benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Consider a three-person game involving the following three types of fair…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Consider a three-person game involving the following three types of fair six-sided dice. - Dice of type AA have faces labelled 2,2,4,4,9,92,2,4,4,9,9. - Dice of type BB have faces labelled 1,1,6,6,8,81,1,6,6,8,8. - Dice of type CC have faces labelled 3,3,5,5,7,73,3,5,5,7,7. All three players simultaneously choose a die (more than one person can choose the same type of die, and the players don't know one another's choices) and roll it. Then the score of a player PP is the number of players whose roll is less than PP 's roll (and hence is either 0,1 , or 2 ). Assuming all three players play optimally, what is the expected score of a particular player?
Plain-text mathematical notation (without MathML)
Consider a three-person game involving the following three types of fair six-sided dice. - Dice of type A have faces labelled 2,2,4,4,9,9. - Dice of type B have faces labelled 1,1,6,6,8,8. - Dice of type C have faces labelled 3,3,5,5,7,7. All three players simultaneously choose a die (more than one person can choose the same type of die, and the players don't know one another's choices) and roll it. Then the score of a player P is the number of players whose roll is less than P 's roll (and hence is either 0,1 , or 2 ). Assuming all three players play optimally, what is the expected score of a particular player?
Original LaTeX notation
Consider a three-person game involving the following three types of fair six-sided dice. - Dice of type $A$ have faces labelled $2,2,4,4,9,9$. - Dice of type $B$ have faces labelled $1,1,6,6,8,8$. - Dice of type $C$ have faces labelled $3,3,5,5,7,7$. All three players simultaneously choose a die (more than one person can choose the same type of die, and the players don't know one another's choices) and roll it. Then the score of a player $P$ is the number of players whose roll is less than $P$ 's roll (and hence is either 0,1 , or 2 ). Assuming all three players play optimally, what is the expected score of a particular player?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
1ffafb54-168a-58e8-b61b-e3ce225266ea
task_key
test--1ffafb54-168a-58e8-b61b-e3ce225266ea
task_revision_id
1
config / split
/ test

Official source

initial import