In calculating probabilities for Roulette, my text book asks me to calculate the probability of winning after 1,000 bets.
Where spending \$1 has a $\frac{1}{38}$ probability of winning \$35 and a $\frac{37}{38}$ probability of loosing \$1.
The answer uses the formula
$P(S>0)=P(S>0.5)$ $\approx$ 1-$\phi$ $(\frac{.5+0.526 n}{\sqrt(33.21 n)} ) $
I understand from this question that the mean works out to be -0.0596 and the variance is 33.21
Why is S>0.5 the same as S>0?
Where does the 0.5 come from?
Why is 0.5 added to the mean?