Gilles I fully agree with you. Your analysis is great.

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In a message dated 99-05-20 04:06:41 EDT, you write:
<< If you don't know the maximum value M, there is actually no rational for
switching. >>
I agree. Unless the maximum value of M is known there is no rational for
switching. If M is selected at random from the set of natural numbers, then
it is likely to be huge, in fact infinite.
A way to go around this problem is to limit M by selecting our test value m
from a ring say (A,B,C) with the property A>B, B>C, C>A ( as in the children
game of paper, stone [or hammer] and scissors.) Consider two boxes X and Y
each holding a random value in (A,B,C). After having selected box X and found
the value m inside, there is no way to know if box Y contains a better value.
Going back to the infinite set and refocussing on the MW topic the question
is how does this problem relates to the SSI thread?