Wednesday, August 27, 2008

Bankroll Utility

Since I had not previously mentioned it, the reason I have been spending an inordinate amount of time at the Horseshoe is because I am extremely cash poor at the moment and I am sadly trying to scrape together some money to have my insurance reinstated and make rent. I do have a large cashout pending but I am finally coming to grips with the fact that I simply can not predict when these things will arrive and what sort of complications may occur. My goal is simple, yet tedious. I am trying to take $100 or so and make about $100 playing in the $2/4/4/8 game where I then hope to parlay that amount to a much greater sum in the $1/2 NL game that has a $100 minimum buy in. If I happen to double it or better at that game, I will leave and then sit down again at another table with the minimum $100 again. Thereby I will be limiting my exposure, but it will be very easy to dump my hard earned winnings in the larger game. Desperate times call for desperate (and pathetic) measures- what can I say? Since I realize that this will almost certainly be comical several months from now, I am definitely not reporting this as any kind of sob story but rather to offer a certain insight into bankroll management.

So here it goes: I managed to make my goal in the smaller game and then promptly moved into the larger game with my $100. Just a few hands in, I was dealt 44 and I limped into the pot to try and see a flop. The guy behind me raised it to $12 and two other guys called. My first instinct was to fold my 44 because from my experience the whole issue of implied odds is rather sketchy. But then I came across an X-factor and that is that even though I may be sacrificing a tiny bit of expectation (which may or may not be the case -- it is certainly debatable), the value of hitting that potential home run would mean that I could probably at least double my stack and then even if I were to dump $100 later on, I would still be able to come back tomorrow and sit in this game. Specifically, the value of calling that extra $10 was more than offset by the chance of hitting a major score. After all, at some point I was going to have to make a major hand in order to truly get rid of the training wheels. Also, having a smaller stack as a result of calling and then folding can actually be quite useful in a game where the typical raise is between 6 and 7 1/2 times the big blind. This can be very beneficial to the short stacker, as a short stacker is far more likely to double or triple his chips with a one pair hand then a larger stack, thereby adding to the total utility of the hand.

So what is utility? Utility is the unique and special value that an individual assigns to something and can vary widely according to different circumstances and situations. Now this is the actual true secret to individual bankroll management. To begin this discussion I will give an example:

Player A and Player B both have a bankroll of $5,000. Player A plays $1/2 NL and Player B plays $5/10 NL. Who has the bigger bankroll? Obviously the smaller player has a large bankroll and the larger player has a tiny bankroll. Assuming that they are both equally talented and winning players and that neither one is willing to you drop down in stakes, the smaller player would need to be catastrophically unlucky to lose his roll but the larger player could lose his entire bankroll through ordinary daily variance. Therefore, as should be clear by now, Player A's bankroll has much more utility than Player B's.

Since it is almost equally improbable that Player A would even lose $4000, it would be perfectly reasonable for him to take a shot at that same $5/10 game if it is beatable provided that he limit it to a single buy in at a time. Or even better, he could 5-table this $5/10 game as long as he quits after the first $1,000 loss. This is assuming that that $1000 is not necessary for other expenditures outside of poker. The reason? If he can string together several good sessions, he can conceivably move up in the limits to become a full time $2/4, $3/6, or higher player.

There are a ridiculous amount of caveats to this conclusion- once again they are all situation specific. Now suppose that I have run my initial $100 into $1000 in my $1/2 NL game. Everyone else at the table only has $200 except for the skilled loose-aggressive player sitting directly behind me who also has $1000. Even though I can theoretically break him with my stack, the probability of getting my entire stack in against his as a superior favorite is so low that my extra $800 has now become a liability since my positional disadvantage and awkward stack size is more likely to create difficult situations than favorable outcomes.

