Lesson 7.08e-f

7.08e-f Mixed strategies and optimal mixed strategies Quiz: OCR Further Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 7.08e-f, Mixed strategies and optimal mixed strategies: 20 multiple choice questions for the OCR Further Maths (H245), Unit 4: Discrete Mathematics (Y544), written with Revision Ninja.

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The 20 questions

  1. When does a two-player zero-sum game require a mixed strategy to solve?

    • Negative game value
    • One saddle point
    • Two saddle points
    • No saddle point

  2. What is the sum of all probabilities assigned to strategies in a mixed strategy?

    • 0
    • 2
    • 1
    • 0.5

  3. Player A plays Row 1 with probability 0.4. Payoffs against Column 1 are 3 and -1. Find expected payoff.

    • -0.2
    • 1.2
    • 0.8
    • 0.6

  4. In a 2x2 game, Row 1 payoffs are (2, 0) and Row 2 payoffs are (0, 4). Find optimal p.

    • 2/3
    • 1/2
    • 3/4
    • 1/3

  5. In a 2x2 game with optimal p = 2/3 and row payoffs (2, 0) and (0, 4), find value v.

    • 2
    • 8/3
    • 2/3
    • 4/3

  6. When using a graphical method for a 2xn game, which boundary forms the optimal solution?

    • Lowest lower envelope
    • Highest upper envelope
    • Highest lower envelope
    • Lowest upper envelope

  7. In a graphical solution for an mx2 game, which region determines Player B's optimal strategy?

    • Lowest lower envelope
    • Lowest upper envelope
    • Highest lower envelope
    • Highest upper envelope

  8. Which principle states that expected payoffs against all active opposing strategies must be equal?

    • Dominance principle
    • Minimax principle
    • Maximin principle
    • Equating expected payoffs

  9. Why might a constant be added to all entries in a payoff matrix?

    • Increase matrix size
    • Remove saddle points
    • Ensure positive payoffs
    • Create dominance

  10. Row 1 payoffs are (5, -2) and Row 2 payoffs are (1, 3). Find expected payoff against Column 1.

    • 4p + 1
    • 4p - 2
    • 5p + 1
    • 6p - 1

  11. Row 1 payoffs are (5, -2) and Row 2 payoffs are (1, 3). Find expected payoff against Column 2.

    • 3 - 2p
    • 3 - 5p
    • -2p + 3
    • 5p - 2

  12. Equate expected payoffs 4p + 1 and 3 - 5p to find the optimal probability p.

    • 2/9
    • 1/4
    • 4/9
    • 2/7

  13. What defines a zero-sum two-player game in matrix game theory?

    • Constant non-zero payoff
    • Negative total payoff
    • Zero total payoff
    • Positive total payoff

  14. Player B plays Column 1 with probability 0.5. Row 1 payoffs are 4 and 2. Find Player A's payoff.

    • 3
    • 2
    • 4
    • 6

  15. In a 2x2 game where Player A plays Row 1 with probability p, what is 1-p?

    • Game value
    • Column 1 probability
    • Column 2 probability
    • Row 2 probability

  16. In a graphical solution, if Column 2 line is not on the optimal envelope intersection, what is its probability?

    • 0
    • 0.5
    • 1
    • 0.25

  17. What is the value v of a zero-sum game if the game is fair?

    • 1
    • 0.5
    • -1
    • 0

  18. Which algorithm solves mixed strategy games with matrix dimensions larger than 2x2 without graphical reduction?

    • Linear programming
    • Dijkstra's algorithm
    • Nearest neighbour algorithm
    • Kruskal's algorithm

  19. In a payoff matrix with Row 1 (3, 4) and Row 2 (1, 2), which row is dominated?

    • Row 1
    • Column 1
    • Row 2
    • Column 2

  20. Which theorem guarantees that every finite two-player zero-sum game has an optimal mixed strategy solution?

    • Saddle theorem
    • Fundamental theorem
    • Minimax theorem
    • Dominance theorem

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