Bankroll Management
Most of the money you win in each pot comes from luck, very little
comes skill. The great players literally "shave" big bets
off for themselves. However, this is not a bad thing, poker players
win/lose money at almost perfect rates. If money were won/lost any
faster the fish would notice their stacks dwindle a lot more and
they could not as easily attribute their losses to some trivial
factor like "bad beats". To be able to withstand any amount
of bad luck you must have a proper bankroll. Even the best players
can easiliy go on 200 big bet downswings, so prepare yourself. Using
mathematics it was found that 300 big bets for a full ring game
could withstand almost any bad streak. Since shorthanded has higher
variance the bankroll requirement goes up to 500 big bets. These
numbers are not opinions or arbitrary but rather calculated to give
you no real chance to bust.
Earnings as you gain skill is exponential, the $2/4 players aren't
twice as good as the $1/2 players but you can earn twice as much.
This is why it is so important to get to the higher limits. The
following example illustrates the need for players to push themselves
to higher limits and then be able to fall down to lower limits if
things don't go well. It turns out that the absolute worst way to
use your bankroll in the example would be to have 300 bb of 1 limit
only, the way most players interpret the rule! If you are on a very
limited bankroll and would like me to calculate how you should optimally
use it send me your exact winrate at 3 consecutive limits you play
on playing at and your bankroll email me
here.
a, b, and c are the # of big bets our player will have at each
level: a is $.5/1, b is $1/2, c is $2/4. We want this value to be
300 since that is the safe bankroll. Now I will calculate the optimal
bankroll usage assuming that our player has a winrate of 5bb/100
at $.5/1, 3bb/100 at $1/2, and 2.5bb/100 at $2/4. These winrates
seem reasonable, and altering them would still illustrate my point.
Lets also assume our player has a bankroll of $600, how much of
his bankroll should he set aside for each level? The first two lines
of the equation come from needing to have 300 big bets with a $600
bankroll. The third finds the expected value, x. If our player plays
"a" number of hands at .5/1$ and wins 5bb/100 hands there
he has an expected value of: a*1*5/100 or... 0.05a. The same is
done for each limit and is added up to find our player's total expected
value, x.
a + b + c = 300
a + 2b + 4c = 600
0.05a + 0.06b + 0.1c = x
Using rowreduction 
1 
1 
1 
300 
1 
2 
4 
600 
0.05 
0.06 
0.1 
x 
~ 
1 
1 
1 
300 
0 
1 
3 
300 
0 
0.01 
0.05 
x  15 
~ 
1 
1 
1 
300 
0 
1 
3 
300 
0 
0 
0.02 
x  18 
~ 
1 
1 
0 
1200  50x 
0 
1 
0 
3000  150x 
0 
0 
1 
900 + 50x 
~ 
1 
0 
0 
1800 + 100x 
0 
1 
0 
3000  150x 
0 
0 
1 
900 + 50x 
Since it would not make sense to have negative big bets a, b, and
c all have to >= 0
so solving the equations we get:
x >= 18
x <= 20
x >= 18 , respectively:
20 >= x >= 18
now solve for a, b, and c for our greatest possible value of x,
20.
a = 1800 + 100(20) = 200
b = 3000  150(20) = 0
c = 900 + 50(20) = 100
That means it would be optimal for our player to play $2/4 until
his bankroll is down to $200 and then play $.5/1.
now solve for a, b, and c for our least possible value of x, 18.
a = 1800 + 100(18) = 0
b = 3000  150(18) = 300
c = 900 + 50(18) = 0
That means it would be least optimal for our player to play $1/2
with his 300bb bankroll.
