Sunday, March 26, 2006

Journey through a Freeroll, Part II

Quick recap: I've entered into a $1000 freeroll with only 59 people playing. I was extremely short around the bubble (525 chips with the blinds at 100/200), but have since come back to take the chip lead at the final table with 7 people remaining.

The play is tight - amazingly tight considering that 7th place pays $65 and winning it all only pays $100. There's really not much difference in payout for anyone else. Weird payout structure, but oh well. I take advantage of this tightness and use my new-found chip lead to steal a bit more than my fair share of blinds.

Then the following gift from the heavens occurs with the blinds at 500/1000:

Stack sizes:
Button: $10970.00
Hero: $23680.00

Hero is BB with 5s Jc

Pre-flop: (7 players)

4 folds, Button raises to $2000, SB folds, Hero calls $2000.

Flop: 7c 5d 5c ($4500, 2 players)
Hero checks, Button is all-in $8970, Hero calls $8970.

Button shows 4d 4c

Turn: Qc ($22440, 1 player + 1 all-in - Main pot: $22440)

River: 7d ($22440, 1 player + 1 all-in - Main pot: $22440)

Results: Hero wins $22440 with fives full of sevens.

He raises more preflop and I lay that hand down. I was planning on check-raising the flop, but didn't expect him to push. I'll take it, though. I bust out a player and now we're 6-handed. I have twice the number of chips of second place, and over 40% of the chips in play. Very next hand I bust out the short stack to my left who can't even complete their BB. 5 handed now. A few hands later:

Stack sizes:
Hero: $37720.00
BB: $8690.00

Hero is SB with 8c 5s

Pre-flop: (5 players)
3 folds, Hero raises to $4800, BB calls $4200.

Flop: 7d 6s Ad ($9000, 2 players)
Hero bets $3600, BB raises all-in $5690, Hero calls $5690.

BB shows 7h Ac

Turn: 5h ($20380, 1 player + 1 all-in - Main pot: $20380)

River: 9c ($20380, 1 player + 1 all-in - Main pot: $20380)

Results: Hero wins $20380 with a nine high straight

Redemption - the exact same situation I got sucked out on before: top two pair vs open ended straight draw. This time I did the sucking out, but I figure this is karma working to balance out the other one. The only disappointment is that it wasn't the against the same guy that sucked out on me. This busts out another player, and we're down to 4 handed. I have a 3-1 chip lead on second place, and over half the chips in play.

I keep using my chip advantage to put the pressure on the small stacks. I get rockets in the BB for the second time in the tournament, but it is folded around to me. Damn. A few hands later, I take a chunk out of the second place player's stack:

Stack sizes:
UTG: $10400.00
Button: $14975.00
SB: $41905.00
BB: $19420.00

Hero is SB with Th 9h

Pre-flop: (4 players)
2 folds, SB calls $1200, BB checks.

Flop: 9d Kd 8c ($2400, 2 players)
SB bets $1855, BB calls $1855.

Turn: 2c ($6110, 2 players)
SB bets $3155, BB folds.

Results: Hero wins $9265 without a showdown

The stack is growing bigger. Someone else busts out, and we're three handed. I catch a few hands where I come over the top of an initial raiser (including a QQ that I was begging for a call), but all fold to me. I am stealing with abondon now, and my stack is over 60K. Then:

Stack sizes:
Button: $10565.00
SB: $17775.00
Hero: $57760.00

Hero is BB with Js Kd

Pre-flop: (3 players)
Button raises all-in $10565, SB folds, Hero calls $10565.

Button shows 6h As

Flop: 6c 6d Kh ($21930, 1 player + 1 all-in - Main pot: $21930)

Turn: 7d ($21930, 1 player + 1 all-in - Main pot: $21930)

River: 10s ($21930, 1 player + 1 all-in - Main pot: $21930)

Results: Button wins $21930 with trip sixes.

Oh well - thought it was a good opportunity to get rid of someone. On the very next hand, the guy that won that pot eliminates the other player, and we're heads up. I have a slight chip lead (48K to 40K), but not the dominating lead that I seem to have gotten used to. :-)

We trade some blind steals and re-steals back and forth, and every once in a while play a small pot on the flop. Then:

Stack sizes:
SB: $49595.00
BB: $36505.00

Hero is SB with Tc Td

Pre-flop:
(2 players)
SB raises to $6400, BB raises all-in $36505, SB calls $38105.

