Confusion over Variance

Variance as it relates to poker is difficult to understand, both because the element of luck is hard to quantify and the mathematical function for variance doesn't provide many answers.

What does variance mean exactly?

In my mind, the term variance is used in poker to describe the amount of luck in any given game -- not the amount of swings. So when you say a game is high variance, that means the game's results are more likely to be determined by the cards that are dealt than by players' decisions.

Here are some definitions of variance:

1. Variance is the statistical measure of dispersion, or just how widely your results will be distributed. When variance is high enough, a small advantage may be of no use during your lifetime. When variance is low enough, a small sample will be much more likely to reflect your real advantage (or disadvantage). In other words, variance describes just how long the long haul is. In poker terms, high variance means that a small number of hands will not be very representative of your long-term expectation.
--Seriouspoker.com

2. The distribution of your results over a a set of hands or sessions, or the swings in a positive or negative direction of cash flow.
--Mike Caro University.

3. If operatorname{E}(X)"> is the expected value (mean) of the random variable X, then the variance is This definition and equation is meaningless to me, but I like weird-looking variables.
--Wikipedia

As a poker player, I want to know which games maximize my skill edge over my opposition.

I asked the question, "what type of game has 'more' variance between no limit, limit and tournament hold 'em?" in the 2+2 Beginners forum. The responses to that thread, Variance: NL vs. Limit vs. MTT, back up my beliefs.

I only got three responses, but they were in agreement. Multi-table tournament hold 'em seems to have the highest variance, followed by limit hold 'em and no limit hold 'em.

While no limit seems to be "high variance" because you may have to put your entire stack at risk at any time, in reality the ups and downs aren't too extreme. No limit provides the best opportunity to get the most money in with the best odds. It's the game that will separate a fish from his money the quickest. It has fewer suckouts than limit or MTTs.

For a closer look at how to attempt a poker calculation of your variance, I found this article titled, "How much bankroll do you need?" in a search.

I also enjoyed a Mike Caro article published in Bluff magazine a few months ago, in which he argued that your luck may not even out in the long run, contrary to popular belief. Check it out here: "The importance of luck in poker."

The Perfect Donkey

After a long road of busting fish, taking small edges and building bankroll, you hope for that golden opportunity in which you'll be able to make a big score.

I stumbled upon that chance at a 10/20 table last night. I can't imagine there was more dead money at any other online table at the time. And it all came from one player, who I will call the Perfect Donkey. I got a seat directly to his left.

Perfect Donkey was loose (55 percent VP$IP), and he spewed chips at every opportunity and in a predictable manner. If he raised preflop and was reraised, he would go all in. If he bet out postflop and was raised, he would go all in with any Ace-high, pair or drawing hand. With made hands, he would minraise.

By sheer luck, he was building a monster stack. In 255 hands, I saw Perfect Donkey win a more than $5,000 pot with King-high, no draw against another player's flush draw with overcards. He got in with a flush draw on the turn and hit on the river against KK. He pushed with A6o on a 579 flop and hit his gutshot on the turn against JJ. He pushed an open-ended straight draw on the flop against QQ and hit on the turn.

I knew I would have a chance soon to pick a spot in a large pot.

It's funny -- after learning and playing day after day, the situation that I've been waiting for is to the left of an idiot with money. Everyone else at the table is a shark, but they didn't even bother to play against each other most of the time as they salivated over the thought of getting it in against Perfect Donkey. If Perfect Donkey wasn't in a hand, no one was.

Against this guy, I would happily take a potential coinflip because I could also have him completely dominated.

So when I was dealt AK, I reraised Perfect Donkey's $80 bet to $240, knowing he would push and I would call.

That's exactly what happened. He turned over KQ, missed a Queen, and I had doubled up!

Now with my double-sized stack, I would have a chance to make some serious money off Perfect Donkey, who somehow kept growing his chips upwards of $10,000 -- five times his initial buy-in of $2,000.

