The Unfair Wager Problem

Things on this page are fragmentary and immature notes/thoughts of the author. Please read with your own judgement!

$X_i \sim Bernoulli(p)$

\bar{X}_n \dot{\sim} N(p, \frac{p(1-p)}{n})

[\bar{X}\pm C_{\alpha} \sqrt{\frac{p(1-p)}{n}}]

\frac{c_{\alpha}}{\sqrt{n}} \le 0.5\times 10^{-10}

n \ge 10^{20} C_{\alpha}^2