BB shows Ac 3c

Flop: 9s 4h 2s ($74610, 1 player + 1 all-in - Main pot: $73010, Sidepot 1: $1600)

Turn: 2h ($74610, 1 player + 1 all-in - Main pot: $73010, Sidepot 1: $1600)

River: 5d ($74610, 1 player + 1 all-in - Main pot: $73010, Sidepot 1: $1600)

Results: BB wins $74610 with the wheel

Ouch. OUCH. OUCH! 70% preflop to end the tournament right there. Even after the flop, he had 7 outs twice, and managed to hit one of them on the river. This quite obviously cripples me. I am down to 12290 with the blinds at 1000/2000. and outchipped 7-1. I actually get as far down as 7290 (less than 4 BB, and outchipped 11-1).

Time to grind and hope to get lucky. My blind steals start working. As my stack starts getting a bit higher, I open up the luxury of a limp in the SB, but most of these are punished by a raise from my opponent - far more often than he can have a hand with. Remember this - it will come in handy later.

Then, another gift from the heavens:

Stack sizes:
Hero: $13290.00
BB: $72210.00

Hero is SB with Kc Kh

Pre-flop: (2 players)
Hero calls $2000, BB checks.

Flop: Jc 10c 9c ($4000, 2 players)
Hero checks, BB bets $22000, Hero calls all-in $12290.

BB shows 2h Jh

Turn: 4c ($28580, 1 player + 1 all-in - Main pot: $28580)

River: Js ($28580, 1 player + 1 all-in - Main pot: $28580)

Results: Hero wins $28580 with a King high flush.

I'm coming back. I have a nice pot when I hit an Ace on the flop to match my one in the hole and then this very fun hand went down:

Stack sizes:
SB: $55920.00
Hero: $29580.00

Hero is BB with 4s 2h

Pre-flop: (2 players)
SB calls $2000, Hero checks.

Flop: 2c 8d 7h ($4000, 2 players)
SB bets $2000, Hero raises to $6000, SB calls $6000.

Turn: 7d ($16000, 2 players)
SB checks, Hero bets $7555, SB folds.

Results: Hero wins $16000 without a showdown.

Now we're getting somewhere. Two more blind steals and a small pot and I regain the chip lead!
We trade another bunch of blind steals, and raises of completed SBs. We trade the chip lead around for a bit, but never get that far from each other. Just jabbing at each other, pretty much, even post flop. Kind of like this:

Stack sizes:
SB: $45365.00
BB: $40135.00

Hero is BB with Td Js

Pre-flop: (2 players)
SB raises to $5000, BB calls $4000.

Flop: 8s 7d 3d ($9000, 2 players)
SB bets $2000, BB raises to $6000, SB folds.

Results: Hero wins $13000 without a showdown.

Cool - the chip lead again. Next hand:

Stack sizes:
Hero: $47135.00
BB: $38365.00

Hero is the SB with Kd Ks

Pre-flop: (2 players)
Hero calls $2000, BB raises to $18000, Hero raises all-in $46135, BB calls all-in $24365.

BB shows 9h Kh

Flop: Qs 9c Ah ($84730, 0 player + 2 all-in - Main pot: $84730)

Turn: 4c ($84730, 0 player + 2 all-in - Main pot: $84730)

River: 6h ($84730, 0 player + 2 all-in - Main pot: $84730)

Results: Hero wins the tournament with a pair of Kings.

As I had mentioned, the SB complete was nearly guaranteed to get raised by him, so I decided to trap him. I'm shocked he called my all-in with K9s, especially given this was the first time I'd come back over the top of one of his BB raises. You can argue I should have either flat called his raise or perhaps raising him less than all-in, but I guess all the chips wound up in the center anyways.

Well, that was a blast, and reminds me why I love the MTT format. I honestly think this is the best tournament I have ever played in terms of moving chips with a variety of hands, based on what I thought my opponents would do in response. As anyone who plays with me knows, I'm not used to playing the big stack, especially not a dominating big stack, and I think I did pretty well with it. I am also proud of the determination I had to come back from the two big setbacks. It was obviously a lot of luck as well, but it would have been easy to "give up" and just go all-in every hand when heads-up and outchipped by 11-1. As I've said before: it is cliche, but true - all it takes is a chip and a (virtual) chair.

Perhaps I will seek out more opportunities to play MTTs again in the future - I truly enjoy the format but don't usually have a 3+ hour whack of time I can devote to playing. But givien my results in both the free ESPN MTTs and the freerolls I've played for money, I may make it a goal to play in a few of them per month, either true freerolls or small-buyin MTTs. After all, if I'm going to make it to the Main Event, I better get some MTT practice in, no? :-)

Saturday, March 25, 2006

Journey through a Freeroll

For a little variety, I decided to do a freeroll MTT this afternoon. My brother (QuadMan) seems to be able to find these short-field freerolls that seem to almost be guaranteed money. Today's event was a $1,000 freeroll with only 59 entrants, paying the top 25. Nice, eh? As he likes to point out, that's the equivalent of a $16.95 entrance fee MTT, based on the amount of prize money. Sign me up.

