Two friends $A$ and $B$ roll a pair of dice. If the resulting sum is $7$, $B$ gives $A$ an amount of $\$10$. Otherwise $A$ gives $B$ $\$4$. After a certain number of rounds, who is expected to have more money?
I was trying t get the amount with each person as a function of n,the number of rounds.
The probability that the sum is 7 is 1/6.So, for A, the amount would be
1/6*10 + 5/6 * 1/6*6 + 5/6*5/6*1/6*2 .... Is this approach correct,or should be calculating amount with probabilities multiplied by amount gained/lost(ie for player A +10 and -4) ?
After each round, B has a net gain (on average) of $\frac{5}{3}=\frac{5}{6}\times 4-\frac{1}{6}\times 10$ dollars. Therefore B will come out ahead on average.