In a minimax tree, a Min node has three children with values −5, 3, and 0. What value does the Min node return?
A3, because Max always wants the highest value
B−5, because Min picks the child value lowest for Max
C0, because the algorithm averages across children
D−5 only if it is the leftmost child; otherwise the first child encountered
At a Min node, the minimizing player picks the move leading to the outcome worst for Max — so the node returns the minimum child value, −5. Returning the average or the maximum would contradict the assumption of optimal play: the minimizing player will never choose an outcome better for Max when a worse one is available.
Question 2 Multiple Choice
A minimax search finds that Move A guarantees a score of +1.5 against a perfect opponent, while Move B leads to +3 if the opponent blunders but −2 if the opponent plays optimally. Which move does minimax recommend, and why?
AMove B — it has higher upside and the algorithm should maximize expected value
BMove A — it guarantees the better outcome against optimal play
CMove B — minimax explores all branches and prefers the one with the highest leaf value
DMove A — but only because Move B has a longer search depth
Minimax assumes the opponent plays optimally. Under that assumption, Move B leads to −2 (the opponent will find the refutation), while Move A guarantees +1.5. The algorithm recommends Move A because it maximizes the worst-case outcome. Move B's +3 upside is irrelevant — it is only reachable if the opponent makes a mistake, which the algorithm does not assume. This is the core meaning of 'minimax': maximize the minimum outcome.
Question 3 True / False
The minimax algorithm finds the move that leads to the best possible outcome for the maximizing player.
TTrue
FFalse
Answer: False
Minimax finds the best *guaranteed* outcome against a perfectly rational opponent — the move that maximizes the worst case. The 'best possible' outcome might be achievable only if the opponent blunders. Minimax explicitly assumes the opponent plays optimally and finds the strategy that is safe against that assumption. A player who optimizes for the best possible outcome (ignoring opponent rationality) is playing a different and riskier strategy.
Question 4 True / False
In a zero-sum two-player game, the outcome that maximizes the score for the Max player is simultaneously the worst outcome for the Min player.
TTrue
FFalse
Answer: True
This is the defining property of a zero-sum game: the players' utilities sum to a constant (often zero). Whatever Max gains, Min loses by exactly that amount. There is no outcome where both benefit, so the Max-optimal outcome and the Min-worst outcome are always the same state. This is precisely why the minimax logic works: choosing the highest value for Max is identical to choosing the worst value from Min's perspective.
Question 5 Short Answer
Why does the minimax algorithm assume optimal play from both sides, and what would be the consequence of not making this assumption?
Think about your answer, then reveal below.
Model answer: Assuming optimal play from both sides guarantees the best worst-case outcome — a strategy that is safe regardless of how well the opponent actually plays. If the algorithm assumed a weak opponent and chose moves that exploit expected blunders, it would be vulnerable to strong play: those same moves might be easily refuted, leading to worse outcomes than the 'safe' minimax choice. By preparing for the hardest possible opponent, minimax produces a strategy that degrades gracefully — it does no worse than expected against a perfect opponent and may do better against a weaker one.
This connects minimax to game theory's concept of a maximin strategy — the strategy that maximizes the minimum payoff. Real-world chess engines use minimax (with alpha-beta pruning) as a foundation precisely because preparation for optimal opposition is the correct competitive stance when the opponent's actual strength is unknown.