Everyone started with 1500 chips so there was 88500 chips in play. Blinds started at 10/20, so everyone started out with 75 Big Blinds. A tad bit shorter than I like to start, but the blinds rose reasonably slowly after that, leaving some play in the tournament.

I picked up a few medium sized pots early on with some top pair /decent kicker hands, and one with a straight with a possible flush out, so I couldn't push it too hard. Up to a bit over $2000, then the following nice hand:

Stack sizes:
Hero: $2050.00
MP3: $2142.50
Button: $1135.00

Hero is UTG with Qd Td

Pre-flop: (9 players)
Hero calls $50, 3 folds, MP3 calls $50, CO folds, Button calls $50, SB folds, 2 folds.

Flop: 6c 8s Ts ($225, 3 players)
UTG bets $105, MP3 folds, Button calls $105.

Turn: 2d ($435, 2 players)
UTG bets $175, Button calls $175.

River: 3c ($785, 2 players)
UTG checks, Button checks.

Results: Hero wins $785 with top pair.

Nice - increased my stack by almost 40%. That'll do. The tables are quite tight, and I'm taking some small pots and even blind stealing every once in a while, which balances the small losses. Then this went down:


Stack sizes:
UTG+2: $1505.00
Hero (BB): $2155.00

Hero is BB with Kc 10d

Pre-flop: (10 players)
2 folds, UTG+2 calls $150, 6 folds, 6 folds, Hero checks.

Flop: Kd 3c 10c($375, 2 players)
Hero checks, UTG+2 bets $300, Hero raises to $955, UTG+2 raises all-in $1055, Hero calls $1355.

Hero shows top two pair. UTG+2 shows Qs Js for open-ended straight draw.

Turn: 7s ($2785, 1 player + 1 all-in - Main pot: $2485, Sidepot 1: $300)

River: 9d ($2785, 1 player + 1 all-in - Main pot: $2485, Sidepot 1: $300)

Results: UTG+2 wins $2785 with king-high straight.

Ouch. Ouch. Ouch. That knocks me down to 800 chips, with the blinds at 75/150, and I have to post 75 as SB. I fold it, and am down to 725 chips. At least that makes my strategy easy - with less than 5 BB, I'm all-in or fold. If I recall correctly, we are just outside the money at this point (30 or less people left).

The big blind comes around, and....

Stack sizes:
MP1: $2935.00
SB: $4065.00
Hero: $525.00

Hero is BB with Qc 9c

Pre-flop: (8 players)
2 folds, MP1 calls $200, 3 folds, SB calls $200, Hero checks.

Flop: 2s Qd Qs ($600, 3 players)
SB checks, Hero checks, MP1 checks.

Turn:10h ($600, 3 players)
SB bets $200, Hero raises all-in $525, MP1 folds, SB calls $525.

River: 2c ($1650, 1 player + 1 all-in - Main pot: $1650)

SB shows Qh 8s

Results: Split pot ($825 apiece) with Queens full of Twos.

OUCH. Friggin board pair on the end. Had his trip queens out-kicked and everything. Oh well, at least got some dead money out of the whole thing. I pass through the next blinds with nothing.

Stack sizes:
Button: $4625.00
Hero: $425.00

Hero is SB with AhAs

Pre-flop: (10 players)
7 folds, Button raises to $400, Hero raises all-in $425, BB folds, Button calls $525.

Button shows Ad 7h.

Flop: 7c 4d 10d ($1150, 1 player + 1 all-in - Main pot: $1050, Sidepot 1: $100)

Turn: 6h ($1150, 1 player + 1 all-in - Main pot: $1050, Sidepot 1: $100)

River: 6c ($1150, 1 player + 1 all-in - Main pot: $1050, Sidepot 1: $100)

Results: Hero wins $1250 with Aces and sixes.

My first rockets in the tourney, and they couldn't have come at a better time. But I'm still short stacked - still about 6 BB. Back to work. My BB is folded to me (would have been all-in push anyways with KQ). In my SB, I steal a small pot from QuadMan who happens to be in the BB. Very next hand:

Stack sizes:
MP2: $6242.50
Hero: $1715.00

Hero is Button with Jc Jd

Pre-flop: (8 players)
3 folds, MP2 calls $300, CO folds, Hero raises all-in $1715, 2 folds, MP2 calls $1715.

