Game Development Reference
In-Depth Information
FIGURE 5.1
The decision matrix for Matching Pennies.
If both players select the same face, player A wins.
If the players select opposite faces, player B wins.
Pure strategies are a gold mine when playing games, but they are a death knell for
game developers. If players discover a pure strategy for playing against your artifi-
cial intelligence (AI), they will be able to win all the time with very little thought or
effort. On the other hand, if AI agents can determine a pure strategy that causes them
to play the same way every time, they become very predictable and, thus, very boring.
In Matching Pennies, since there is no knowledge of the game environment,
nothing to perceive, and no calculations to make, even normative decision theory
can't come to the rescue and tell us what we
should
do on any given play. Therefore,
there is no pure strategy to play. There is no “best� thing to do at any one time.
Interestingly, despite there being no “best� strategy, over time there
is
a
worst
strategy… always selecting the same face for your coin. If you were to do that, it
wouldn't take long for the other person to determine your pattern and respond
accordingly. Likewise, a parallel worst strategy is to always alternate between heads
and tails. Your opponent should be able to pick up on your method and play in
such a way that your predictable repetition words to his advantage. Notice that at
that point, we have not introduced some knowledge to be aware of… the pattern of
play. If an agent were able to discern that and calculate accordingly (i.e., extending
the pattern), then it could make a pretty good stab at what it
should
play as per nor-
mative decision theory.
Barring that, about the only hope we have is to apply some sort of psychology
and hope to ascertain what your partner's pattern is—and, therefore, his next
move. If your opponent is even reasonably adept at obfuscation, though, nothing
short of the Jedi Mind Trick is going to yield any better results than chance.
