BGonline.org Forums

The Backgammon Solution

Posted By: Bob Koca
Date: Sunday, 16 October 2016, at 3:32 p.m.

In Response To: The Backgammon Solution (Rick Janowski)

The breakdown comes that once you see the amount in the envelope the 50% chance of being the larger value is no longer a valid assumption. If you have a postulated prior distribution for example "The smaller value is uniform on (0,10000)" then you could assign a probability after seeing the amount. With that assumption a seen value of 2000 is indeed still equally likely so switch. Suppose instead that the prior distribution is "The smaller value is uniform on (0, 1500)" then a seen value of 2000 must be the larger value so do not switch. Other distribution types other than uniform could also be considered.

When you say "Let's assume it isn't relevant and let's also assume there is no other way to ascertain how much prize money there might be altogether, either fairly or covertly." it seems like you are effectively saying that every value is equally likely but a uniform distribution on (0, infinity) doesn't make sense.

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.