In the past, I have railed against the 300 big bet "theory" of bankroll management for limit games. This simply does not make sense to me and the reason is because you will not be expending 299 big bets in any game because at that point you will have violated all known bankroll limitations and will be sitting there with only a chip and a chair. Furthermore, at some point far sooner than that, you will have crossed the threshold of the minimum buy in for that game. Supposing that you do have the "required" 300 big bets, your actual bankroll for that limit might be only 50 big bets, since at that time you might be forced to move down or even worse, maybe that game is not beatable for you at all, meaning that NO bankroll is large enough. Likewise if 300 big bets is the absolute minimum for a given limit, does that mean you should pack up and leave if you lose your first hand? Of course not!

The bankroll "requirement" really is only a measuring stick for a player who would never be disciplined enough to use it. Knowing your personal psychological makeup and tendencies is the only way to establish your own limits. I have found that as long as I have at least $400 in my online account I can make thousands of dollars in any given month because I have the discipline to move up or down accordingly. I will touch on this topic more as I have found it to be an endlessly ridiculous debate that people try to quantify through mathematics and repeating book knowledge. All I have to say is, if this is the requirement for true poker success, then where are all those success stories of people who have followed this formula and used to reach the greatest heights of success?

2 comments:

Rob Wilco said...

Lorin-

I found your blog off Ed Miller's. Like it. I started one like this a few months ago but dropped it because I wasn't writing enough.

Per 300 big bets- When I started my online poker career, I used this "artificial threshold" because, well, that's what the pros said to do. (I find this reason to be acceptable when one is first beginning an endeavor). Since then, I have stuck to that mark even through my rise in limits simply for the comfort level. If I have SO MANY bets in my BR, then I find that it's a lot easier to make the gutsy call/raise/bluff without even thinking about it. Could I cut it to 200 and still be fine? Probably. But I'm not a pro yet; this is still just a hobby for me. ;)

Anyway, nice job on the blog. I'll check in from time to time.

Rob- $0.50/$1.00 and $1.00/$2.00
limit player on Pokerstars

PS- The Horseshoe in Indiana, is that the one in Hammond? If so, how is the room? I used to go with my friends to play at the Majestic Star and Resorts in East Chicago/Gary, but I haven't been to the Horseshoe since it opened.

Lorin Yelle said...

Thanks for the compliment Rob!

No doubts there about being comfortable at your chosen limit- that is of the utmost importance. Even though I have found from my own personal experience that I can always make a living at NL if I have at least $400 in my online account, I would never recommend that to anyone as it can become a harrowing experience. The reason that I have found that I can do this is because I have learned to avoid situations where my ego quickly gets involved (see my newest post for a commentary on this situation "Ego as Currency") and have personal stop loss points when I know to drop down to the next lowest level.

It all comes down to knowing yourself personally and your own strengths and limitations. The whole bankroll debate to me seems like arguing how many angels can dance on the head of a pin. No one really knows, yet everyone feels likes the they are the expert on the topic. While I am no general expert on what works for anyone else, I am the closest thing to an expert on myself.

So where did the concept of 300 big bets come from? It was a calculation having something to do with standard deviation X win rate X hours X the rotation of the earth = a bunch of theoretical bullshit. Now they are saying 400 big bets- AT LEAST!! While all this is surely done with the best on intentions, if I were a $300/600 online player, there is no freaking way that I am leaving $240,000 parked in one site!!!!!!

If you ever choose to read any of the two most recent works by Nassim Nicholas Taleb, you will see how this line of thinking might work in a lab but has little use in the real world. The truth is that no one really knows their true win-rate because it is based on an unknown factor of hands played and a constantly shifting player base fluctuation in the quality of your own play. So without true knowledge of your win-rate, you can never calculate your true standard deviation, ad infinitum....


So the Horseshoe: it is actually located in Elizabeth, IN at the southernmost part of the state. It is actually widely regarded as being the best poker room in the entire mid-west on the nation's largest riverboat casino. It really is something and you might have actually heard of it as before the casino was known as Caesar's Indiana.