MP2 shows 3d 3s

Flop: Kc 6h Qd ($3880, 1 player + 1 all-in - Main pot: $3880)

Turn: 6d ($3880, 1 player + 1 all-in - Main pot: $3880)

River: 8h ($3880, 1 player + 1 all-in - Main pot: $3880)

Results: Hero wins $3880 with Jacks and sixes

Whew. Little bit of breathing room now - about 12 BB. Don't pick up anything for abit to be able to call the onslaught of all-ins before I act. Howeverm for whatever reason both of my BBs in this time were folded around to me. Thanks! Picked up a significant chunk of change (about 50% of my stack) on this one with the blinds at 200/400:

Stack sizes:
Hero: $3730.00
BB: $3630.00

Hero is Button with As 6d

Pre-flop: (6 players)
3 folds, Hero raises to $855, SB folds, BB calls $855.

Flop: 6c Ks Kc ($1910, 2 players)
BB checks, Hero bets $855, BB folds.

Results: Hero wins $1910 with no showdown

I do a blind steal or two and bust a small stack all-in with my TT, which puts me up to around 6300 - about 10 BB at 300/600. Amazing to me, as I was down to 525 not that terribly long ago. Somewhere in here, we get down to 10 people. Woooo hooo - final table time! I do an appropriate amount of blind stealing. Then comes the hand that was (essentially) the Hand of the Tournament for me:

Stack sizes:
UTG+1: $2850.00
Hero: $4670.00
BB: $10555.00

Hero is MP1 with Tc Th

Pre-flop: (9 players)
UTG folds, UTG+1 raises all-in $2850, Hero raises all-in $4670, 5 folds, BB calls $4670.

BB shows 9c 9d
UTG+1 shows 6s 6h

Flop:
Qd 4s Kc ($12590, 1 player + 2 all-in - Main pot: $8950, Sidepot 1: $3640)

Turn: 7h ($12590, 1 player + 2 all-in - Main pot: $8950, Sidepot 1: $3640)

River: 7c ($12590, 1 player + 2 all-in - Main pot: $8950, Sidepot 1: $3640)

Results: Hero wins $12590 with tens and sevens

Wow - way to dodge the two underpairs. This puts me in 4th chip position out of the 8 people left, although the leader only has about 17500, so he's by no means a dominant leader. Few hands later:

Stack sizes:
Hero: $11090.00
BB: $19912.50

Hero is SB with Th Tc

Pre-flop: (7 players)
5 folds, SB raises to $5000, BB raises all-in $19912.5, SB calls all-in $7090.

BB shows Ks Qd

Flop: 4c 2h Ah ($24180, 0 player + 2 all-in - Main pot: $24180)

Turn: 3c ($24180, 0 player + 2 all-in - Main pot: $24180)

River: 7h ($24180, 0 player + 2 all-in - Main pot: $24180)

Results: Hero wins $24180 with a pair of tens

Welcome to the chip lead! I have about a quarter of the chips in play with 7 players left.

Well, this seems like as good a place as any to end this tale for the night. The post is long enough, and I will finish the rest of it soon. Cliffhanger? Likely not, as the only two people who read this blog already knows what happened in the end.....

Monday, March 20, 2006

Bonus Chasing, Earn Rates, and Variance

As promised in the last blog post, today's post will be about bonus clearing, its effect on your earn rate, and what that means for variance.

First, a very basic introduction to bonus clearing: many sites have bonuses that clear at a specific "multiplier" to the amount of money you have to clear. For example, River Belle (a Prima skin) currently has the following bonus, which will be used as the ongoing example throughout this post.

"50% up to $100, plus $25 if deposited via an ADM, clearing at 7x raked hands"

Wow - that's a mouthful. What this means in English is that they will give you 50 cents on the dollar (50%) for any money you deposit, and they will do this until their match reaches $100. They will give you an additional $25 if you deposit via Neteller or Firepay. Thus, if you deposit $200 via Neteller, they will throw $125 in your bonus account. This bonus will clear at 7x, which means you will have to play $125 x 7 = 875 raked hands for your bonus to be released to you. That's pretty much it. Some sites do things in terms of "points" to clear bonuses, but these can almost always be converted back into multipliers with appropriate massaging. Also, some sites release your bonus to you in "stages" instead of giving to you as one lump sum at the end - this does not affect the calculations in this post, but is nice to know.

So, in order to clear the $125 bonus, we have calculated that 875 raked hands are necessary. Next step is to determine how the site determines a "raked hand". At River Belle, a raked hand is any hand where you are dealt cards and the pot is raked at least $0.25. Other sites (such as Party Poker) count any hand which is raked (even at $0.05) as a raked hand, which has major implications on the bonus clearing rate. More on this later.

