
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.

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