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

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?

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