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Feb
4
revised What is the difference in chance, based on foreknowledge of the resolution?
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Feb
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revised What is the difference in chance, based on foreknowledge of the resolution?
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Feb
4
revised What is the difference in chance, based on foreknowledge of the resolution?
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Feb
2
comment What is the difference in chance, based on foreknowledge of the resolution?
@alancalvitti: We do not disagree. But the player who does not know will perforce calculate the odds as 4/52. With respect to the omnicient player all probabilities are 0 or 1.
Feb
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revised What is the difference in chance, based on foreknowledge of the resolution?
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Feb
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revised What is the difference in chance, based on foreknowledge of the resolution?
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Feb
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revised What is the difference in chance, based on foreknowledge of the resolution?
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Feb
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revised What is the difference in chance, based on foreknowledge of the resolution?
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Feb
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revised What is the difference in chance, based on foreknowledge of the resolution?
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Feb
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revised What is the difference in chance, based on foreknowledge of the resolution?
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Feb
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revised What is the difference in chance, based on foreknowledge of the resolution?
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Feb
2
answered What is the difference in chance, based on foreknowledge of the resolution?
Feb
1
comment Sequence of squares $\pi(x^2)$
I think your answer is helpful for looking at the problem. Before posting I found 14 2-strings less than 300,000. So for small numbers there isn't much.
Feb
1
comment Sequence of squares $\pi(x^2)$
This is helpful if we know there is a longest string and we expect to find it in a short finite search. What if the one given is the longest? Or what if there are arbitrarily long strings if we go "far enough" out?
Jan
30
asked Sequence of squares $\pi(x^2)$
Jan
26
comment $x \sim y \implies \log x \sim \log y$?
Appreciate the counter-example.
Jan
26
comment $x \sim y \implies \log x \sim \log y$?
I like the economy of this and noting of tacit assumptions.
Jan
25
accepted $x \sim y \implies \pi(x) \sim \pi(y) $ and repeated applications of PNT
Jan
25
comment $x \sim y \implies \pi(x) \sim \pi(y) $ and repeated applications of PNT
I think the point is much stronger now. I think error for $\pi(x)$ is $O(x/(\log x)^2))$ so it may be possible to prove/disprove.+1
Jan
25
comment $x \sim y \implies \pi(x) \sim \pi(y) $ and repeated applications of PNT
Yes I think I agree with your last statement. I'm definitely not making the claim! I think yours is a good example of why the claim is suspicious.