GATE DA 2026 Set 1 — Question 30
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Artificial Intelligence → Adversarial Search → Minimax Search
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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)
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)
Correct answer
2 to 2
Solution
We evaluate the game tree using the Minimax algorithm. The root is a MAX node. The next level contains MIN nodes.
1.Left Branch (Strategy 1):
- Leaf values: 8, 6, -1
- MIN chooses
- Leaf values: 1, 5, 7
- MIN chooses
- Leaf values: -4, -3, 12
- MIN chooses
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