GAMES
Cutthroat Pool DFA
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CASE ANALYSIS
Scenario
Modeling cutthroat pool game rules as a DFA where each player starts with one ball, and transitions represent shot outcomes. The automaton accepts a string if the corresponding player wins after all symbols are consumed.
Key decisions
- Each player starts with exactly one ball to keep the state space finite and deterministic.
- Accepting states (P1_Wins, P2_Wins) are sinks with self-loops for any remaining input.
- Transitions distinguish pocket_own (eliminates yourself, opponent wins if they still have a ball) vs. pocket_opponent (eliminates opponent, you win if you still have a ball).
When to reuse this
Use when teaching finite automata with a concrete, game-based example that illustrates deterministic transitions and accepting states without requiring a final/terminal node.
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state-cutthroat-pool-dfa