Guesses and Bets

For some reason, you must enter an even wager for $1 — win or lose — on one of two outcomes, but there’s a twist: Instead of a fifty-fifty choice like a coin toss, or picking 1-3 or 4-6, this one is pretty easy.  Using a fair die (not crooked or “funny” in any way), you can bet that it will show 1,2,3, or 4 on the one hand, or you can bet that it will show 5 or 6 on the other.  Those are your choices — 1-4, or 5-6.  You know that if you had to do this a hundred times, you would come out money ahead by standing on 1-4, as this will win two times of three.

However, you only have one swing at this.  Probably you will still choose 1-4.  If you disagree, please let me know why.  Assuming that you choose 1-4, there are only two outcomes.  Obviously if you win with 1-4, you have chosen correctly.  However, if you lose, because in your only throw, the die came up 5-6 — were you wrong?

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23 Responses to Guesses and Bets

    • AdministratorAdministrator says:

      That is the most helpful, least sought feedback a writer can get :-)

      • MLHMLH says:

        It’s early here in AZ.

        • AdministratorAdministrator says:

          I am reminded of a quote I took to heart in my youth — “A joke that needs explaining needs burning”. That is, it’s not the listener’s fault if he doesn;t get a joke. BURDEN ON THE TELLER of the joke to judge the audience and adjust accordingly. Part of being clever is being clever about being clever.
          Likewise, advice I have tried to honor is that if your writing is unclear (unintentionally), then you should re-write it. So I have expanded the first paragraph.
          Thank you both for the feedback!

  1. BrentB67BrentB67 says:

    Question 1: How can a die with 2 possible outcomes where the likelihood of the outcomes are 1/3 and 2/3 be a ‘fair’ die?

    • AdministratorAdministrator says:

      What I intend here is to specify that the die is fair, and offer two options — you can cover 1-4, or 5-6. The die itself is fair — it’s the wager that is unrealistic.

  2. BrentB67BrentB67 says:

    If you only have the capital for a single wager, you are not wrong to bet on the outcome with the 2/3 likelihood of winning, however with only one opportunity this still becomes a binary outcome. A single wager and you are either still in the game with $2 on a positive outcome or out of the game all together.

    The question becomes vastly more interesting with 3 $1 bills to wager and then allocating capital, managing, and so forth to stay in the game.

  3. AdministratorAdministrator says:

    SO back to the question. You bet on 1-4, but it came up (say) 5. Were you wrong?

  4. RightAnglesRightAngles says:

    What is this, the Mensa test?

  5. NandaNanda says:

    I don’t gamble and I’m math-phobic, but I agree w/M; you didn’t win, no rectitude/wreckeditdude at play here. (-:

  6. AdministratorAdministrator says:

    EThompson? Your answer?

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