4 people play a game of chance. They each take turns until everyone has taken a turn, then they begin a new round. They stay in the same order every round. Every time a player takes a turn, they have a certain chance of winning. When someone wins, the game ends. They all have even odds of winning a game. The chance of someone winning in any given round is 3/5.
What is the probability for each person to win during their turns?
(In reply to
re(3): another remark to SK 'S solution by Ady TZIDON)
"I believe that further correspondance is really counterproductive, since both of us define different games."
As noted, my initial post assumed the same game you are talking about. I later modified it to treat the whole event as the single game.
"Your remark about inserting x instead of pb and pc is a valuable one and I am going to correct my answers accordingly later. "
Hopefully, when you do the math, you will see that what you call x is 1 minus the fourth root of 2/5.
"It would be beneficial for everybody if the author (Tristian) will specify the nature of the game e.g. in terms of marbles in a bag. As you know in my model one draws a marble( the same distribution for everybody) if won the game ends, if not the marble is returned. "
Two problems here: (1) Tristan's idea was that the puzzle was to find the nature of the game given the specifications. (2) In this case marbles in a bag wouldn't work for the idea of the game as you see it, and as I originally saw it: the odds are irrational. As it turns out, in the other interpretation, the odds are rational, and can be expressed as I stated in a previous post, in terms of marbles in a bag.
Perhaps Tristan was infelicitous in specifying "Every time a player takes a turn, they have a certain chance of winning," making it sound as if each turn by each player had the same probability of a win. What apparently was meant was that "Every time a given player takes a turn, he or she has a certain chance of winning."
"I do not know how to pass my remarks to the author of the puzzle may be you do. "
I'm sure Tristan will be logging on to see these comments.

Posted by Charlie
on 20040131 14:09:22 