Can a pure strategy adapt to observations?

Yes. It can prescribe different actions for different information situations; it just does not randomize within a specified situation.

Does a pure strategy guarantee a fixed outcome?

No. Other players or chance can change the outcome.

Is a pure strategy always optimal?

No. Its quality depends on the game and the other players' behavior; some strategic settings make randomization important.

AI Glossary / Graphs and symbolic AI / Intermediate

Pure strategy

Definition

A pure strategy is a complete, deterministic plan specifying which action a player will choose at each of that player's decision situations in a game. It contains no randomization in those choices. In a one-move game, it may be just one action; in a sequential game, it includes actions for contingencies that may never occur during the actual play.

What it means

“Pure” does not mean simple, honest, or guaranteed to succeed. A pure strategy can be a complicated conditional plan: do one thing after observing one situation and another after observing a different situation. Its defining feature is that the prescribed action is fixed for each information situation.
An information set groups situations the player cannot distinguish when choosing. A valid strategy cannot condition on hidden facts unavailable to that player. A mixed strategy instead assigns probabilities to pure strategies. The distinction describes how choices are specified; uncertain outcomes can still arise from another player's decisions or from chance, even when one's own strategy is pure.

How it works

Describe the game's players, timing, available actions, information, and payoffs. For a particular player, list each information set where that player might choose. Select one available action for each information set. Together, these selections form a pure strategy.
For a finite game, if the player has two actions at one information set and three at another, there are 2 × 3 = 6 such plans, assuming those are the only choices. Evaluating a strategy requires pairing it with other players' strategies and the game's chance rules. A realized sequence of moves is only one path produced by those plans, not the complete strategy itself.

Three practical examples

A game-playing agent can specify a fixed response for every observable position it may encounter.
A bargaining simulation can represent a participant's offer and its response to each possible later counteroffer.
A coordination exercise can compare deterministic communication plans before introducing randomization or uncertainty about other participants.

Think of it this way

Think of a complete instruction sheet with an answer for every permitted decision situation: “if this happens, choose that.” Only some lines may be used on a particular run. The analogy is limited because game-theoretic information sets constrain what the sheet may refer to; it cannot prescribe different actions based on hidden information the player cannot observe.

Worked example

Consider an invented sequential game. Player 1 first chooses Left or Right. Player 2 observes that choice and then chooses Accept or Reject. Player 2 has two distinct information sets, one after Left and one after Right, with two actions at each.
Player 2 therefore has four pure strategies: Accept after both choices; Accept after Left and Reject after Right; Reject after Left and Accept after Right; or Reject after both. Simply saying “Accept” is ambiguous unless it means Accept in both contingencies.
Suppose Player 2's payoffs are: after Left, Accept gives 3 and Reject gives 1; after Right, Accept gives 0 and Reject gives 2. The conditional plan Accept after Left and Reject after Right chooses the better action at each of Player 2's decision situations. If Player 1 chooses Left, only the first instruction is used, but the strategy still specifies the response after Right.
Now change the game so Player 2 cannot observe whether Left or Right was chosen and must decide at one information set. The earlier conditional plan is no longer implementable. Player 2 then has only two pure strategies, Accept or Reject, because it cannot choose differently based on the hidden first move.

Illustrative case study

Fictional case: Alder Games stores an agent's strategy as the moves observed in one successful match. When an opponent makes an unexpected opening, the stored sequence has no suitable response.
The team rewrites the representation as a mapping from information situations to actions. It includes off-path contingencies and checks that no rule refers to concealed opponent information. This fictional example illustrates why a successful play record is not automatically a complete strategy. It does not report a deployed system, measured playing strength, or a claim that every contingency can be stored explicitly at scale.

Common misconceptions and mistakes

Do not confuse one action with a complete strategy in a game containing later choices. Do not omit an instruction simply because the current plan seems unlikely to reach that situation. Such contingencies matter when comparing strategies and deviations.
A pure strategy need not choose the same action everywhere; deterministic conditional behavior remains pure. Conversely, a randomly selected pure plan is part of a mixed strategy description even though the chosen plan is deterministic once selected. Some games have no pure-strategy Nash equilibrium. The existence of available pure strategies does not imply that one deterministic combination is stable against every player's unilateral deviation.

Business use

Pure strategies provide a clear baseline for studying strategic interaction in simulations. They help teams specify how an agent responds before evaluating whether that response performs well against other agents. A strategy table can expose missing contingencies or unrealistic access to information.
For a business-facing simulation, distinguish the model from a forecast of what people will do. Payoffs, information, and available actions may be simplified. Review those assumptions before interpreting a recommended response. If the simulation includes randomization, document whether it occurs when choosing an entire plan or at individual decisions, because those representations require careful comparison in extensive-form analysis.

Check your understanding

A player can choose among three actions at one information set and two actions at another. How many pure strategies are available?

Answer: Six, because a complete plan selects one action at each set: 3 × 2 = 6. This count assumes the two listed information sets fully describe that player's decisions.

Related terms

Mixed strategy
Information sets
Strategy profile
information set
extensive-form game
normal-form game
best response
Nash equilibrium
deterministic policy

Learn next

Learn mixed strategies and information sets next. Draw the worked game's two versions, first with the opening observed and then hidden. Explain why an action plan based on the unseen opening is not a valid strategy in the second version.

Information sets

Sources

Xiaojin Zhu, University of Wisconsin–Madison, Game Theory teaching slides: https://pages.cs.wisc.edu/~jerryzhu/cs540/handouts/gametheory.pdf Washington State University, pure strategies and game representation teaching material: https://s3.wp.wsu.edu/uploads/sites/1790/2017/11/finding_ne.pdf

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