Obviously, if you play at a lower level (say, $0.25/$0.50) the pots will not be raked at $0.25 or more as often as if you play $2/$4. This implies you will need many more dealt-hands at a lower level to get a fixed number of raked-hands than you will at a higher level, and this needs to be taken care of in any calculation.

So, to take our above example, let's assume we decide to play $0.25/$0.50 to clear our $125. So far, my experience shows that about 20% of hands at that level are raked at $0.25 or above. Thus, in order to get in our 875 raked hands, we will need to play about (875 / 20%) = 4375 hands. This allows us to calculate two numbers:
  • Our BB/100 just for clearing the bonus: $125 is 250 BB ($125/$0.50), and we need to play 4375 hands to earn that, so our BB/100 just from bonus clearing is (250 BB / 43.75 ) = 5.7 BB/100
  • Our hourly earn rate: Assume 60 hands per hour per table. 4375 hands should take 72.9 hours of single-table play, thus meaning you earned $125 / 72.9 = $1.71 / hour per table.

We can do this calculation for a variety of levels, and a variety of bonus structures, and the result is the below table (click for larger image):

You can see our previous 5.7 BB/100 and $1.71/hr/table numbers in their appropriate spots in the table. A few things to notice about this table:

  • In terms of BB/100 winrate, there seems to be a bit of a "sweet spot" around $0.50/$1.00 - it seems to be the "ideal" level to clear bonuses in terms of BB/100
  • In terms of hourly rate, the larger limits are always better (to a point, as the next table will show)
  • The winrate numbers are much larger at the lower levels than even a good 2 BB/100 player could generate via their play alone.

But the story gets better - check out the following table for sites (such as Party) that have a very low limit for what constitutes a raked hand (click for larger image):

Technical note: the usage of 95% in the above models for the higher levels assumes a "no flop / no drop" policy whereby if no flop is seen, no rake is taken. 95% corresponds to not seeing a flop once every two button revolutions, which seems about right for the low levels I've played so far. This number may actually have to be lowered as higher levels are reached, as the games may tighten up and blind steals may succeed more often than at the lower levels. Also note that as nearly every hand becomes raked, the hourly rate to clear your bonus becomes constant regardless of what level you play.

These numbers are HUGE for the lower levels, and are quite respectable even for the upper levels shown in the chart. Remember - this is just the clearing rate for the bonus. Any winrate you have from playing poker goes on top of this!

So, let's take our group of 10000 clones from the earlier post (2BB/100, SD=16BB/100) and put them on this RiverBelle bonus playing at $0.25/$0.50. Let's see how they stack up over the first 4375 hands against a group who isn't playing the bonus. The non-bonus players should win right around 88 BB (4375 * 2BB/100 / 100), so their bell curve should center around there. The bonus players should win the same but have an extra 250 BB ($125 / $0.50) for a total of 335 BB, so their curve should center around that. Cue the graph (again, click for larger image):



Perhaps as expected, the result of the bonus is to merely shift the bell curve to the right by 250 BB without increasing its width (a measure of standard deviation). This is as a result of the fact that adding your bonus does notincrease your Standard Deviation at all - in effect, your bonus is the equivalent of a 5.7 BB/100, 0 SD player playing "alongside" you. Ignore the fact that the curves look slightly different in shape - this is an artifact of the fact that the bonus is not an exact multiple of the bin size.

But look at what this "trivial" result means for the "unlucky" low-end of the tail! Whereas over 20% of the non-bonus players would have lost money over these 4375 hands, only 6 of the bonus players have lost money! (the bar representing these 6 players is actually too short to see on the diagram - the first bar you see is the 91 players who are up between 0 and 88 BB). The breakdown of that 20% group is:

  • 1573 players lost between 0 and 88 BB
  • 425 players lost between 88 and 176 BB
  • 62 players lost more than 176 BB

So which group would you rather be in? I know I'd rather take a 0.06% chance (6 out of 10000) of being down between 0 and 88 BB rather than a 20% chance of being down that much or worse.

For the hell of it, let's take all these players and let them all play out the rest of their 15000 hands under non-bonus conditions. Obviously the players who have played the entire time without a bonus will be identical to the population from my last post - about 6.4% of them would still be down money. What about the group that played the bonus at the start? The details are boring and I'll omit them, but it turns out only 23 of those 10000 players will be down money at the end of 15000 hands. Again, I know which group I'd rather be in - the group where I have a 0.23% chance of losing a little bit of money rather than a 6.4% chance of losing that or more.

