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GATE DA 2026 Q30: Best MAX strategy in a two-level minimax tree

Question

Consider the game tree for a two-player turn-taking minimax game as shown in the figure. The value of a terminal node represents the utility of the game state if the game ends there. The numbers written next to the edges denote the strategies.

There are two players MAX and MIN. At any particular state of the game, MAX prefers to move to a state of maximum value. On the other hand, MIN prefers to move to a state of minimum value.

Suppose MAX starts the game at the root and has three strategies: 1, 2 and 3. Next, MIN plays and also has three strategies: 1, 2 and 3. The game ends there. Both players always take optimal strategies throughout the game.

At the root, the best strategy for MAX is ___________. (Answer in integer)

Game tree: MAX root with strategies 1, 2, 3 leading to MIN nodes; leaves 8, 6, −1 under strategy 1; 1, 5, 7 under 2; −4, −3, −12 under 3
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Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 2 (official GATE 2026 final answer key)

Concept used: Minimax: each MIN node takes its smallest leaf, then MAX picks the largest of those.

First step: The MIN values are min⁡(8,6,−1)=−1\min(8, 6, -1) = -1, min⁡(1,5,7)=1\min(1, 5, 7) = 1 and min⁡(−4,−3,−12)=−12\min(-4, -3, -12) = -12.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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