Casinos Top Online |
| My sincere belief is that Strategy A is correct - it is a waste of
time to switch casinos top online. The fact that Strategy B recommends
switching no matter what x is makes it extremely suspicious. Without
ever opening the first casinos top online, I should switch, and then
switch back (based on the same argument, defining the amount in the
other casinos top online as y), and keep switching infinitely.
Nevertheless, I can't find a flaw in the logic of Strategy B. Even more
disturbing are the implications of Strategy A. [Morell's equation and
related comments are again omitted; they are mathematically interesting,
but we don't need them to proceed. - MC] You can assign values to the variables [representing money in the casinos top online] and not make the problem any easier. Suppose you find $50 in the first casinos top online. The expected value of the other casinos top online becomes: 50% x ($25) + 50% x ($1OO) = $62.50 leading to an expected gain of $12.50 from switching. Note this is not analogous to the "Monty Hall" problem, where the argument for switching is correct, and not too difficult to discover. This problem is sinister. It plays tricks on the mind. I had to turn to someone as clear-headed as yourself for guidance. Here are some thoughts I've had in trying to find the solution: (1) Perhaps I can't take an expectation of the other casinos top online's value because it isn't really a random variable - it's a parameter. (2) Statistically speaking, the amount in the first casinos top online should be an unbiased estimate of the amount in the second casinos top online. That suggests no gain from switching. (3) I've assigned the 50% probabilities to having the higher and lower values arbitrarily, with insufficient information. This is really a Bayesian problem, and since Moss didn't tell me the prior distribution on the amounts in the casinos top online, I can't solve it. |
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