A decision state is the information used to determine which actions are available and how their possible consequences are distributed. A score records credited progress, while a decision state also represents constraints and remaining options relevant to the next choice.
Baseball’s base-out states omit the lineup
Before the side-retiring third out, each of baseball’s three bases is either occupied or empty. That produces eight occupancy configurations. Combining them with zero, one or two outs gives 8 × 3 = 24 base-out states.
This partition answers a specific indexing question. It does not encode inning, score, count, batting order or player identities. Two situations with a runner on first and one out can therefore share a base-out label while presenting different batters and different available substitutes.
Under MLB’s 2026 rules, the batting order continues across innings. It does not restart at the first hitter each time a new inning begins. Rule 5.10(d) also prevents a removed player from re-entering that game. A substitution changes the remaining option set even when it leaves the score unchanged.
Take two otherwise comparable situations in which the same bench player is available in one game and has already been removed in the other. The next legal substitution choices differ. A model retaining only the score and base-out label cannot represent that distinction.
Survivor entries retain different teams
A one-use survivor rule creates a similar information requirement through a different mechanism. The 2026 March Mania rules allowed each team to be selected only once and eliminated an entrant without an unused surviving team to select.
Two entries can reach the same round with the same number of successful picks while having used different teams. A team still available to one entry can be unavailable to the other. Their visible progress matches, but their next legal choices do not.
The useful history is the history that changes the remaining decision. Recording the used-team set preserves the restriction without treating every past detail as equally relevant. Future eligibility still requires the tournament’s advancement state.
A disclosed feature can change a game’s rules
The May 7, 2024 versions of Great Britain’s remote gambling technical standards provide another bounded example. For covered games, RTS 3B requires relevant current-state information to be displayed as play progresses; its guidance includes accumulated tokens and active feature rules. Lotteries are excluded from that provision.
RTS 7A distinguishes prohibited adaptive compensation from bonus features whose different rules are triggered by random events. A game can therefore have a disclosed feature state without that state being evidence that probabilities are adjusted to compensate for past results.
The transition mechanism determines what the state means. A token counter alone does not specify the next-outcome probabilities, the feature’s value, whether the state persists between sessions, or who retains access to it. Those properties require the particular game’s rules and return model.
State sufficiency depends on the decision
A state representation is insufficient for a decision when it merges situations with different available actions or different conditional consequences for the same action. The missing information must either be added or represented through an explicit model of uncertainty.
Base-out labels remain useful for organizing baseball observations even though they cannot answer every substitution question. A survivor entry’s success count remains an accurate progress measure even though it omits team availability. A displayed feature counter remains observable even when it is insufficient to calculate a return.
The common requirement is to preserve distinctions that change the decision being modeled. Baseball substitutions, one-use picks and game features have different rules; equal visible progress does not erase those rules.
Pricing a position requires the payout distribution conditional on the relevant state. A richer state description changes value only through the actions, probabilities, payouts or costs it reveals. Positive expected net return still requires the resulting expected payout to exceed the full participation cost.