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Game of luck (Posted on 2004-01-27) Difficulty: 2 of 5
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?

See The Solution Submitted by Tristan    
Rating: 3.4000 (5 votes)

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re(4): another remark to SK 'S solution | Comment 17 of 22 |
(In reply to re(3): another remark to SK 'S solution by Ady TZIDON)

"I believe that further correspondance is really counter-productive, 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 2004-01-31 14:09:22

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