These numbers will obviously vary depending on what bonus multiplier and level you clear them at, but the message is undeniable. Playing a bonus doesn't actaully reduce your variance in real-dollar terms, but does raise your expectation enough that even a quite hefty variance can be borne. And I haven't even focused on the other (cheery) end of the distribution tail, whereby you make far more money under bonus that you ever could have without it!

My natural "instinct" before writing this post was to be a bonus chaser, and after writing this post it only reinforces that tendency. Given these numbers, I think I'm a LONG way off from playing at a level where I can afford to ignore the positive effects that I've outlined here.

Wednesday, March 15, 2006

Thoughts on Bankroll Growth and Variance

First an apology – this blog post is very long and contains math. You’ve been warned….

This post is based on some thoughts I had around how fast I could reasonably grow my bankroll. Some basic assumptions:

1) You are comfortable at playing at a limit where you have 300 BB (Big Bets). Where this number comes from and how to derive your own “comfortable” bankroll size will be a topic for a future blog post.
2) You are a good player in the games and limits you choose.
3) You see 60 hands per hour per table.

Given these assumptions, you can make some rough time estimates around your bankroll progression – specifically, how long it will take to double your bankroll to allow you to move up to the next level if you desire.

A standard metric for the rate at which a good player can beat a game is for 2 Big Bets per 100 hands (2 BB/100). To double your bankroll requires you to earn another 300 BB. At the "standard" rate, this should take you 15000 hands (300 BB needed @ 2 BB/100) or 250 table-hours.

So, how long should it take you to put in 250 table-hours? That obviously depends on how much you play and how many tables you play:

The numbers in the table represent how long (in weeks) you would need to play to double your bankroll from 300 BB to 600 BB. For example, I currently 2-3 table about 10 hours per week, so I would need somewhere between 8 and 12 weeks to accomplish a doubling of my bankroll. Those who play more often or on more tables would obviously require less time – in the extreme case in this table, someone playing 40 hours per week and 4-tabling would only take about a week-and-a-half to double their bankroll!

These timeframes are very short, especially when a typical “double your money” timeframe in the stock market is measured in multiple years. WOOO HOOOOOOO – let’s quit my job, cash in the retirement account, mortgage the house, and play poker – I’ll be a millionaire in no time!!!!

Except for one thing: variance - the variance around this 2BB/100 earn rate is extraordinarily large, and we can actually estimate how large via basic statistical methods. For instance, take a hypothetical player with a 2 BB/100 win rate, with a standard deviation of 16 BB/100 (which is actually a little low by some measures. Let’s say this player plays a low-variance strategy). Let’s say you clone 10000 identical copies of this player and send them all out to play 15000 hands. As a group, they would average a 300 BB win. But the individual breakdown of the population would be something like the following (from a basic simulation done in Excel):

10 people would be down more than 300 BB (and thus be broke!)
102 people would be down 150-300 BB (and may have dipped below 300 BB in the process)
524 people would be down 0-150 BB
1560 people would be up 0-150 BB
2843 people would be up 150-300 BB
2767 people would be up 300-450 BB
1585 people would be up 450-600 BB
493 people would be up 600-750 BB
102 people would be up 750-900 BB
14 people would be up more than 900 BB

When graphed, the shape of this is a classic “bell curve”

Thus after 15000 hands a total of almost 6.4% of the players would be losing (instead of up their “expected” 300 BB profit) and over 2% of the unlucky souls will be down over 100 BB! That is a huge variation, and is solely attributable to randomness – remember, these are all clones of the same player with the same win rate and standard deviation! Also remember that these are good players, playing a low variation strategy!

So if 6% of the players are losing over a span of 15000 hands, then that really implies 15000 hands is not enough to truly determine who is profitable or not. Let’s ask some more questions:

  • How many hands does this group have to play before (say) 99% of the population will at least be positive? Via the same simulation, this number is somewhere is the neighborhood of 33000 hands – which will take you about twice as long as the number in the table above.
  • How long do they have to play before 99% of them get to their “expected” 300 BB profit? Via the same simulation, somewhere around 60000 hands, or 4 times the amount of time as in the table above.

OK, great! So even if it takes me 32-48 weeks to double my bankroll (instead of the original 8-12 weeks, before we included variance), that’s still better than waiting years in the stock market!

However, let’s think about that last bullet for a bit. As stated, after 60000 hands, 99% of the population would be at 300 BB or better. Great. But let’s look at what the clones would calculate for their own individual winrates: the very lower end of that spectrum would think they were 0.5 BB/100 players (300 BB / 60000 * 100), and (since the distribution is symmetrical) the upper end would think that they were 3.5 BB/100 players. This is from a group of identical 2 BB/100 players! Even after 60000 hands, the calculated winrates can be far, far off the actual winrates solely due to variance. To be fair, about 70% of that population would calculate their winrate to be between 1.3 BB/100 and 2.7 BB/100, but that is still quite a wide variation!

