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Tournament Prize Money Conundrum

Posted By: Rick Janowski
Date: Saturday, 15 October 2016, at 8:06 p.m.

Tournament Prize Money Conundrum

Paul Lamford gave me an interesting theoretical probability puzzle which I would like to share.

At a tournament there are two prizes for winner and runner-up. The specific amounts are unknown by the players and sealed in two separate unmarked envelopes. There are two joint winners of the tournament. After drawing lots, one player is asked to pick one of the two envelopes. He opens the envelope which contains £2000. He is told that it is not known whether this is the intended prize for the winner or the runner-up and that runner-up prize is 50% of the winner’s prize. So the other envelope will contain either £1000 or £4000. The player is then given the option of sticking with his original choice or switching to the other envelope. Making some insurance/hedging deal with his opponent or others is not allowed. What should he do: stick or switch, and for what reason?

Messages In This Thread

• Tournament Prize Money Conundrum
  Rick Janowski -- Saturday, 15 October 2016, at 8:06 p.m.
  • Tournament Prize Money Conundrum
    KenB -- Saturday, 15 October 2016, at 8:30 p.m.
  • Tournament Prize Money Conundrum
    Tom Keith -- Saturday, 15 October 2016, at 8:46 p.m.
  • The Backgammon Solution *SPOILER ALERT*
    Fender -- Saturday, 15 October 2016, at 8:58 p.m.
    • The Backgammon Solution *SPOILER ALERT*
      Bob Koca -- Sunday, 16 October 2016, at 4:25 a.m.
      • The Backgammon Solution
        Rick Janowski -- Sunday, 16 October 2016, at 7:18 a.m.
        • The Backgammon Solution
          Casper Van der Tak -- Sunday, 16 October 2016, at 9:21 a.m.
          • The Backgammon Solution
            Rick Janowski -- Sunday, 16 October 2016, at 9:45 a.m.
            • The Backgammon Solution
              Casper Van der Tak -- Sunday, 16 October 2016, at 10:27 a.m.
              • The Backgammon Solution
                Casper Van der Tak -- Sunday, 16 October 2016, at 11:18 a.m.
                • The Backgammon Solution
                  Rick Janowski -- Sunday, 16 October 2016, at 11:40 a.m.
                  • The Backgammon Solution
                    Casper Van der Tak -- Sunday, 16 October 2016, at 12:15 p.m.
        • The Backgammon Solution
          Bob Koca -- Sunday, 16 October 2016, at 3:32 p.m.
          • The Backgammon Solution
            Rick Janowski -- Sunday, 16 October 2016, at 5:43 p.m.
            • The Backgammon Solution
              Casper Van der Tak -- Sunday, 16 October 2016, at 6:10 p.m.
              • The Backgammon Solution
                Rick Janowski -- Sunday, 16 October 2016, at 6:41 p.m.
            • The Backgammon Solution
              Timothy Chow -- Sunday, 16 October 2016, at 6:41 p.m.
              • The Backgammon Solution
                Rick Janowski -- Sunday, 16 October 2016, at 8:11 p.m.
                • The Backgammon Solution
                  Timothy Chow -- Sunday, 16 October 2016, at 10:01 p.m.
                • Another worked example
                  Timothy Chow -- Sunday, 16 October 2016, at 10:48 p.m.
                  • Another worked example
                    Bob Koca -- Sunday, 16 October 2016, at 11:42 p.m.
            • The Backgammon Solution
              Bob Koca -- Sunday, 16 October 2016, at 7:15 p.m.
              • The Backgammon Solution
                Rick Janowski -- Sunday, 16 October 2016, at 7:57 p.m.
                • The Backgammon Solution
                  Casper Van der Tak -- Monday, 17 October 2016, at 7:03 a.m.
  • Tournament Prize Money Conundrum
    Timothy Chow -- Saturday, 15 October 2016, at 9:09 p.m.
    • Tournament Prize Money Conundrum
      Rick Janowski -- Saturday, 15 October 2016, at 10:32 p.m.
      • Tournament Prize Money Conundrum
        Chuck Bower -- Sunday, 16 October 2016, at 12:52 a.m.
        • Tournament Prize Money Conundrum
          Rick Janowski -- Sunday, 16 October 2016, at 1:22 a.m.
      • Tournament Prize Money Conundrum
        Timothy Chow -- Sunday, 16 October 2016, at 5:07 p.m.
        • Tournament Prize Money Conundrum
          Rick Janowski -- Sunday, 16 October 2016, at 6:24 p.m.
    • Equity calculation question?
      Rick Janowski -- Sunday, 16 October 2016, at 9:30 a.m.
  • Tournament Prize Money Conundrum
    Casper Van der Tak -- Saturday, 15 October 2016, at 9:39 p.m.
  • Tournament Prize Money Conundrum
    Dmitriy Obukhov -- Monday, 17 October 2016, at 6:15 p.m.
  • Tournament Prize Money Conundrum
    Stein Kulseth -- Tuesday, 18 October 2016, at 8:45 p.m.