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An unfair coin is tossed giving heads with probability $p$ and tails with probability $1-p$. How many tosses do we have to perform if we want to find $p$ with a desired accuracy?

There is an obvious bound of $N$ tosses for $\lfloor \log_{10}{N} \rfloor$ digits of $p$; is there a better bound?

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    Can you explain the obvious bound? I'm curious.2011-04-13
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    @GWu: $\lfloor\log_{10}{N}\rfloor$ is how many decimal digits number $1/N$ has. It is also how much a $N$th toss will influence your knowledge of $p$.2011-04-13

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