I didn't have to wait long.

I raised from under the gun with A9s. Perfect Donkey called in the big blind. The flop came a beautiful 8d, 9c, 5d to give me top pair with a nut flush draw. My only goal was to get all my money in the middle as soon as possible, and I knew it wouldn't be hard against this guy.

He bet out $60, and I raised him all in to $4,100. He called and turned over J8o for second pair, no draw.

http://twodimes.net/h/?z=2725493
pokenum  -h ad 9d  - 8h jd  -- 8d 9c 5d
Holdem Hi: 990 enumerated boards containing 9c 8d 5d
cards  win   %win  lose  %lose  tie  %tie     EV
Ad 9d  812  82.02   169  17.07    9  0.91  0.825
Jd 8h  169  17.07   812  82.02    9  0.91  0.175

The Jack on the river cost me that $8,500 pot when he made two pair. Damn! I would have to rebuy and start over.

Only a few hands later, Perfect Donkey minraised to $40, and I cold called from the button with KQ. The flop was nice, if a little dangerous: Ts, 7h, Kh. My top pair, middle kicker, no-draw hand was probably good here.

Perfect Donkey bet out $100, I raised to $300, he pushed and I called. He turned over Ah 5d, failed to improve, and I was back in business.

I chipped up to over $5,000 with the hopes of one more strong hand against this guy. One more hand to win the biggest pot of my life. One more hand to erase this month's losses. One more hand to make everything right, put a bad player in his place and feel good until I sit down at the World Series of Poker in less than two weeks.

Perfect Donkey raised to $80, and I found AK again. I know how to play this hand against this guy. I re-raised to $300, and he went all in for his entire $11,000 stack.

Did I have a decision to make here? Was there any doubt about calling another $4,700 and taking a potential coinflip?

No, there was no question. I know full well what this guy is capable of. If I fold a premium hand like AK preflop against Perfect Donkey, I might as well put my bankroll in low-risk bonds and never take another chance again in my life.

This is what I had been waiting for. I knew what I had to do. I called.

I got my coinflip. Perfect Donkey had JJ, I failed to improve, and I had lost my biggest pot. So be it.

I rebought a third time, prepared to stay up all night if that's what it took to bust this guy. But it was no use. He quit shortly afterward, leaving the table with more than $20,000. I went on to a 5/10 table where I made top set of Aces and got it all in on the turn, but an 8 on the river gave my opponent his one-outer for quads. Flopped set over set no good.

Time to rebuild. Time to grind it out. Time to get ready for the next Perfect Donkey, in hopes that I can take those same bets for thousands of dollars but perhaps with different outcomes.

Squeeze play river bluff

One of the things I've quickly noticed at 5/10 NL and above is that the squeeze play becomes a common and important move. It isn't just for tournaments anymore.

I've always sucked at running the squeeze play, mostly because I prefer to bluff postflop. But I've learned that I can't ignore it anymore, and it can be very profitable.

I like to run the squeeze play from the big blind against a button steal raise and a cold call by the small blinds. There are many other situations when you can put in that third raise as a bluff when trying to trap dead money in the middle, but this one is pretty efficient. The button's hand range is pretty wide, and the small blind is likely to fold against a big re-raise. They both usually conclude that you have a monster.

The squeeze worked well against the small blind in the following hand. He was a loose-passive calling station, and I wasn't sure that I would be able to move him off any hand that had at least one pair. But a "value bet" river bluff won the pot for me when the small blind timed out before folding.

