Minimax in its basic form does not directly work well for imperfect-information games like poker or bridge because the game state is not fully observable. Standard Minimax assumes both players know the exact state and can choose optimal actions based on that complete information. In poker, you don’t know the opponent’s hole cards; in bridge, you don’t know all hands during play. If you run plain Minimax on a single guessed “true state,” your AI will overfit to that guess and make decisions that look strong only if the hidden information matches your assumption. The right mental model is that you’re operating over a belief state (a distribution over possible hidden states), not a single fully-known state.
To adapt the idea, developers usually shift from “state-based Minimax” to approaches like belief-state search, information set minimax, or determinization (sampling possible hidden states and averaging). A practical pattern is: maintain a set of plausible hidden states consistent with what’s been observed, sample a number of them, evaluate each sampled world using a perfect-information solver (often Minimax or expectiminimax), and then aggregate results to pick an action. This can work surprisingly well but has known pitfalls: it can leak information in the evaluation (your simulated opponents accidentally “know” hidden cards), it may be biased if sampling is poor, and it can become expensive. A more principled direction is to treat each decision point as an information set and compute strategies that are robust across that set, but implementing full game-theoretic solvers is a bigger project than “drop-in Minimax.”
Example: in poker, if the board is Ah Ks 7d and you hold As Qs, the opponent’s range is unknown. A determinization approach might sample 1,000 opponent hands consistent with betting history, run a depth-limited search to estimate EV for “bet” vs “check,” then pick the higher EV action. You can improve realism by modeling opponent behavior and by using an evaluation function that outputs expected chip gain rather than win/loss only. The analogy to vector retrieval is about partial observability: if your “state” includes uncertain facts retrieved from embeddings, your system is effectively operating under incomplete information. When you use a vector database such as Milvus or Zilliz Cloud, you often don’t know whether the top result is truly correct—so treating retrieval outputs as a belief distribution (multiple candidates with weights) and making decisions that are robust to uncertainty is closer to how imperfect-information search needs to behave than a brittle single-path Minimax.