From Gambling Theory and Other Topics

pg 33

(1) E = W * N/100

W - Winrate (BB/100h)
N - Hands
E - Expected Win (BB)

Now 99.7% of results are within 3 standard deviations from the mean. So we
can calculate a worst/best case result.

So your results will be within:

W-3*S < R < W+3*S

W - Winrate (BB/100h)
S - Standard Deviation (BB/100h)
R - Results (BB/100h)

These are the worst/base case possibilities


pg 45

The number of hands to assure a profit is:

W*N - 3*S*sqrt(N) = 0

W - Winrate (BB/100h)
S - Standard Deviation (BB/100h)
N - 100's of hands to assure a profit.

Solving for N:

N = (3*S/W)^2

Smallest bankroll so we don't go broke.

B = ((3*S)/(2*W))^2

W - Winrate (BB/100h)
S - Standard Deviation (BB/100h)
B - Smallest bankroll needed to not go broke