Bankroll formulas with hourly rate and standard deviation
 

After over a year of playing poker online for stakes that were too high for my bankroll, I think I've finally learned my lesson, and I'm trying to play with a proper strategy that will insure that I gradually increase my bankroll and insure that i have virtually no chance of going broke.

I am following Mark Blade's reccomendation of four hundred big bets. I am four-tabling $0.50/1 Limit Hold'em (full table) on PokerStars, and I started with $400. I have forced myself to play absolutely nothing else. I am keeping track of my results with CardPlayer's Poker Analyst, and so far after 76:36 of total playing time, I have made $116.50 for a total of 1.52 BB/hour. I am adding up the time for each individual table I play, so for every one hour of real time, it amounts to approximately four hours of total playing time, so the figure is really 1.52 BB per table per hour. Poker Analyst also tells me that my standard deviation, through 19 sessions of around one hour each (12 wins 7 losses), is 22.62. Here is what I want to know:

1. Does multi-tabling increase my fluctuation/volatility or increase my risk of going broke wiht 400 BB?
2. Is it accurate for me to record four hours of time if I play for one hour at four tables?
3. How many hours and/or sessions do I need to play for my hourly rate and standard deviation to be stable enough to be truthfully reflected by my results?
4. What is a "typical" standard deviation, and if my standard deviation is low enough, can I jump up to $1/2, or whatever the next level is, with fewer big bets in my bankroll? How low would my standard deviation have to be to do this?
5. Once I have acccurate enough figures for hourly rate and standard deviation, how do I then calculate what my bankroll should be? What is the formula?
6. Is there any literature about bankroll strategy and formulas (other than Blade, who I have read) that would be helpful to me?

Whoever has gotten to this point, thank you for reading the entire query and hopefully answering some of my questions.

Re: Bankroll formulas with hourly rate and standard deviation
 

when multi-tabling, use bb/100 not bb/hr. then you can calculate the hrly rate by estimating how many hands/hr.

i estimate each table plays around 60 hands/hr. that'll give you 240 hands/hr four-tabling.

bb/100 * 2.4 = bb/hr, which answers most of your questions.

high stdev isn't a bad thing. more aggressive you play, higher variance you'll have. your goal to move up isn't to lower your variance. your goal is to make money. once you have enough bankroll, you can probably move upto 1/2, given you have played enough hands to determine that you're a winner at .5/1.

there's a post on risk of ruin- which i believe was posted by ed. it's a lot of math but the conclusion: if you're a winning player, starting with 400 bb at a limit will give you the risk of ruin to less than 10 percent. if you move down to the next limit, it'll be less.

you can search the forum for that article. it was a really cool article actually...

Re: Bankroll formulas with hourly rate and standard deviation
 

Before you do anything else, shell out the bucks for PokerTracker. It will do all these calculations for you, including adjusting your WR/hands per hour for multitabling. Well worth the cost and then some.

1) Multi-tabling generally decreases your overall volatility. If you are playing a good tight/aggressive game and not repeatedly making mistakes, you benefit from every hand you play. Therefore, the more hands you play, the more likely it is that you will achieve your "true" win rate; by multitabling, you increase the number of hands you play/hour, which decreases the luck factor as it pertains to you. Of course, this assumes that your own game does not drop off heavily when dividing your attention among several tables.
2) Accurate enough. But like I said, PT will do this for you.
3) It'll never happen. Seriously, the amount of hands needed to give you your "true" win rate/standard deviation is so huge that by the time you pile them all up, your gameplay will have improved and/or the conditions of your games changed enough that it will affect your figures. There's a math formula that you can use to figure approximate numbers once you've played a decent enough sample (tens of thousands of hands at least), but you'll never know your precise, "true" figures.
4) I honestly don't know. I don't pay much attention to standard deviation, which may or may not be a good practice. It would stand to reason that the lower your SD for a particular game, the lower your bankroll requirements would be.
5) Most people go with 300 big bets. I've never attempted to figure out "exactly" how many I need because honestly, I don't think it really matters. A winning player who is disciplined enough to step down/take a break if he hits a huge downswing should be okay with 300, but more never hurts.
6) Most likely, but I couldn't tell you what they are. You might try asking this question on the books/software forum.

In all seriousness, don't sweat the small stuff. You're playing with a healthy bankroll for your limit, and you're winning. It doesn't really matter if you can reduce your risk of ruin from 2% to 1.3% by adding 13 BBs to your bankroll. Instead, focus on improving your game (which will reduce your SD & RoR as well).