Gambler's ruin problem

[XIPP]

Question from DeGroot:

Consider the following three different possible conditions in the gambler’s ruin problem: (a) The initial fortune of gambler A is two dollars, and the initial fortune of gambler B is one dollar. (b) The initial fortune of gambler A is 20 dollars, and the initial fortune of gambler B is 10 dollars. (c) The initial fortune of gambler A is 200 dollars, and the initial fortune of gambler B is 100 dollars. Suppose that p<1/2. For which of these three conditions is there the greatest probability that gambler A will win the initial fortune of gambler B before he loses his own initial fortune?


I know the answer is condition (a), but how is answer obtained ?
Please explain.

[XIPP]

Someone help me, too , please !

[Akshay Jain]

actually i hav never read degroot's book, after u posted this prblm i went thru dis concept bt got confused...:( ..dis book is dere in my 2nd sem syllabus.....so cant help u out on dis now....:(

[XIPP]

Akshay, will you please just suggest me some good book for ISI and DSE exams?
Actually, I heard about Freund's book, but amazon.com's posts criticise it.
I also know about VK Kapoor and SC Gupta, but there are many books on stats by these authors.Which should I follow?

I have Nagar-Das and DeGroot. Are they enough?

Please help.

[Akshay Jain]

visit dis......u will get to jo everything
http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/study_guide.pdf

[XIPP]

Great job by you, Akshay!! Thank you.

[greenworld666]

thanks a ton!!! Akshay!!!


On Thu, Oct 10, 2013 at 7:23 PM, XIPP [via Discussion forum]
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> Great job by you, Akshay!! Thank you.
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[melodydurrant]

That was very interesting question. My friend http://dead.net/member/cruzlorenzo helped me (i am so bad with math). In a condition person B has only 1 dollar and he is using all his money to get a bet. That's why there is strong possibility that he will lose after first round.