Just a brief update on the State of the Bankroll......
Total Bankroll: $814.47
consisting of
Cash: $746.62
Non-Cash: $67.85
The breakdown is:
Bonuses: $571
$75 - Instant Bankroll Promotion
$25 - Party Poker signup bonus
$50 - Golden Riviera signup bonus
$81 - Party Poker reload "Triple Bonus"
$90 - Poker Rewards signup bonus
$25 - River Belle "spot bonus"
$100 - Poker Rewards reload bonus
$125 - River Belle signup bonus
Freeroll Tournaments: $114.40
$1.40 - Golden Riviera freeroll (87th out of 3000+ (a lot) )
$8.00 - Poker Rewards $1K freeroll (18th out of 650)
$100.00 - Poker Rewards $1K freeroll (1st out of 59)
$5.00 - River Belle $1K freeroll (33rd out of 499)
Limit Ring Game Play: $61.22 (0.98 BB/100)
Pending bonuses
None
Non-cash:
$60.00 (6000 PSO points)
$7.85 (785 Poker Rewards VIP points)
It has been a wild, wild ride over the last month in terms of bankroll swings - less than 3 weeks ago I was down $65 in limit ring game play.
In terms of basic statistics, in the 2.5 months I've been doing this, I have just short of 15,000 hands. I have played an (estimated) 105 hours over this time, which is about 10 hours per week - about what my intial "target time investment" was. In terms of dollars per hour, it looks like I'm making somewhere around $7.75 / hr - not exactly enough to quit the job, but better than minimum wage for the same amount of time.
Never did I think I'd be approaching $1,000 in less than three months starting from absolutely zero money. Next up - how fast can I get to $10K? :-)
Next post - some basic Poker Tracker statistics about the first 15,000 hands.....
Saturday, April 22, 2006
Wednesday, April 12, 2006
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:
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):
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:
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)
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.
Monday, April 03, 2006
Variance, on a personal basis
This seems like as good a time as any to talk about variance in less of a theoretical / math sense and in more of a personal / psychological sense.
At this time, I'm going through a 125+ BB downswing at the same time I've increased the level that I'm playing (I have jumped to $0.50/$1.00 almost full-time) and to use a phrase coined by poker1eh, its starting to hurt.
In ring games, I have gone from a rate of 1.5 BB/100 with $45 of profit to a rate of 0.35 BB/100 and a loss of over $50 in ring game play (a swing of $95) in the span of about 1300 hands. At River Belle alone, I am down $86 in the midst of trying to clear my $125 bonus.
This wouldn't be my blog without a nifty graph, so here goes. As always click for a larger version, but you may want to avert your eyes first:
The self-doubt that has crept into my game is amazing, to the point that I get a sinking feeling everytime I see a premium hand. I honestly don't think I have become weak-tight, as I don't think I have backed down on the aggression with the premium hands. However, I either seem to win a small pot or lose a big pot with them recently - it seems to be a "steal the blinds or get sucked out on" situation.
I am in the process of reviewing my play, looking for leaks. In general, I feel I may be calling down to the river a bit too often lately, figuring that people are trying to run me over. But I suppose that is a vicious cycle - if I start folding to raises late in the hand, then people WILL start taking shots at me. I am also conscious of not becoming weak-tight, so need to make sure I'm betting for value where appropriate.
Let's look at some PT stats:
For my first 9800 hands, my VP$IP / PFR / W$WSF / WtSD / W$SD was:
16.41% / 5.96% / 30.5% / 34.0% / 50.5%
For my (1400-ish) hands since then, those same stats are:
15.29% / 6.7% / 30.0% / 27.0% / 40.3%
For my last 700 hands (the last half of the downswing), they are:
14.77% / 5.9% / 30.6% / 30.6% / 40.5%
So, I seem to have tightened up a bit preflop. All other stats seem to be within a reasonable range of each other, except WtSD and W$SD. W$SD is (quite obviously) lower in the midst of a downswing. What is reassuring (at least at this "100,000 foot view") is that I don't seem to be chasing more than I used to - in fact, if anything, WtSD shows I'm folding more often than I used to. Perhaps that is the leak - I'm actually letting people take me off hands. More detailed analysis of individual hands is surely needed.
In looking for the bright spots:
At this time, I'm going through a 125+ BB downswing at the same time I've increased the level that I'm playing (I have jumped to $0.50/$1.00 almost full-time) and to use a phrase coined by poker1eh, its starting to hurt.
In ring games, I have gone from a rate of 1.5 BB/100 with $45 of profit to a rate of 0.35 BB/100 and a loss of over $50 in ring game play (a swing of $95) in the span of about 1300 hands. At River Belle alone, I am down $86 in the midst of trying to clear my $125 bonus.
This wouldn't be my blog without a nifty graph, so here goes. As always click for a larger version, but you may want to avert your eyes first:
The self-doubt that has crept into my game is amazing, to the point that I get a sinking feeling everytime I see a premium hand. I honestly don't think I have become weak-tight, as I don't think I have backed down on the aggression with the premium hands. However, I either seem to win a small pot or lose a big pot with them recently - it seems to be a "steal the blinds or get sucked out on" situation.
I am in the process of reviewing my play, looking for leaks. In general, I feel I may be calling down to the river a bit too often lately, figuring that people are trying to run me over. But I suppose that is a vicious cycle - if I start folding to raises late in the hand, then people WILL start taking shots at me. I am also conscious of not becoming weak-tight, so need to make sure I'm betting for value where appropriate.
Let's look at some PT stats:
For my first 9800 hands, my VP$IP / PFR / W$WSF / WtSD / W$SD was:
16.41% / 5.96% / 30.5% / 34.0% / 50.5%
For my (1400-ish) hands since then, those same stats are:
15.29% / 6.7% / 30.0% / 27.0% / 40.3%
For my last 700 hands (the last half of the downswing), they are:
14.77% / 5.9% / 30.6% / 30.6% / 40.5%
So, I seem to have tightened up a bit preflop. All other stats seem to be within a reasonable range of each other, except WtSD and W$SD. W$SD is (quite obviously) lower in the midst of a downswing. What is reassuring (at least at this "100,000 foot view") is that I don't seem to be chasing more than I used to - in fact, if anything, WtSD shows I'm folding more often than I used to. Perhaps that is the leak - I'm actually letting people take me off hands. More detailed analysis of individual hands is surely needed.
In looking for the bright spots:
- I have the self-awareness and diligence to go back and review my game to see if there are leaks instead of just raging about my bad luck (although poker1eh and QuadMan may differ on this opinion of complaining!)
- I have people that can (and will) review my play
- I have the sense (mostly) to get away from the tables if I feel like I'm tilting. If I'm completely honest with myself, I need to work on this a bit more strongly though.
- I have the bankroll to absorb this variance - in the grand scheme of things, 125 BB is a reasonably small bit of variance, and need to remind myself of this. There is a reason why our bankroll needs to be 300+ BB, and this is it. A look back at my very own variance post "proves" this.
- My bonus clearing almost covers this loss, which is a testament to the HUGE power of bonus chasing. I am 555 hands through my bonus, which means my bonus cleared "so far" is (555/875) * $125 = $79.29. So in a very real sense, I'm "only" down a little over $6 in real money. Simply amazing.
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