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  1. #16
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    Re: need help understanding interview question




    Dason I accept your explanation, but please read the original question. As you say I lose $1 in first roll, I think question is now how many times we play more such that my lose goes to $0, vice versa. You all are focus on over all expected gain should be zero, yes I accept it because for fair game it is necessary, keep in mind if you and me win same Dollars it is also a fair game, thats why I put probability=0.5, The original question was "How many rolls would be required to make it a fair game?", If you have other solution please share it, It will be useful for discussion.

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    Re: need help understanding interview question

    Quote Originally Posted by BGM View Post
    The winning probability is \frac {2} {6^2} + \frac {1} {6^2} = \frac {1} {12}

    It is a fair game if the expected outcome is 0

    The expected outcome (per roll) is

    \frac {x} {12} - \frac {11y} {12}

    So for any x, y satisfying x = 11y would be a fair game.

    Maybe there is some wording problem (or extra information), not sure what the question is asking for.

    This makes sense, but the question is HOW MANY throws would make it a fair game... Using Azeem's answer it's roughly ~8.. but I am not sure if thats the correct way of going about it.


    I understand the x/12 - 11y/12 such that it = 0 would make it fair.. but what if there are X values and Y values that don't match? What relationship am I missing here??

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    Re: need help understanding interview question

    Is it supposed to be that if you get a 11 or higher on any of the rolls then you win, if not then you lose? If so then for certain values of X and Y there could be some fair games for certain values of n...
    I don't have emotions and sometimes that makes me very sad.

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    Re: need help understanding interview question

    Quote Originally Posted by Dason View Post
    Is it supposed to be that if you get a 11 or higher on any of the rolls then you win, if not then you lose? If so then for certain values of X and Y there could be some fair games for certain values of n...
    Yes 11 or higher you win, otherwise you lose. and the question was phrased as "so many many rolls do you think would make it a fair game"

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    Re: need help understanding interview question

    I think you misunderstood my question. I was trying to figure out what the original question could mean. I was conjecturing that it might be saying that instead of just doing a single roll to attempt to achieve the success condition you get multiple rolls?

    For example maybe you get 3 rolls to try to get 11 or greater and if you get 11 or greater on ANY of those rolls then you win, otherwise you lose. Not that you play the game 3 separate times and each time you either win or lose.

    If it's that first case I mentioned then there might be a solution. If it's the second case then there isn't a solution unless X and Y are chosen properly.
    I don't have emotions and sometimes that makes me very sad.

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    Re: need help understanding interview question

    Dear r4qx and Dason, I try to illustrate in a simple manner
    $X is winning gain of person A, and $Y is lose of A associated with same trial or throw, if a pair of die rolled the sum of upper faces is greater or equal 11 and less than 11 respectively.
    His expected win in single roll of two dies is=3/36*$X
    His expected lose in single roll of two dies is=-33/36*$Y
    BGM Says it will be fair game if his overall expected gain is zero i.e 3/36*X-11/12*Y=0
    and X=11Y
    actually this is misleading and interpretation of the above equation is just as, if Person A likely to win $X it is obvious he has chance to lose 11 times of $Y (it is because probability of winning is very low) where $X and $y should be predefined before game or throw.

    and my be leaves above equation does not provide any information regarding the original question.
    Last edited by Azeem; 06-25-2013 at 03:59 AM.

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    Re: need help understanding interview question


    The term "fair game" has its special meaning in a probability context. I cannot quote any explicit, strict definition for it, but you can find many examples when you search Martingale on the web. So in #5 I just state the conditions for the game to be a fair game and I must admit that I have no idea/direction to answer the question itself as I am also confused.

    Of course everyone may have his own interpretation/definition for the term, so I am not going to argue for that. Maybe the question is just want you to answer like "you need at least 12 rolls (smallest positive multiple of 12) such that the current balance will be 0" (it is my best guess responding the question); I do not know. Probably I will require a clarification and share my view to the one who ask me the question.

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