Anyone have data on potential variance in the bankroll?

I'm currently playing some small stakes hold'em ($1/$2) and have a bankroll of $600(2xbb). Does that sound about right? Does anyone know how to explain to me the possibility of going bankrupt assuming I'm winning 1xbb/100 hands? Thanks in advance!

Do a search for "risk of ruin"

I think that's enough if you're beating the game, but if you take a 100bb hit or so you may want to go do some bonus whoring and build it back up. Hell if you are at $600 you should be doing that stuff anyways!

Good luck.

If you're winning 1.0BB/100H (over a decent sample size, of course), then 300 BB should be fine.

[Brom]

With a winrate of 1.0 bb/100, standard deviation of 15 bb/100, and a 95% confidence interval, it will take 86000 hands to determine your results within +/- 1.0 bb/100. In other words with those numbers, it would take 86k hands just to know if you are even a winner in the game for sure.

With those same numbers you should also have a bankroll of about 500 big bets to cover all downswings that will occur during those 86k hands.

[Chobohoya]

[ QUOTE ]
With a winrate of 1.0 bb/100, standard deviation of 15 bb/100, and a 95% confidence interval, it will take 86000 hands to determine your results within +/- 1.0 bb/100. In other words with those numbers, it would take 86k hands just to know if you are even a winner in the game for sure.

[/ QUOTE ]

Except there's a large chance you wouldn't be sure of it. 50% of the time you're going to have an observed winrate of less than 1BB/100, and you're going to be pulling your hair out because of the swings. Not only that, but you're going to be "overrolled" for your stakes, and when you try to move up, you're going to lose money and confidence.

[ QUOTE ]
With those same numbers you should also have a bankroll of about 500 big bets to cover all downswings that will occur during those 86k hands.

[/ QUOTE ]

Except that you're going to end up with 800-1800 BB for your limit and feel like you "should" move up.

[pzhon]

[ QUOTE ]
If you're winning 1.0BB/100H (over a decent sample size, of course), then 300 BB should be fine.

[/ QUOTE ]
What makes you say that?

The standard 300 BB mantra so many people repeat without understanding assumes that you have a higher win rate than 1 BB/100. If you win only 1 BB/100, you should have 450-900 BB for the level of security that many people mean by 300 BB.

[pzhon]

From an old BruceZ post:

<ul type="square">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[/list]You want to use the second formula. You SD is probably about 15 BB/100.

r = exp(-2*1*300/(15^2)) ~.0695 ~ 7%.