The point is that you really have no way to determine that you are a 2 BB/100 player without playing an incredible amount of hands – your at-any-given-point-in-time current calculated BB/100 rate is pretty much worthless without tens of thousands of hands behind it, and who knows if you’re even playing at the same winrate as you were when you started the series of hands? Hopefully you’re getting better over time……

Is there a lesson here? It certainly isn't "don't bother to calculate your BB/100, because it can't ever be pinned down." You have to have some number to gauge your ability, and even if it comes with large "error bars" it is better than nothing. Perhaps the lesson is to not make any long-term plans based on whatever your current BB/100 is - that if you play a lot of hands, play them well, and accept variance as part of the game, that bankroll considerations will take care of themselves. This is easier said than done, as both poker1eh and myself have learned in our very short stint into this silly game.

My next post will likely be math as well - about bonuses and bonus chasing, and what they can do to modify the figures above.

Sunday, March 12, 2006

Bankroll current state

Just a brief update and thoughts on the State of the Bankroll......

Total Bankroll: $200.26

Consisting of:

Bonuses: $150
$75 - Instant Bankroll
$25 - Party signup bonus
$50 - Golden Riviera signup bonus

Tournaments: $9.40
$1.40 - Golden Riviera freeroll (87th out of ??? (a lot) )
$8.00 - Poker Rewards freeroll (18th of 650)

Limit Ring Game Play: $40.86
$10.11 - Party
$25.45 - Golden Riviera
$5.30 - Poker Rewards (so far)

I'm somewhat disappointed in my win rate at limit ring game play - I don't have Poker Tracker yet, but I figure I have to be somewhere in the general vicinity of 1 BB/100 (about 8000 hands at an average of 0.25/0.50). With all the bad play I see out there, I figure I ought to be beating these games at twice this rate. Perhaps just variance, perhaps I just need more practice at limit hold-em. After all, almost my entire "experience" before starting on this journey was NL holdem (cash, SnG, MTT) and that is still where I feel most comfortable.

All of this points to the obvious question - why are you bothering to play limit ring games when both your experience and your feel is all in the NL arena? Perhaps another post for another day......

Saturday, March 11, 2006

Books, books, and more books

As mentioned in the subtitle of my blog, I tend to do a lot of reading about poker. Below is the list of books I've read, along with some comments on each.

Harrington on Hold 'em Vol I & II (Harrington)
The absolute bible on NLHE tournament play. Could possibly be the best (pair of) poker books I've ever read. Have likely read both of them 3 times through.

Small Stakes Hold'Em (Miller)

Likewise, the bible on low-stakes limit hold-em play. I try to play in alignment with the principles outlined in this book. I think I may be on my 4th read through this one.

Theory of Poker (Sklansky)

A great book for the theoretical underpinnings of all games of poker (not just hold-em). Sklansky is a very dry read, but given I used to read advanced physics textbooks for fun, the dryness tends not to bother me. :-)

Hold'Em Poker for Advanced Players (Sklansky)

Another extremely complete book on hold-em, in typical Sklanksy fashion.

Inside the Poker Mind (Feeney)

A very, very interesting book about a variety of mental factors in the game of poker.

Psychology of Poker (Schoonmaker)

Another interesting book that focuses on the mental aspects of poker.

Phil Gordon's Little Green Book (Gordon)

A nice little book giving an extremely good look into the thought processes on a pro.

The other books below I really don't think enough of to make a comment one way or the other. Your mileage may vary. At the very least, I think I've learned at least a little something from all of them. I really enjoy Bob Ciaffone's writing and thinking style, thus all the books from him. Check out all his past articles on cardplayer.com for good examples.

Ace on the River (Greenstein)
Championship No Limit & Pot Limit Hold 'Em (McEvoy/Cloutier)
Improve Your Poker (Ciaffone)Middle Limit Holdem Poker (Ciaffone/Brier)
Play Poker Like the Pros (Hellmuth)
Poker: The Real Deal (Gordon)
Pot-Limit & No-Limit Poker (Reuben/Ciaffone)
Super/System (Brunson)Tournament Poker for Advanced Players (Sklansky)
Win Your Way Into Big Money Hold'em Tournaments (Daugherty)
Winning Low-Limit Hold'em (Jones)

In terms of what is next to read, I (and a lot of other 2+2 readers) am eagerly anticipating Ed Miller's upcoming NL book "No Limit Hold-Em: Theory and Practice" and Harrington's Volume III, both scheduled to be out in May. I am also interested in "How Good is your Limit Hold'Em" by Jacobs which is a book full of limit hold-em quizzes to test your skill level.

