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 win-rate 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 win-rate of 5bb/100 at $.5/1, 3bb/100 at $1/2, and 2.5bb/100 at $2/4. These win-rates 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

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.