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The Backgammon Solution
Posted By: Timothy Chow
Date: Sunday, 16 October 2016, at 10:01 p.m.
In Response To: The Backgammon Solution (Rick Janowski)
I'm not sure I fully understand your hypothetical, but if you're asking whether it can make a difference whether it's $2000 or £2000, then the answer is yes, it can make a difference.
As for an example, I already gave an example, where the way the prize money is determined tells you that you need to employ a different strategy depending on whether Q is less than or greater than 7000.
It seems that you're still under the illusion that the problem specification provides enough information to derive a mathematically correct answer. It doesn't. Some information about the prior probability of the prize money being £2000 is needed before any kind of calculation can be done. Depending on what that prior probability is, the decision about whether to switch will depend on the precise amount that you observe in the envelope.

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