People often ask how much of a bankroll they need to play a certain game. I am currently reading Mason Malmuth's Gambling Theory book and decided to post what I have learned. Here goes...
First thing you need to know is your standard deviation. 10 sessions is the absolute minimum to determine this but 30 is recommended. The easiest way to figure this out is to go to Poker Charts and log your sessions. The website is kind enough to determine SD for you . I tried to enter the actual equations but I had a hard time getting all of the symbols to line up correctly when viewed in this forum. If you are really curious about the equations, buy Mason's book.
There is another point I would like to make before we move on. Here is a quote from MM's book: "The standard deviation is a statistical measure of dispersion, and most statisticians agree that for all practical purposes, the total population of possible results is contained within 3 standard deviations"
Next, you will need your win rate. This can be obtained by keeping accurrate records, or once again, using Poker Charts.
Now, the next equation will give you how long you must play in order to assure a win. Note that I have added some intermediate calculations here since I can't get a damn thing to display correctly on the page.
x = (3)(Standard Deviation)
# of hours = (x/win rate)^2
For example, I just checked my stats on Poker Charts for my 5/10 game. I only have 15 5/10 sessions but that is enough to generate some numbers. My SD is $48.30/hr and my win rate is $6.34/hr. So, in order to ensure a profit, I need to play:
522 hours = ((3*48.30)/6.34)^2
As a side note, here is another quote from Mason's book: "At the middle limits, we discovered that the expert's standard deviation could be as low as six big bets per hour. This was about half that of a typical player, and a bad player could be much higher."
To find the minimum bankroll to ensure not going broke, use the following 2 equations:
SD = Standard Deviation
WR = Win Rate
N = ( (3*SD)/(2*WR) )^2
LL = (WR*N)-(3*SD*N)^(1/2)
As an example, here are my numbers for my 5/10 game:
N = ( (3*48.3)/(2*6.34) )^2 = 130
LL = (6.34*130)-(3*48.3*130)^(1/2)
or $687
Now, this number seems WAY too low to me. The only thing I can figure is that my SD is much lower than typical. This means I am more consistent, but I don't think this is a good thing at this point (or maybe it is). As you can see, I am not even hitting 1 BB/hr after 15 sessions of 5/10. But, 15 sessions doesn't really tell you crap anyway. Also, my total hours for 5/10 are only 62. This is about right as I usually play 4 hour sessions for 5/10.
