Game Development Reference
In-Depth Information
always jumping to one side or the other. For example, if the kicker chose
his good side 65% of the time instead of 59.7%, he would make only 72.6%
of his shots against a goalie who exploited his strategy by always jumping
at his good side.
The key to mixed Nash equilibria is that in equilibrium, each possible
move has an equal payoff.
When playing the equilibrium strategy, on any given shot, the kicker
expects a 74.0% chance of a goal regardless of which side he kicks on. If
he expected a better chance on either side, the goalie would respond more
often to that side, pushing down his success rate there. This equal-payoffs
property is a useful intuitive way of thinking about equilibrium strategies
without using math. Just look for the proportions where each option leads
to the same average payoff.
Can players actually do this kind of numerical analysis? No, but aver-
aged over many players, people are incredibly good at intuitively finding
optimally mixed strategies. Studies on real-life kicking percentages reveal
that kickers as a whole kick on their good side with almost exactly the
correct frequency.
So is that it? We simply count the payoffs, work out the mixed strategy
percentages, and let players flip their weighted coins? Thankfully, no—in
real games, game theory interactions are only a foundation for a fuzzier,
more psychological, more human type of interaction called yomi .
Yomi
YOMI is the mind game of predicting, deceiving, and outwitting an
opponent to get advantages outside the game theory math.
I'm borrowing the term yomi from fighting game designer David Sirlin,
who borrowed it from the Japanese word for reading (as in reading the
mind of the opponent). Flipping weighted coins isn't interesting, but
trying to read a person's mind is. That's why design patterns like rock-
paper-scissors and matching pennies are only a skeleton of a game. The
emotional value of the game grows from the yomi flesh around that
skeleton—from making your opponent think you'll use one move so that
you can counter with another, or letting him think he has tricked you