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Omni-MATH / New this year at HMNT: the exciting game of RNG baseball! In RNG baseball, a team of infinitely many people play on a square field, with a base at each vertex; in particular, one o…

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problem

New this year at HMNT: the exciting game of RNGR N G baseball! In RNG baseball, a team of infinitely many people play on a square field, with a base at each vertex; in particular, one of the bases is called the home base. Every turn, a new player stands at home base and chooses a number nn uniformly at random from \{0,1,2,3,4\}. Then, the following occurs: - If n>0n>0, then the player and everyone else currently on the field moves (counterclockwise) around the square by nn bases. However, if in doing so a player returns to or moves past the home base, he/she leaves the field immediately and the team scores one point. - If n=0n=0 (a strikeout), then the game ends immediately; the team does not score any more points. What is the expected number of points that a given team will score in this game?
Plain-text mathematical notation (without MathML)
New this year at HMNT: the exciting game of RNG baseball! In RNG baseball, a team of infinitely many people play on a square field, with a base at each vertex; in particular, one of the bases is called the home base. Every turn, a new player stands at home base and chooses a number n uniformly at random from \{0,1,2,3,4\}. Then, the following occurs: - If n>0, then the player and everyone else currently on the field moves (counterclockwise) around the square by n bases. However, if in doing so a player returns to or moves past the home base, he/she leaves the field immediately and the team scores one point. - If n=0 (a strikeout), then the game ends immediately; the team does not score any more points. What is the expected number of points that a given team will score in this game?
Original LaTeX notation
New this year at HMNT: the exciting game of $R N G$ baseball! In RNG baseball, a team of infinitely many people play on a square field, with a base at each vertex; in particular, one of the bases is called the home base. Every turn, a new player stands at home base and chooses a number $n$ uniformly at random from \{0,1,2,3,4\}. Then, the following occurs: - If $n>0$, then the player and everyone else currently on the field moves (counterclockwise) around the square by $n$ bases. However, if in doing so a player returns to or moves past the home base, he/she leaves the field immediately and the team scores one point. - If $n=0$ (a strikeout), then the game ends immediately; the team does not score any more points. What is the expected number of points that a given team will score in this game?

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Source and history

task_id
92873dc7-5801-55d3-9fdd-77b64802457e
task_key
test--92873dc7-5801-55d3-9fdd-77b64802457e
task_revision_id
1
config / split
/ test

Official source

initial import