Three players A, B, & C take turns rolling a pair of dice. The winner is the first player who obtains the sum of 7 (P[7] = 1/6) on a given roll of the dice. If A rolls 1st, then B, then C, then back to A (etc. etc. etc.). What is the P[A wins], P[B wins], P[C wins]?

suchonosdy

suchonosdy

Answered question

2022-07-17

A, B, and C Roll Dice
Three players A, B, and C take turns rolling a pair of dice. The winner is the first player who obtains the sum of 7 ( P [ 7 ] = 1 / 6 ) on a given roll of the dice. If A rolls 1st, then B, then C, then back to A (etc. etc. etc.). What is the P[A wins], P[B wins], P[C wins]?

Answer & Explanation

i4epdp

i4epdp

Beginner2022-07-18Added 12 answers

Step 1
Round 1 : A wins with probability 1/6
Round 2 : B wins with probability 1 / 6 × ( 5 / 6 )
Round 3 : C wins with probability 1 / 6 × ( 5 / 6 ) 2
Round 4 : A wins with probability 1 / 6 × ( 5 / 6 ) 3
Step 2
There is a cube because A has to wait three times for his turn to come again.
chivistaelmore

chivistaelmore

Beginner2022-07-19Added 2 answers

Step 1
A wins if they succeed immediately, or if there are first three(!) failures by A, B, C and then a success by A, etc.
Alternative approach: If A happens to fail on first roll (with probability 5 6 ) , we essentially start a game with players (B,C,A) instead of (A,B,C). Therefore P [ B ] = 5 6 P [ A ], P [ C ] = 5 6 P [ B ], and P [ A ] = 1 6 + 5 6 P [ C ]. You can solve these three equations in three unknowns

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