Bankroll Requirements

A while back, I mentioned an upcoming post on bankroll requirements. Since I haven't written in a while, it seems as good a place as any to start, especially since I have existing material to work with.

First of all, what is the purpose of a bankroll? At its most basic level, the purpose of a bankroll is to help you survive the short-term fluctuations inherent in poker or any other game of chance. I have already written about how big some of these fluctuations can be in the short term, and your bankroll needs to be sized to absorb these types of blows.

Problem is, there is no bankroll big enough to protect you with 100% certainty. Even if you started out with $1,000,000, played $1/$2 limit, and played a winning poker game, there is a non-zero chance that you will go bust. That chance is very, very small for the numbers I picked, but non-zero. This risk is called your Risk of Ruin (RoR). In general, you want your Risk of Ruin to be as small as possible without having to have a hugely oversized bankroll to do so.

Luckily, the formula for an appropriate bankroll size has been derived quite some time ago by Mason Malmuth, and it depends on 3 parameters:

• your Winrate (WR)
• your Standard Deviation (SD)
• your desired Risk of Ruin (RoR)

In other words, you take how well you play (WR), how "steady" that winrate is (SD), and your own personal risk tolerance for losing all your money (RoR) and the bankroll needed (BR) can be calculated from:

BR = -ln(RoR)*(SD^2)/(2*WR)

Looks somewhat complicated, but nothing that a calculator or Excel can't handle. Poker Tracker (or equivalent) can give you both WR and SD. Your RoR is a personal decision, or you can just plug different numbers in to see what your bankroll requirements would be. Cue the below table, which was done at a SD of 16 BB/100):

For example, if you are a 1 BB/100 player and desire a 5% RoR, you will need 383 BB. If you play with a BR of any less than that and your RoR exceeds 5%.

A few things about this table:

• As you become a better player (increase your winrate) your bankroll requirements go down - this is common sense. This relationship turns out to be linear - if you become twice as good a player (e.g. 1 BB/100 to 2 BB/100), you need half the bankroll (383 BB to 192 BB) for a given RoR.
• If you wish to decrease your risk of ruin, your bankroll requirements go up - this is also common sense. The "surprise" is that a slight increase in your bankroll reduces your Risk of Ruin substantially. For example, take the 1 BB/100 column. To decrease your RoR by a factor of 5 (from 5% to 1%) your only need to increase your bankroll by 54% (from 383 to 589). In fact, to go from 20% RoR to 0.1% RoR (a factor of 200!) you only need to increase your bankroll by a factor of 4.

As a sidenote, you may have heard the "300 BB bankroll" metric tossed around, including in one of my previous posts. You can see (about) where that comes from - a person with (about) a 2 BB/100 winrate, desiring a RoR of (about) 1%.

Your personal risk tolarance may vary, and may also vary depending on whether your bankroll is a few hundred dollars (and thus replaceable) vs. a few thousand (and thus more painful to lose). I know personally my risk tolerance will go down as my bankroll grows for thsi very reason, so my desired bankroll size (in BB) will likely go UP as I increase in levels.

As one more example, I'd like to use my brother's (QuadMan) actual numbers over his first 11,000 hands or so. He has been playing some incredible poker, and is sitting at 3.21 BB/100 for these hands. Very nice, but more incredible to me is his (lack of) variance: only 12.11 BB/100. Here's what that looks like:

He had one single 125 BB downswing at the beginning, but has had no downswing greater than about 35 BB since. Amazing - I need to ask what his hourly rate is for lessons......

Anyways, if you plug his numbers into the above formula, you get some crazy numbers:

• for a 1-in-1000 chance of going broke (0.1%), he only needs 158 BB
• for his actual bankroll (estimated at 800 BB at the level we are playing), his RoR is 0.00000000000006%

I am envious.

In other random news, I received my Poker Rewards hat and golf shirt for winning their freeroll a while back. I'm sure I will wear these to the next home game and get a lot more respect. :-)

Next blog update will probably be a bankroll update after I finish clearing both my Poker Rewards reload bonus and my River Belle signup bonus. Unless something better comes along in terms of reloads, my next step may be to Paradise where the signup bonus is not that great, but with the PSO points I can get through pokersourceonline.com and the Refer-a-Friend bonuses it may be worth my while.