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."

Poker Piggy Banks: Bankroll Management 101

Well, there's no time like the present to jump and start putting together some lesson notes and outlines, and the place that seems best to start is on the bottom rung of the pyramid, all the way to the left:

This bad boy anchors the lower left corner of the entire pyramid because, in my humble opinion, it is perhaps the most important of all off-table prep skills you can master as a newbie to poker. Is it sexy? Uh, no. Is it important? Uh, yes. Actually, a better way to state this is: HELL YES! 

Personally, proper bankroll management (BRM) has always been my nemesis. Said simply: it's been the single biggest leak in my poker career. I still struggle with it. For whatever reason, I have perpetually found it really, really, really  hard to play within my bankroll limitations. Because of this I've had some really, really, really big swings in my game, coming close a few times in the past to breaking the proverbial poker piggy bank. And I'm not alone; a big fraction of players--especially new ones--move too fast and far up the stakes ladder--usually because they're running good--and eventually go busto because they're playing way above their skill, abilities.... and most importantly: their bankroll limitations.

The first thing I need to do in this lesson set is define some terms, such as what bankroll actually is. The way I see it, there are really two types of bankroll: 1) the amount you have immediately available to play with (e.g., your account size for online gaming, or the amount in your left front pocket or in a box behind the cage in live games at the casino); and 2) the total, macro, global amount of money you can afford to lose in toto playing poker, period. While the former is important, it's the latter that really matters. Why? Because that old adage still applies: a poker player's bankroll is like a carpenter's hammer; you can't go to work without the tools of your trade available. Lose your tool (bankroll) and you can't play. Period.

I also need to (ultimately) explain how to calculate/determine what stakes you should be playing at given your bankroll size (that's the whole point of this lesson, right?) but to do that I need to explain the concept of variance and risk of ruin. It's really hard for a newbie to buy into (no pun intended) the idea that BRM is so important and simply has to be abided by without giving some concrete examples.

And this all goes back to our old friend Expected Value. As I've been pondering this particular BRM lesson plan, I've been researching and experimenting around with the EV formula. Assuming you learn to get your money in good with your poker decisions, then over time EV will work out in the long run, and you will get rich. But the required long run can be, well, significantly long. And, more importantly, you need a theoretically large amount of money to start with to cover the occasional (but certain to appear) big downswing. There's the whole concept called "Risk of Ruin" or RoR in gambling that I will explain in this lesson set, but the easiest way to visualize it is with some simple examples.

For instance, I've played around recently with some coin flip and dice rolling simulations in an Excel spreadsheet, and the results were eye opening. For example, one basic sim I ran was the classic dice rolling EV example of "I'll give you $1 if the dice comes up on 1, 2, 3, 4, or 5, but you have to give me $6 if the roll comes up on the 6". Simple math can show us that the EV of this gamble is in our favor; the expectation of a single roll is $0.17, so in general you should take the bet if you can…. but there are obviously no guarantees you're going to make money on a single roll of the dice. In fact, 5 out of 6 times you roll the die you're going to be handing a buck over to the other guy. But over the course of time--meaning a large number of rolls--you will come out ahead at the average rate of 17-cents per roll.

Okay, fine. This is just EV in action, right? Well, yes, but the interesting part is just how much the results fluctuate in reality, how long it can take for the results to even out and show a profit, and, more importantly, how much initial starting bankroll you'd need to take this bet. I ran a simulation  in a spreadsheet with 1000 rolls of the dice and was pleased to see that the results matched pretty closely to what the theoretical solution should have been; the first time I ran the simulation the net profit realized by taking the bet climbed steadily upward to a little over $175, which is almost perfectly spot on with the theoretical expectation of $170 (i.e., $0.17 x 1000 trials). Here's the graph of that first sim:

Note that there were some nearly $50 swings up and down along the way, but overall: woo hoo, EV works... but then I ran the 1000 sims again and… wow, this time I dropped over $30 immediately over the course of 200 rolls before coming back to show a modest profit of $72. Hell, it wasn't until after 400+ rolls of the dice that I actually stayed above zero profit. Also, the chart was really "choppy" and not smooth. Here's that second sim chart:

Folks, this is called variance, and it really intrigued me, so I ran the simulation over and over (25 times in total), noting how much I made overall each time, but also how much the graph swung up and down along the way. I was expecting swings, but the results really surprised me; I was expecting variance, but not this much. Most of the time everything worked out fine, and after 25 sets of 1000 dice rolls, I indeed made on average the theoretical $170 profit. Sometimes I made significantly more than the theory said I should, such as this 1000-roll example that netted me $250:

Sometimes I barely broke even, like this next run, below. Note that I was actually still $110 in the hole at around the 700th roll of the dice, and didn't even break zero until well past the 900th roll:

And occasionally, I ended up losing money, despite starting relatively strong. In this particular example I finished in the hole $40:

So what's all this dice rolling mean to us poker players? Variance happens, dude, that's what. And while we're rolling dice in these examples, this scenario is actually quite similar to poker situations you face all the time on the felt. For example, let's say you're on the river with over cards against a villain's made under pair, facing a bet, and the immediate pot odds are sufficient to draw. Most of the time you're not going to get there, but when you do make an over pair you will more than make up for the times you lose. Said another way: plus EV is plus EV, folks, whether it's dice or cards or the ponies.

And this leads to the ultimate lesson of this lesson: you need a bankroll significantly large enough to handle the swings of whatever game you're playing and it's expected EV. Poker is tricky to pin down in this regard, primarily because there are so many different draws, value hands, bluffs, etc., not to mention implied odds to factor in. But these can actually all be accounted for, and general bankroll guidelines created for your particular playing style and risk aversion level. Which is what I will do in this lesson.

To recap, in this lesson, I'm going to:

• Define the key terms, like bankroll, BRM, variance, and risk of ruin.
• Explain with examples (like the dice rolling one) how variance can get you broke, quick. I'll also give examples in poker, of course. (And I'll do yet another reiteration that poker is a game of the long run, and that in the short run it can be frustrating as hell due to just the short term effects of chance).
• Provide rules of thumb for minimum bankroll size to minimize your risk of ruin (and, while the focus of my lessons is on cash game play, I'll give some guidelines for SnGs and tourneys, too.) These rules of thumb will necessarily be based on the concept of risk aversion and your style of play.
• Give rules of thumb on when you can/should move up to the next level/stakes.
• Discuss the importance (and method) of moving down when the 'roll gets too small (and give some advice on how to handle the psychological aspects to moving down in stakes).
• Talk about strategies for actually taking money out of your bankroll. The purpose of playing poker, ultimately, is to actually make money (and spend it), right? Ergo, managing your 'roll to allow for variance (but also to allow for withdraws) is a balancing act, but one that can be actively managed with some simple guidelines.
• Finally, give some closing thoughts on:
• The dangers of playing too small w.r.t. your bankroll (i.e., playing too small leads to poor, loose, inattentive play), which is just as dangerous as playing too high (i.e., playing "scared" and unable to make +EV draws and other high variance plays)
• Absolute vs. Relative utility of money and bankrolls, and why +EV bets should sometimes be passed on.
• The dangers (and rewards) of "taking shots" at the higher limits, and when this is appropriate.

I'm still outlining and pondering this topic, so more will be added as I delve into it deeper.

As usual, comments and suggestions are most welcome...

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In other news, saw this on Twitter from Phil the Duck today:

phil_hellmuth ‏@phil_hellmuth17h

$1,000 buy in, $1 Million Guarantee! My next poker tournament, Phoenix, Aug 9: http://www.talkingstickresort.com/arizona-poker-championship-tournaments.aspx … At beautiful Talking Stick Resort

If I wasn't traveling that week, I was seriously considering playing in this AZ State Championship tourney. Guess Phil will have to take it down by himself...

All-in for now...
-Bug