flush and be less likely to be beaten
by some other player's bigger flush. The consideration
of having a big flush is an important one in stud.
If you make a flush, the distribution of the other
cards is such that the likelihood of someone else
also making a flush in a different suit increases.
If there are two flushes out, you want the best, not
the second best. This is a recurring theme in initial
hand selection in all forms of poker-don't even get
involved when it's likely that the best you can hope
for is second best.