Calculate win chance in three-player dice game
Probability of Winning in a Three-Player Dice Game with Rerolls
This problem involves calculating your win probability in a specific three-player dice game.
Setup
- Players: Three players: A (you), B, and C.
- Die: A fair six-sided die is used for all rolls.
- Initial State: Players B and C have already rolled, and both showed a 4.
- Your Turn (Player A): You now roll the die once. The outcome of your roll determines the game's progression:
- If your roll is greater than 4: You win immediately.
- If your roll is equal to 4: All three players (A, B, and C) reroll their dice simultaneously. This reroll process continues until a single player achieves a unique highest face. If the highest face is tied by two or more players, all three players reroll again.
- If your roll is less than 4: You lose immediately.
Question
What is the probability that you (Player A) ultimately win the game?
AI interview prep
Core dilemma
Correctly modeling and calculating the probability of winning in a multi-stage game that includes immediate outcomes, immediate loss, and a recursive reroll condition that can theoretically go on indefinitely, specifically handling the 'unique highest face' tie-breaking rule.
2 tradeoffs and 2 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Calculate win chance in three-player dice game
Probability of Winning in a Three-Player Dice Game with Rerolls
This problem involves calculating your win probability in a specific three-player dice game.
Setup
- Players: Three players: A (you), B, and C.
- Die: A fair six-sided die is used for all rolls.
- Initial State: Players B and C have already rolled, and both showed a 4.
- Your Turn (Player A): You now roll the die once. The outcome of your roll determines the game's progression:
- If your roll is greater than 4: You win immediately.
- If your roll is equal to 4: All three players (A, B, and C) reroll their dice simultaneously. This reroll process continues until a single player achieves a unique highest face. If the highest face is tied by two or more players, all three players reroll again.
- If your roll is less than 4: You lose immediately.
Question
What is the probability that you (Player A) ultimately win the game?