as you can use game theory to bluff, you can also
use it to call possible bluffs. Usually when your
hand can beat only a bluff, you use your experience
and judgment to determine the chances your opponent
is bluffing. If your hand can beat some of your opponent's
legitimate hands, then you do a standard comparison
of your chances of having the best hand plus the chances
your opponent is bluffing against the pot odds you
are getting. However, against an opponent whose judgment
is as good as or better than yours, or one who is
capable of using game theory to bluff, you in your
turn can use game theory to thwart that player or
at least minimize his profits.
Suppose the pot is $100, and your opponent assumes
you will fold one out of three times rather than call
a $20 bet. It then becomes profitable for that opponent
to come out bluffing $20 to win $100 because he figures
to lose $20 twice but steal $100 once for a net profit
of $60 and an expectation of $20 per bet. By the same
token, if your opponent thinks you will never fold
in this situation, he will never bluff. Therefore,
it behooves you to have an opponent think you might
sometimes fold, but you should call sufficiently often
to catch his bluffs.
When you use game theory to decide whether to call
a possible bluff, you make calculations similar to
those you make when deciding whether to employ a bluff
yourself - and you randomize your calls just as you
randomize your bluffs. You figure out what odds your
opponent is getting on his possible bluff, and you
make the ratio of your calls to your folds exactly
the same as the ratio of the pot to your opponent's
bet. If your opponent bets $20 to win $100, he is
getting 5-to-1 on a bluff. Therefore, you make the
odds 5-to-1 against your folding. That is, you must
call five times and fold once. You can use key cards
to randomize again - for example, if you catch certain
unseen cards, you fold. Otherwise, you call.
In contrast to using game theory to bluff, using game
theory to decide whether to call doesn't turn an unprofitable
situation into a profitable one. All it does is prevent
your opponent from outwitting you - just as using
a coin in the odds-evens game prevents your opponent
from outwitting there. If your opponent is using optimum
game theory strategy to bluff, there is still nothing
you can do to get the best of him.
I play this pair?
No, I shouldn't. I've got one 5 gone, and one 10 gone.
My two-card flush is alive but this is a long shot,
because my pair isn't live and my kicker is small
and not completely alive. And I have two players behind
me with bigger upcards than my cards. A pair of l0s
isn't a bad starting hand, but this situation is a
pretty easy fold in a no-ante $1 to $5 game.
If you're playing in a higher limit game, with antes,
and if there's some chance that a raise will steal
the antes, then a raise might be appropriate, but
even then it's close. In the typical $1 to $5 game
with no antes, the risk that a player behind you has
your pair beat isn't large, but it's too large to
be worth the gamble. Because of all your dead cards,
your chances of catching up are pretty slim.