Sunday, March 05, 2006

March Home Game

As I may have mentioned before, I play a monthly poker night with the guys - we usually have between 6 and 10 guys and play as many NLHE tournaments in an evening as we can. Last night we got in 5 of them:

$10 buy-in, 11 players, split $70 / $40
$20 buy-in, 11 players, split $120 / $80 / $20
$20 buy-in, 10 players, split $120 / $60 / $20
$20 buy-in, 8 players, split $90 / $50 / $20
$20 buy-in, 8 players, split $90 / $50 / $20

(the 2nd and 3rd tournaments I may have the payout slightly wrong on. If they are, I'm sure poker1eh will correct me.....)

The lesson of the night came in the last two games. That lesson is patience - you never have too few chips to win. Sounds cliche to say "chip and a chair", but......

In the next-to-last game, I believe I played a grand total of 3 hands or so before I was heads up at the end. My chip stack was approximately where it started, and thus my opponent had me outstacked by 7-1. Came back to win it.

In the last game, I came up on the wrong end of an AK vs QJ pre-flop all-in from a true maniac who had pushed all in with regularity with almost anything. He hit his J, and I had no help which left me crippled with only 175 chips and 5 players left. There were total 26000 chips in play, and the blinds were 200 / 400. So not only did I have well under 1% of the chips in play, but I couldn't even post a full small blind. Very long story very short, I came back and won. Obviously to come back from that sort of deficit you have to have a ton of luck, but I also think I was as patient as I could be, once I built the stack back up to the point I could survive a few rounds.

The final results of the evening were 2 wins and a second out of the 5 tourneys, leaving me $170 in the black for the evening. Not bad.

For all of you who may think online poker is rigged - I saw just as many (if not more) brutal beats and big hand vs. big hand than on any poker site I've been on. Off the top of my head:

  • Nut flush vs. two pair, all in on the turn. Two pair hit their 4-outer boat on the river.
  • Middle set vs. overpair, all in on the flop. Overpair hits their 2-outer on the river.
  • QQ vs Ax on AQy board. Ax hits runner-runner Aces for quads.
  • AJ vs K7 on AKJ board, all-in on the flop. AJ was a 90% favorite (according to Poker Stove), but lost when the 2-outer K got there. (I think this is correct - the AJ was poker1eh's hand, and I'm sure he has a better recollection of it than I do)
  • KK vs. AQ. Board comes KJT single suited. Set vs. made straight. Only thing that was missing was the made flush. For the record, the KK made a boat.
These all happened in a span of 7 hours of live play, so all this was in a span of 300-400 hands, at most.

Can't wait until the April game!

Friday, March 03, 2006

Random thoughts after about a month of internet play

For more detail about the history of what I'm trying to do, please my initial "Background" post from the beginning of February.

I started with Instant Bankroll / Party promotion, and played my first hand of internet poker for Real Money on February 7, 2006 at Party Poker. Whether this was a start of something good or a downward spiral I had no idea, but was going to have fun trying to find out.

After clearing my bonus, I left Party on February 26 with $110 ($75 of it Instant Bankroll money, $25 of it bonus money, $10 profit) and went to Golden Riviera (GR), as they had a $50 bonus that looked easy to clear (5x, which means 250 raked hands to clear the $50 bonus). As it turns out, I had a better string of cards than by buddy poker1eh, and cashed out of Golden Riviera last night just short of $190 ($50 of which was bonus from GR, and a total of $150 is bonus overall). So up $40 so far playing online. Is it variance or skill? Hard to say at this point.

The site we (poker1eh and myself) will go to next is more than likely Poker Rewards, with a 50% bonus that clears at 10x, but am primarily choosing this site as it will allow me to obtain Poker Tracker (PT), one of the coolest pieces of software I have seen. If you are an online poker player, you owe it to yourself to get a copy of this software, by hook or by crook. It is simply that good, both for reviewing your own play, and gathering stats on your opponents. Once I get
PT, I will likely use one of the Heads Up Displays like Poker Ace or Poker Office to overlay real-time statistics of all my opponents on my tables. How can that not help your game?

I have drug both my brother and a coworker into this online poker thing, although I don't think they came unwillingly. My brother is henceforth known as QuadMan, as he gets quads (and paid on them) more often than anyone rightly should. I may post a few of his hands here soon.

Tonight my money is in limbo in between GR and Neteller, so I believe I may play a few STTs at ESPN.com to warm up for a home-game tournament tomorrow night. Should be fun. As long as poker1eh doesn't take all my money, that is......