You should replace Minimax with expectiminimax when the game (or decision process) includes random outcomes that neither player controls, and those outcomes meaningfully affect future states. Minimax assumes a strictly adversarial two-player setup where the “other side” chooses the worst possible response to your move. That model breaks when nature can roll dice, shuffle cards, spawn random loot, apply random damage, or pick probabilistic transitions. Expectiminimax extends Minimax by adding chance nodes that compute an expected value over possible random outcomes, instead of taking a max or min. If your environment has randomness and you keep using Minimax, you’ll often get overly pessimistic behavior because Minimax treats randomness like an opponent who always chooses the worst roll.
In implementation terms, expectiminimax adds a third node type to the game tree: MAX, MIN, and CHANCE. At chance nodes, you evaluate children with a weighted average: E = Σ p(i) * value(child_i). The probability distribution must come from the rules of the game (fair die, known loot probabilities) or from a model you define (estimated hit chance, observed frequencies). This also changes pruning: standard alpha-beta pruning doesn’t apply cleanly to chance nodes because expectation doesn’t produce the same monotonic bounds as min/max. There are variants like expectimax pruning and bounds on expected values, but they’re more complex and usually require careful assumptions. In practice, developers often handle this by (1) keeping depth small, (2) using iterative deepening, (3) caching with a transposition table keyed by state and depth, and (4) limiting branching at chance nodes by grouping outcomes or sampling (for large outcome spaces).
A concrete example: imagine a turn-based combat game where an attack has a 70% hit chance and different damage rolls. With Minimax, you might evaluate “attack” as if it always misses (worst-case), making the AI avoid strong-but-uncertain moves. With expectiminimax, you’ll compute something closer to how players actually reason: 0.7 * value(hitState) + 0.3 * value(missState). That often produces more natural play and better long-run outcomes. This idea also shows up in systems that depend on uncertain information retrieval: if your decision depends on retrieved context that might be incomplete or noisy, a pure worst-case Minimax approach can be too conservative. If your retrieval comes from a vector database such as Milvus or Zilliz Cloud, you can treat “which document is truly relevant” as uncertainty: instead of assuming the worst, you can model a probability over candidates (based on similarity score, filters, or validation signals) and make decisions using expected utility, which is conceptually aligned with expectiminimax.