Sunday, August 4, 2013

Bankroll Management: Bottom Line

Okay, I've done a ton of research this past week on things like risk of ruin (RoR), variance, swings, standard deviations, risk aversion, expected value, and general bankroll and win rate statistics. I've also run a lot of EV simulations with varying sizes of starting bankrolls. I won't go into any significant detail here, but suffice it to say that I have developed what I believe are some relatively solid recommendations on how to do good/proper bankroll management (BRM). Before I get to my charts, however, a couple of things need to be explained.

First, I believe far too many people think about BRM backwards. They invariably say, "I want to play at $X NL, so what size bankroll do I need?"  What they should be saying is the opposite: "I have $X available in my bankroll, what stakes should I play at?"

Second, players should  ask themselves how risk averse they are, and honestly how good of a player they really are. The more risk averse you are, the bigger the bankroll. Conversely, the better the player, the lower the required bankroll.

Third, poker variance sucks. Even the best player, sitting down with below average villains, runs a risk of significant downswings. Suck outs, bad beats, coolers... you name it, it happens. Big swings happen, and unless your bankroll is sufficiently large enough to handle these swings, you're gonna go broke at some point. Period.

And this brings me to my final point: the primary goal of BRM is to ensure you don't ever have to redeposit in the future*. If redepositing is easy (read: you can readily find the money in your budget) then you can potentially play with a riskier BRM approach. The advantage of doing this means that you can potentially move up to higher stakes sooner, where the rake is lower, more profit awaits, etc. On the other hand, if your bankroll is the sum total of your discretionary money, however, you should probably take the conservative approach.

So, assuming that you're an average, slight-winning player (e.g., ~1 BB/100), here's what I recommend for the three risk aversion categories of conservative player, moderate risk aversion, and risk lover.


And here's the micro- and small-stakes version of the same chart:

Here's how to use the charts. Let's assume you have a $500 bankroll. This is all the money in the world you have to play poker with. Using the bottom chart, we can find $500 midway across along the bottom. Now if we go up from there, we see that for a conservative player, we should be playing no greater than $5NL (i.e., 2/5-cent). This keeps your RoR well down into a very safe zone, where you almost assuredly won't go broke. (Remember, one way to think of BRM is that it's a method of keeping us from ever having to quit poker and/or rob a bank so that we can redeposit.)

Moving further up, we can see that if we're moderately risk averse, we can go up as high as $15NL, and if we're risk-taking individuals, willing to gamble it up (and therefore risk going broke and/or redepositing) so that we can play at higher stakes sooner, we can play as high as $25NL.

Similarly, if our bankroll were, say, $10K, we can see from the top chart that we could/should be playing between $100NL and $500NL, depending again upon how risk averse we are.

For what it's worth, I've really felt like I've had my eyes opened during this little BRM research project. Based on a bunch of risk of ruin analyses I ran, I now realize that I have routinely played off the charts, so to speak, as far as risk goes. The good news is that I have won consistently at a significantly higher win rate than 1BB/100, so the effect wasn't as bad as it could have been. But still.... this exercise really hammered home how easily variance can rear its ugly head and bust your bankroll wide open--even if you're a pretty good player. Variance sucks.

And finally, remember this: understanding BRM is the easy part. Adhering to it is the really hard nut to crack. At least for this Bug.

All-in for now...
-Bug
*The other primary goal of BRM is so that you don't "play scared" and therefore play poorly as a result. As Tommy Angelo famously wrote in his excellent Elements of Poker book: "I heard someone say that a poker player's bankroll is like a carpenter's hammer. It's his main tool. He has to have it or he can't work. I've always liked that analogy, [but] I did a little adding on. [A] poker player's money is [more] like a carpenter's nails. A good carpenter brings lots of extra nails to the job site so that he 1) doesn't run out, and 2) doesn't worry about running out."

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