If you toss a coin 100 times, the mean is 50 heads, and one standard deviation from the mean is the square root of npq, where n = 100, p = 0.5, and q = 0.5.
Thus SD = sqrt25 = 5. Quick way: take half of the square root of 100. Half of 10 is 5.

But stating what the SD of one hand of BJ is has nothing to do with this. It is simply 1.13 times the square root of the number of hands played (assuming flat betting). We aren't considering straying from the mean; rather, we're considering an absolute value.

See BJA, pp. 151-152 for a discussion of why, in this instance, the SD for the 100 coin tosses is sqrt100 = 10, and not 5.

Don