Game Theory - Behavioral Mathematics for Game AI - page 59

Mixing It Up
This opposite approach from pure strategy is called a mixed strategy . In this ap-
proach, you select between a variety of strategies that are available to you. Often,
you can assign probabilities to these decisions to select which one you can do. This
is something that we address in depth later on. Suffice to say that in Matching
Pennies, there are only two choices at any one time.
That being said, the best approach is to vary your plays in a somewhat random
fashion. Of course, if you do that, you are no better off than if you had flipped your
coin. Taken one step further, why flip two coins and see if they match when you
and your opponent could simply flip a single coin and be done with it? But now I'm
arguing with the entire premise of this delightfully simple game. Occam would not
approve.
As I mentioned, the game is roughly analogous to Rock-Paper-Scissors. The
difference is that there are three possible plays in Rock-Paper-Scissors rather than
simply two. That makes the scoring grid 3 3 as well. Regardless, as with Matching

Pennies, there is no “pure strategy� to Rock-Paper-Scissors that you can follow to
achieve any more success.

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I NTHE G AME Matching Punches

At first, it would seem that something as simple as Matching Pennies would have no
real comparison to the world of computer and video games. However, over the
years plenty of games have used this mechanism in some form or another. In fact,
one could claim that some games still do.
If we were to imagine a fighting game of the simplest sort, we could start to
draw a parallel. Let's say that player A has two attacks—high and low punches.
Player B, on the other hand, has two defenses—high and low blocks. The goal of the
game is for player A to get past player B's block and score a hit. If B's block is in the
same area as A's attack (i.e., high vs. high), then A fails to score a point. If B's block
is in the wrong area (i.e., high vs. low), then A scores a hit.
Given the parameters of this game, we can analyze it in exactly the same way as
Matching Pennies. There is no “best� strategy to play—other than not repeating the
same sequence over and over. The only thing you can do is observe the other player
for potential clues that he is playing dumb and repeating patterns. If both players
are mixing their choices appropriately, the best you can attempt to accomplish here
is a random button-masher.