Game Theory to Bluff
this site we are mainly concerned with how game theory
can be applied to the art of bluffing and calling
possible bluffs in poker. For this purpose we will
talk about mixed strategy, a strategy in which you
make a certain play - specifically a bluff or a call
of a possible bluff - a predetermined percentage of
the time, but you introduce a random element so that
your opponent cannot know when you are making the
play and when you are not.
You will recall from the last site that, everything
else being equal, the player who never bluffs and
the player who bluffs too much are at a decided disadvantage
against a player who bluffs correctly. To illustrate
this point and to show how game theory can be used
to decide correctly when to bluff, we'll set up a
We are playing draw lowball with no joker, and we
give you a pat :
We take a :
You stand pat, and I must draw one card. If I catch
a five, a six, a seven, an eight, or a nine, I beat
you with a better low than yours. If I catch any other
card, you win. That means that of the 42 cards remaining
in the deck, I have 18 winners (4 fives, 4 sixes,
4 sevens, 3 eights, and 3 nines) and 24 losers, which
makes me a 24-to-18 or 4-to-3 underdog. We each ante
$100, but after the draw - which you do not see --
I can bet $100.
Suppose I said I'm going to bet $100 every time. Clearly
you would call every time because you would stand
to win $200 the 24 times I'm bluffing and lose $200
the 18 times I have the best hand for a net profit
of $1,200. On the other hand, suppose I said I will
never bluff; I will only bet when I have your 9,8
low beat. Then you would fold every time I bet, and
once again you would win 24 times (when I don't bet)
and lose 18 times (when I do) for a net profit of
$600 since you win or lose $100 in each of these hands.
So with either of these variations of the proposition,
you definitely have the best of it.
spouse comes home one day from shopping. She or he
has bought the most hideous, impractical, overpriced
sofa/motorcycle/carpet/computer you can possibly imagine.
You think that the purchase was a huge, ponderous
waste of money, and you say so. "Oh, yeah?"
your spouse snaps back. "Well, what about all
the money you spend on poker?" You don't bother
pointing out that you're investing, not spending;
you've been down this road be fore. You break off
the argument before it goes ballistic, but it's on
your mind later that day when you head down to the
club. You carry it with you into battle. Maybe somewhere
in a dark corner of your mind there's even a tiny
motivation to lose-or at least a higher tolerance
for losing than usual. After all, your spouse has
shown a fabulous capacity to waste money, why should
you be any different?
Those prone to this "I'll show me!" state
of mind willfully commit self-destructive acts in
the misguided hope or expectation that the damage
they're doing to themselves is actually afflicting
someone else. Other stimuli can trigger this sort
of revenge-against-the-world response. Maybe you're
being treated unfairly at work. Maybe your parents/children/
siblings are driving you crazy. Maybe you think you're
only seeking a little peace and quiet, or alone time,
or a distraction when you race off to play poker.
That may seem benign enough-we all can use a little
distraction from time to time. But it's hardly a reason
for playing poker, and it hardly augers well for the
success of your session. Worse, it may mask a deeper
resentment, which will manifest itself in repressed
anger, poor judgment, flawed decision-making and,
ultimately, failure and loss.