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Math Help - Expected value and decimal odds

  1. #1
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    Expected value and decimal odds

    Hi guys

    In a game of chance where the player knows the expected value (say -0.37), how do you work out what the decimal odds should be in order to break even in long run?

    (Decimal odds 2.0 = 1/1)

    Any help much appreciated

    Mike
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  2. #2
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    Hello, Mike!

    If I understand your question, there is no unique answer.


    In a game of chance where the player knows the expected value (say -0.37),
    how do you work out what the odds should be in order to break even in long run?

    Without knowing the rules of the game,
    . . the expected value is insufficient information.


    Game 1

    You flip a coin.
    . . If you get Heads, you win $0.63
    . . If you get Tails, you lose $1.00
    The expected value is -$0.37.

    I'm not sure how to "work out the odds"
    . . since the nature of a coin flip cannot be changed.
    We can, however, change the payoffs (and bet "even money").


    Game 2

    You roll a die.
    . . If you get a "1", you win $0.78.
    . . Otherwise, you lose $0.60.
    The expected value is -$0.37.


    Game 3

    You randomly select a card from a full deck.
    . . If it is an Ace, you win $1.19.
    . . Otherwise, you lose $0.50.
    The expected value is -$0.37.


    Get it?

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