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Figure the Odds

Discussion in 'Anything goes' started by slappy4428, Apr 30, 2010.

  1. Ben_Hecht

    Ben_Hecht Active Member


    I said that . . . but will note that the tax attitude of the Brits and their associated countries
    are lightyears ahead of the Merrikans.
     
  2. The Big Ragu

    The Big Ragu Moderator Staff Member

    You need to do a bit more math to come up with the odds (assuming this was for 40 balls, pick 6 numbers).

    You are correct about the first part of the equation. You have 40 balls. With each ball picked, you decrease the number of balls left by 1. So you do that 6 times (number of numbers you pick), to come up with 40 X 39 X 38 X 36 X 35 X 34. Which gives you 2,763,633,600 to 1. Those would be the odds if you had to pick your numbers in an exact order. But you don't.

    So there is a second half to this. Since the order of the balls doesn't matter, to come up with the odds, you divide that two-and-a-half-billion number by the number of ways the numbers can be arranged (they can be chosen in any order). There are six possibilities for the first ball. If you choose one of the six right with that ball, then there are five for the second, etc. Four for the third, 3, 2, and one left you have to get with the 6th ball. That gives you 6 × 5 × 4 × 3 × 2 × 1 = 720. i.e. 720 different combinations that will give you the winning number -- different orders of the correct numbers coming up.

    To figure the true odds, you take the 2,763,633,600 number you came up with and divide it by those combinations, or by 720.
    2,763,633,600 ÷ 720 = 3,838,380. So your odds of picking six numbers correctly in any order are 3,838,380 to one.

    I won't bog you down with a formula for what the expected payout on those odds should be, but you are getting a small fraction of what you should see, if you defy astronomical odds and pick a 3.8 million to one shot. That kind of vig -- in gambling parlance -- is obscene. You will do better with a local bookie, who will rip you off, but to an extent that is downright charitable compared to the percentage of the winnings you should expect that the state doesn't give to you in the lottery.
     
  3. 93Devil

    93Devil Well-Known Member

    (40/6) x (39/5) x (38/4) x (37/3) x (36/2) x (35/1)

    Right?
     
  4. The Big Ragu

    The Big Ragu Moderator Staff Member

    Exactly.

    Or, I believe: 40! / ((40 -6)! * 6!)
     
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