[punter11235]

PairTheBoard, thank you for your cruciate to educate people here. These are interesting problems and I needed some time to understand them at one point in my life.
I think there is another way to look at these problems. Here it is :
a)2 envelope problems : strategy "switching is best" assumes that number N was chosen equiprobably at random from all integers which is of course nonsense. If we assume that number wasnt chosen at random, we cant assume that there is 50-50 probability that another envelope contains higher amount cause we dont have information about chosing amounts in envelopes. This is why we cant determine proper strategy here.
b)Twins with tony haircut problem : again, to give proper strategy we need to know probability of older twin having tony haircut.
c)Another problem for all nonbelievers: Someone gave us rigged coin, say with probability of 70% to flip head but we dont know this. We take this coin and flip. If we agree with all this people :

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After reading this thread, it is quite clear that your understanding of the term probability is far worse than the people you describe, especially DS.

I'm going to be really disappointed if the answer is shown to be pointless and a huge waste of my time

To PairTheBoard: I read the whole thread, and I've come to the conclusion that you are a moron. Please never again use the word probability, you have no idea what it means.


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We can tell that probability that our flip will be head is 50% which is of course nonsense.

Basic intuition is this : if in any given situation there are outcomes A and B and we say that A have probability of say 40% we should expect that if this situation reoccures many times our distribution will be in fact 40% for A and 60% for B. This is not the case in all abovementioned problems.


By the way I am amazed that so many posters here dont have respect for people who try to educate them and so many of them while lacking basic understading of the subject are sure of being correct.

Best wishes