This is my second question following this post.
Three players are playing a game. They all have small amounts of money, let say: player 1 has $\$a$, player 2 has $\$b$, and player 3 has $\$c$, where $a<b<c$. The probability of each player wins each turn of the game is $p$ for player 1, $q$ for player 2, $r$ for player 3, and $s$ for having draw, where $p+q+r+s=1$. The losers will transfer a dollar ($\$1$) to the winner for each turn. The game ends until one player has all the money. What is the probability of each player going bankrupt? What is the expected number of turns so that only one player left as the winner?
Suppose that they play blackjack, if player 1 gets 20 points, player 2 gets 19 points, and player 3 gets 18 points, then the winner of that turn is player 1, so the other two players must pay a dollar to the player 1. If there are two players get, for example, 19 points and the another player gets 18 points, then that turn is considered draw. If they all get 19 points, this is also considered draw. If one player loses all the money, then he will stop playing and only two player will continue the game with probability of winning for each player is $x$ and $y$, also the probability of draw is $z$. Each turn will be repeated until one player has all the money.
To be honest, I can't answer this question and I really don't get it. I left my answer sheet totally empty for this one. (─‿‿─)
Please help me to answer this question and provide a simple explanation about the answer you submit. Every answer would be greatly appreciated.