GlemZurg
10-01-2004, 12:43 AM
I'm working through the bankroll equations from Gambling Theory and Other Topics p.44-48.
Can someone confirm (or deny) that I'm using them correctly?
From Pocker Tracker I have the standard deviation and win rate (both in big bets per 100 hands).
sd=56
wr=13
The number of hours to assure a win equation (p.44) is
n = (3 x sd / wr)^2
and to "assure" a 95% chance of a win using 1.64 standard deviations (p.48) is
n = (1.64 x sd / wr)^2
In the case of Poker Tracker we're using "per 100 hands" instead of "per hour" so to assure a win I need to play
n = (3 x sd / wr)^2
n = (3 x 56 / 13 )^2
n = (12.9)^2
n = 167 units of 100 hands
n = 16,700 hands
To have a 95% certainty of win I need to play
n = (1.64 x sd / wr)^2
n = (1.64 x 56 / 13 )^2
n = (7.1)^2
n = 49.9 units of 100 hands
n = 4990 hands
For the bankroll calculations to assure that I wont go broke the equation is:
bankroll = wr x n - 3 x sd x (n)^0.5
n = (3 x sd / 2 x wr)^2
and for a 95% certainty of not going broke (again using 1.64 standard deviations)
bankroll = wr x n - 1.64 x sd x (n)^0.5
n = (1.64 x sd / 2 x wr)^2
So to assure I don't go broke I need a bankroll of
n = (3 x sd / 2 x wr)^2
n = (3 x 56 / 2 x 13)^2
n = (168 / 26)^2
n = (6.5)^2
n = 41.8
bankroll = wr x n - 3 x sd x (n)^0.5
bankroll = 13 x 41.8 - 3 x 56 x (41.8)^0.5
bankroll = 543.4 - 3 x 56 x 6.5
bankroll = 543.4 - 1092
bankroll = -548.6 units of big bets (twice size of big blind)
bankroll = -1097.2 big blinds
Since I play in a 0.1 big blind NL game, to assure I don't go broke I need
bankroll = $109.72
To give me a 95% chance of not going broke, I need a bankroll of:
n = (1.64 x sd / 2 x wr)^2
n = (1.64 x 56 / 2 x 13)^2
n = (91.8 / 26)^2
n = (3.5)^2
n = 12.5
bankroll = wr x n - 1.64 x sd x (n)^0.5
bankroll = 13 x 12.5 - 1.64 x 56 x (12.5)^0.5
bankroll = 162.5 - 1.64 x 56 x 3.5
bankroll = 162.5 - 321.4
bankroll = 158.9 units of big bets (twice size of big blind)
bankroll = 317.8 big blinds
Since I play in a 0.1 big blind NL game, for a 95% certainty I don't go broke I need
bankroll = $31.78
Does that all sound right?
Any help with these calculations appreciated.
Thanks,
Justin
Can someone confirm (or deny) that I'm using them correctly?
From Pocker Tracker I have the standard deviation and win rate (both in big bets per 100 hands).
sd=56
wr=13
The number of hours to assure a win equation (p.44) is
n = (3 x sd / wr)^2
and to "assure" a 95% chance of a win using 1.64 standard deviations (p.48) is
n = (1.64 x sd / wr)^2
In the case of Poker Tracker we're using "per 100 hands" instead of "per hour" so to assure a win I need to play
n = (3 x sd / wr)^2
n = (3 x 56 / 13 )^2
n = (12.9)^2
n = 167 units of 100 hands
n = 16,700 hands
To have a 95% certainty of win I need to play
n = (1.64 x sd / wr)^2
n = (1.64 x 56 / 13 )^2
n = (7.1)^2
n = 49.9 units of 100 hands
n = 4990 hands
For the bankroll calculations to assure that I wont go broke the equation is:
bankroll = wr x n - 3 x sd x (n)^0.5
n = (3 x sd / 2 x wr)^2
and for a 95% certainty of not going broke (again using 1.64 standard deviations)
bankroll = wr x n - 1.64 x sd x (n)^0.5
n = (1.64 x sd / 2 x wr)^2
So to assure I don't go broke I need a bankroll of
n = (3 x sd / 2 x wr)^2
n = (3 x 56 / 2 x 13)^2
n = (168 / 26)^2
n = (6.5)^2
n = 41.8
bankroll = wr x n - 3 x sd x (n)^0.5
bankroll = 13 x 41.8 - 3 x 56 x (41.8)^0.5
bankroll = 543.4 - 3 x 56 x 6.5
bankroll = 543.4 - 1092
bankroll = -548.6 units of big bets (twice size of big blind)
bankroll = -1097.2 big blinds
Since I play in a 0.1 big blind NL game, to assure I don't go broke I need
bankroll = $109.72
To give me a 95% chance of not going broke, I need a bankroll of:
n = (1.64 x sd / 2 x wr)^2
n = (1.64 x 56 / 2 x 13)^2
n = (91.8 / 26)^2
n = (3.5)^2
n = 12.5
bankroll = wr x n - 1.64 x sd x (n)^0.5
bankroll = 13 x 12.5 - 1.64 x 56 x (12.5)^0.5
bankroll = 162.5 - 1.64 x 56 x 3.5
bankroll = 162.5 - 321.4
bankroll = 158.9 units of big bets (twice size of big blind)
bankroll = 317.8 big blinds
Since I play in a 0.1 big blind NL game, for a 95% certainty I don't go broke I need
bankroll = $31.78
Does that all sound right?
Any help with these calculations appreciated.
Thanks,
Justin