Why do we reccommend 300BBs for a limit player, and 15-30 buy ins for a NL player?

Using the BR equation above:

var=SD^2

B = -(sigma^2/2u)ln(r)

r = exp(-2uB/sigma^2)

where u is your hourly rate
sigma is your hourly standard deviation
r is your desired risk of ruin
B is your bankroll
A good winrate for a limit player would be 3BB/100 with a StdDev of about 17BB/100

substituting in to find the risk of ruin
we have

r = exp(-2uB/sigma^2)
= exp[ -2(3)(300)/17^2]
= 0.002

or a risk of ruin of 0.2%


The equation works for NL also.

If we want to determine the bankroll required to achieve the same risk of ruin in NL
Assuming a player with a 10BB/100 winrate and StdDev of 50BB/100

B = -(sigma^2/2u)ln(r)
= -[50^2/2(10)ln(0.002)
= 776BBs

Given that BBs in this example is 2xbig blind, this would equate to 1552 times the big blind, or just over 15 buy ins.


Note how much of an effect your winrate and Standard deviation have on your bankroll requirements.
Increasing your standard deviation, or decreasing your winrate would require your bankroll to be much larger.