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Math Help - bookies odds vs real odds

  1. #1
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    bookies odds vs real odds

    QUESTION 1

    I have a brother who plays the irish lottery every week , he picks 3 numbers and if he matches
    them in the 6 drawn he wins 600 . so the bookies odds are 600 to 1 to match 3 numbers.
    have i calculated the real odds correctly?

    total numbers in draw = 47
    numbers drawn per draw = 6
    my brother picks 3 numbers only for a 1

    47*46*45 / 1*2*3 = 16215 . total number of 3 number combinations out of 47 numbers
    6*5*4 / 1*2*3 = 20 . total number of 3 number combinations from 6 numbers drawn
    16215/20 = 810 , so are the real odds are 810 to 1 ?

    not sure if my workings are correct

    QUESTION 2
    expected value for this game

    bookies odds 600 to 1
    real odds 810 to 1

    210 / 810 = -0.25
    so on average my brother loses 25 pence every time he plays?
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  2. #2
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    There must be sense in your reasoning, because your numbers are coming out right (but why round down to 810? And strictly the bookies' odds for a probability of, e.g., 1/810 would be 809 to 1).

    But if you can't explain your own reasoning, you may find it easier to ask: how many ways can the draw of six numbers include your brother's three?

    And that's out of how many possibilities for the draw of six?

    Get the probability and multiply it by 600 for the expected value of a ticket.

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  3. #3
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    so tom your saying my calculations for the real odds are almost correct 809 to 1
    but my calculations for the expected value of this game is wrong , i guess i'l look in to it more
    tx for your help
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  4. #4
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    No I'm saying your probability is exactly right if you leave it at precisely 1/810.75 or better still 4/3243, which the bookie should be using to offer odds of 3239 to 4. Just that I thought my explanation of the fraction (number of winning ways as a fraction of the total number of ways) was more intuitive than yours, which I'm still trying to bend my brain around. (That might be my brain's fault.)
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  5. #5
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    so tom my calculation for expected value is right , not totally right , but about right , if its around - 25 pence or - 27 pence or - 29 pence
    im ok with that , as long as im about right, thats good for me
    im in the ball park!! im happy , im not trying to split the atom , just want to know that im about right
    just wanted to know the formula to calculate these type of questions .
    these type of questions have been playing on my mind for years
    time to move on to new problems
    tx friend
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  6. #6
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    Yeah, ok, but as long as you mean the expected value is about 25p LESS than the ticket price - which I think you do, or did earlier.
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  7. #7
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    yes tom i did mean that .
    so what answer did you get for the expected value for the game my brother plays
    question . would you play it?
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  8. #8
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    4/3243 * 600 pounds = approx 74 pence.

    Is it really your brother, then? I took it for a made-up question.

    I've hardly ever played, myself. Sometimes I join the queue for my sister's ticket. It doesn't seem like a happy crowd.
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  9. #9
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    lol yes your right it doesnt seem happy
    but would you play with a stop point
    i meen your total win is 600
    would you play up to say 550 and if you dont win by then ...stop playing for ever
    you might get lucky and beat em
    Last edited by jickjoker; February 18th 2011 at 04:45 PM.
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  10. #10
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    I suppose my stop point was about 2. Maybe you're asking or thinking about stuff like http://en.wikipedia.org/wiki/Martingale_(betting_system) ? Probably best to start a new thread - in the chat room if the question is only vague.
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  11. #11
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    stop point of 2 pounds for you .................thinking..................ok
    im talking with mr math here the math man mr tom
    math is always right , it is the best..........is that what you think to yourself ?..................
    it is not always right tom to many variables in this world my friend
    determinism, fate , destiny ,your destiny , call it what you like
    what im trying to say , its like gamblers falicy
    just because on the roulette table 25 reds have hit in a row , doest meen the chances of black
    are more likely , the roulette table has no memory
    somtimes the math involved do not apply to to certain people , places , times
    i believe some peoples destiny is to win , they are on a path to win..
    determinsm
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