is the right bluffing frequency? It is a frequency
that makes it impossible for your opponents to know
whether to call or fold. Mathematically, optimal bluffing
strategy is to bluff in such a way that the chances
against your bluffing are identical to the pot odds
your opponent is getting. Thus, if, as in the example
just given, an opponent is getting 6-to-1 from the
pot, the chances against your bluffing should be 6-to-1.
Then that opponent would break even on the last bet
by calling every time and also by folding every time.
If he called, he would lose $20 six times and win
$120 once; if he folded, he would win nothing and
lose nothing. Regardless of what your opponent does,
you average winning an extra $100 every seven hands.
However, mathematically optimal bluffing strategy
isn't necessarily the best strategy. It is much better
if you are able to judge when to try a bluff and when
not to in order to show a bigger overall profit.
To make sure we agree on what is meant by a bluff,
we will define it as a bet or a raise with a hand
which you do not think is the best hand. Bluffing
can be separated into a couple of different categories.
There is bluffing when there are more cards to come
and when there are no more cards to come. Secondly,
within each of these categories, there is intuitive
bluffing, which is the subject of this page, and mathematical
bluffing, which will be discussed in the next page.
bet on the river was probably a mistake. He wasn't
likely to fold a pair or to call without one. But
I thought I might get a call from him with a worse
Ace high than mine. Not likely, but maybe. Also, I
didn't want to have to showdown my hand and show the
table that I'd been betting without a pair. This latter
reason was the main reason I bet. Even so, in retrospect
I think the bet was a mistake. It's often better to
check on the river to entice a bluff than to make
a thin value bet.
But a debate about whether I should have bet the river
or not isn't really the point here. The point is to
consider how differently this hand would have played
out if I'd been in early position rather than on the
If I'd limped from early position and gotten a caller,
I don't know that I would have bet the flop. I probably
would have still won the pot, but it would have been
a very small pot. And if I checked on the flop and
he took the lead and kept betting, I probably wouldn't
even have won it.
If I had opened with a raise and had a player cold
call, would I like betting that flop as first to act?
I might have bet the flop but checked the turn after
he called. I don't think he had a pair, so I probably
would have won a showdown on the river. But the pot
would have been one big bet of his money smaller if
I'd checked the turn. Those extra bets you can get
from late position add up.