Miscellany

Well, I figure in tribute to my new reader from work (hey, Shane!), the "official" passing of 3 months since I started, just clearing a bonus, and running insanely well that I'd throw a hodge-podge of junk into a post:

I've changed some of the sidebar items to have a "permanent" home for my bankroll updates and any assorted statistics / trivia / leaks may be on my mind at the time.

Summary of my journey so far: started with $75 from an Instant Bankroll promotion, and played at the PartyPoker $0.15/$0.30 beginner tables. I have had some success at both freeroll No Limit tournaments and ring limit play, and have built my bankroll to over $1,000 playing (on average) about 10 hours per week. I am thinking about clearing at least a portion of my new bonus at $1/$2. At the very least I am bankrolled for it now.

From a previous post on personal variance, the last graph you saw of mine was a 120BB+ downturn. As a result of this downturn I posted on a question on the 2+2 message boards about what win rate was likely sustainable. As chance would have it, a very generous guy (hey, Chuck!) offered to review my hand histories. Since literally that moment on, I have been playing well and running well (click image to enlarge):



The very bottom of that downswing is where Chuck started critiquing my hand histories, and I have been running at nearly 5.4 BB/100 over the nearly 6000 hands since then.

I mentioned I may try to clear my next bonus (Poker Rewards, 25% up to $50, 10x) at $1/$2. One of the reasons I am even considering this is it would be a good experiment in using all the data I have gathered via datamining the Prima sites. I have almost 45,000 hands in my PokerTracker database at $1/$2, even though I have never played a single hand at that level. Pretty cool for getting a line on people you've never played against before at a new level.

My overall assessments of the poker sites - Party and Paradise are absolute fish havens, but the Prima skins are pretty well populated with a much higher percentage of good players. I plan on continuing to bonus-whore for quite some time, but could really see myself settling down ay Party and/or Paradise. The games are just that soft there.

Well, I told you all this was a random assortment. Shane, between myself, poker1eh, and my brother (QuadMan) I think we've all proven that money is here to be made online. It isn't easy by any stretch of the imagination, and you'll go through some emotional rollercoaters - far more than you would think over this "insignificant" amount of money. But if you're really interested and willing to put the time in to study and get better, it can be fun and profitable. Come join the club!

Next up, the $10,000 Poker Rewards freeroll on Sunday night. I sure hope my No Limit game hasn't suffered from playing limit for so long.....

Basic Hand Statistics after 3 Months of Play

Well, I'm about 3 months and 16000 hands into this journey, and thought I'd write a brief post on some PokerTracker stats. Some of these stats (especially the individual hand discussions) may not be worth much. 16000 hands seems like a huge amount, but that means I've (on average) only seen each of the pairs 72 times, the suited hands 48 times, and the offsuit hands 145 times. A bad (or good) hand or two can definitely still affect the average in a major way with this few hands. That being said.....

The first stat I will look at is BB/hand - a measure of how much you expect to win with a hand, on average. My top 5 hands are (in order):

KK: 1.99 BB/hand
QQ: 1.55 BB/hand
AKs: 1.33 BB/hand
JJ: 1.17 BB/hand
AA: 1.05 BB/hand

Those would be the 5 hands I would expect, although not quite in that order. My AA average is horrid. I have reviewed the hand histories on these, and I don't think it is a case of "falling in love" with the hand. I think it is simply variance over having only seen the hand 84 times, and losing with it the first 6 times in a row. Scary thing is that I would have to earn 3 BB/hand with it over the next 3 months just to get it to exceed my KK average!

My worst five hands are:
88: -0.50 BB/hand
Q9s: -0.36 BB/hand
A9s: -0.35 BB/hand
76s: -0.32 BB/hand
T9s: -0.31 BB/hand

Most of these (being suited hands) could likely be as a simple result of variance - again, I only have 50 or so sample size on the suited hands. However, 88 being my worst hand is certainly concerning. I would expect 88 to be at least marginally profitable.

It wouldn't be my blog without a graph and a table or two, so here goes: Here's a graph of BB/hand for all my hands. Click for larger version, as usual.



Note the graph looks amazingly like the graph in Small Stakes Hold-Em, page 47, including the bizarre downturn at the right hand side. The "blind steal" line corresponds to 0.75 BB/hand; the amount you get out of a blind steal. The "fold every hand" line corresponds to -0.075 BB/hand; the amount you'd lose if you simply fold every single time you got dealt the hand.

Many things are apparent from this graph:

1) There are VERY few hands that are more profitable than a "simple" blind steal. In my case, I have exactly 7 hands in this category (the previously mentioned 5 hands, along with AQs and AQo)

2) No hand in my database is worth more (on average) than a scenario where I raise preflop, drag both blinds with me, they check to me on the flop, I bet, and take it down. That is a 2 BB profit, and no hand currently exceeds that winrate. Long term, AA and KK probably take down more than 2 BB/hand but not significantly more than that.

3) Only 50 of the 169 hands are profitable at all. As it turns out, only 12 of those 50 profitable hands are offsuit, and only 7 of THOSE hands I believe are long-term profitable - the other 5 are only marginally profitable through short-term variance in my database. Those 7 hands are: AKo, AQo, AJo, ATo, KQo, KTo, QJo. Yes, KJo is unprofitable in my hands so far, but I would imagine that this would join the 7 hands above in the long term. Two big Broadway cards seem to be the only profitable offsuit hands.

4) I am losing more than a simple strategy of "fold every hand" with 64 of my 169 hands. Even if I "cut myself a break" and say that some of them are worth completing in the SB, then get folded (meaning a loss rate of -0.1 BB/hand), I still lose more than that on 42 hands, including 44, 66, 77, and 88. Other than the pairs, most of the hands are suited hands that I am either only playing out of the SB, or maybe calling a single raise in the BB with, so I'm not too worried - sample size variance and draws not coming in could be a source of that. But the mid/small pair loss bothers me quite a bit, and a few offsuit hands are in there that I have no business playing at all (Q4o? 52o? Q8o? J5o? J7o? K7o? T4o? - these are all hands that I am losing over 0.1 BB/hand that I really have no business playing from anywhere). This needs to be fixed.

For the truly curious, here are all my 169 hands and their profitability:



Green correspnds to "better than a blind steal", red corresponds to a loss of greater than 0.1 BB/hand, and light blue (arbitrarily) corresponds to a prfoitability greater than 0.1 BB/hand. The other hands are between -0.1 BB/hand and 0.1 BB/hand, so it is unclear where they really lie.

That's about all for today - In the future I may break these out by position once I get a few more hands in to see how profitability varies by position. I also may compare these to the EV values published at pokerroom.com. Fun, fun!

Bankroll Update

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.....

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.

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:

• 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.

I don't know if I have a neat ending to this post. I think simply going through the thought process of writing it has helping in-and-of itself. That being said, I think I'm going to take a break from playing for a few days just to get my head on straight. And not the kind of straight that keeps sucking out on my sets either..... :-)