Zero-Sum Games and Minimax
Optimal mixed strategies.
Key idea
Optimal mixed strategies.
In depth
In a zero-sum game, one player’s gain is the other’s loss. Von Neumann’s minimax theorem: there are mixed strategies for which the row player’s maximin equals the column player’s minimax, the value of the game. It can be solved by linear programming.
Worked example
Rock–paper–scissors has value 0, with the optimal mix 1/3 each.
Real-world uses
- Choosing defence and attack strategies in security, sport and military planning
Common mistake
Applying zero-sum reasoning when both players can gain.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Zero-Sum Games and Minimax?
Optimal mixed strategies. It is a topic at the expert level in Differential Equations, Abstract Algebra & Applied Math.
Where is Zero-Sum Games and Minimax used in real life?
Real-world examples: Choosing defence and attack strategies in security, sport and military planning.
What should I learn before Zero-Sum Games and Minimax?
Make sure you are comfortable with Nash Equilibrium, the previous topic in Differential Equations, Abstract Algebra & Applied Math.
What is a common mistake with Zero-Sum Games and Minimax?
Applying zero-sum reasoning when both players can gain.
How can I practise Zero-Sum Games and Minimax?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Zero-Sum Games and Minimax?
Move on to Operations Research Overview next.
Related expert topics in Differential Equations, Abstract Algebra & Applied Math
- Exact Equations – M dx + N dy = 0 with Mᵧ = Nₓ.
- Bernoulli Equations – Substitute v = y¹⁻ⁿ to linearise.
- Runge–Kutta Methods – Higher-accuracy numerical solvers.
- Second-Order Homogeneous Equations – Use the characteristic equation.
- Undetermined Coefficients – Guess the particular solution form.
- Variation of Parameters – General method for particular solutions.