Fish posts small blind $5
Hero posts big blind $10
*** Dealing down cards ***
Dealt to Hero [ Ts Js ] (JTs is a decent enough hand. I would also attempt this move with many weaker hands as well)
Button raises $35
Fish calls $30
Hero raises $140 (I raise, you should fold!)
Button folds. (Thanks for folding)
Fish calls $115 (You were supposed to fold too)
*** Dealing Flop *** [ 4d, 7c, 9c ]
Fish checks.
Hero bets $250 (A continuation bet is essential after showing such strength preflop)
Fish calls $250 (Dammit. I don't know if I can get this guy off his hand. He could have anything, from overcards to a pocket pair to a flush draw)
*** Dealing Turn *** [ 3h ]
Fish checks.
Hero checks. (I think about pushing all in with my last $600, but I worry he would call with almost any draw and any pair)
*** Dealing River *** [ 6d ]
Fish checks.
Hero bets $300 (I decided to bet half my stack in a last desperate bluff attempt. I know my opponent will call with a wide range of made hands, but he'll finally fold any busted draw)
Fish folds. (It must be my lucky day)
Hero wins $1,133

"Winning in Tough Hold 'em Games"

I don't know what it was exactly that made me think limit hold 'em would be more profitable than no limit. Part of it was the allure of make 2 BB/hr at 15/30, which I thought would be an incredible winrate. It seemed like it would be easy to win one decent pot per hour at those full-ring donkfests back in the Party Poker days, when there were plenty of tables and they all seemed loose.

When I finally got to 15/30, I got smacked. I lost 2/3 of my bankroll and spent five months rebuilding it. Shortly afterward I began focusing on no limit, but I'm glad I spent time learning limit because it made me a stronger, more analytical player.

Two of the biggest leaks in my limit game were that I couldn't figure out how to play well from the blinds, and I didn't know how to handle loose-aggressive players.

"Winning in Tough Hold 'em Games: Short handed and High-Stakes Concepts and Theory for Limit Hold 'em," by Nick "Stoxtrader" Grudzien and Geoff "Zobags" Herzog is the book that I wish I had back then.

This is easily the best limit hold 'em book I've read, better than "Small Stakes Hold 'em," "Winning Low-Limit Hold 'em" and "Hold 'em for Advanced Players." That's saying a lot.

The great thing about this book is that it's practical, and it reflects the reality of today's online limit games. It's written by experts who know what the 6-max tables are like -- often with table VP$IPs around 40 and filled with aggressive players who will see showdowns at a rate that would quickly break no limit players. And the reason the games are filled with those kinds of players is that they're not very wrong to be playing like that.

For example, according to the book:

If you're not seeing showdown near 37 percent of the time you see a flop, you're probably folding too much. If you don't 3-bet preflop from the small blind around 90 percent of the time you're going to play a hand against a steal raise, you're making a big mistake. If you fold Axo or Qxs in the big blind vs. a steal, you're giving away money.

From reading board texture to adjusting for different styles to determining when it's safe to fold for one more bet on the river, this book covers a lot of ground.

It starts out with several hand charts, PokerTracker records and equity values in the first chunk of the book. These form the reference material that the rest of the book is based on, but I didn't spend a lot of time trying to memorize any of these data.

Then the book moves on to stealing, blind defense, semibluffing, betting lines, modernized bankroll advice and hand quizzes. This is great stuff.

I like to evaluate books based on whether they make me a better player when I sit at the tables. Unlike some poker books I've read, I notice the difference in my play on many hands. I've been winning more often and stealing more pots.

Online limit has died down over the last couple of years, but the shorthanded games especially are still wild. I've seen some god-awful play at all limits. Everyone wants to be an aggressive force who can control the action and get in with the best of it. "Winning in Tough Hold 'em Games" tells you how to do it.

A great day for poker

There will be on action aplenty Sunday, and I hope to see a lot of people playing.

There's the Big Game, hosted by MiamiDon!



And we have the FTOPS Main Event at 6 p.m. on Full Tilt. I just barely won an entry by playing in a $100+9 satellite that awarded 98 seats. I already see plenty of bloggers registered: Hoy, Fuel, Cracknaces and oossuuu754. I'm sure I missed a few more in the long list of registered players, and hopefully some more will win satellite entries. Good luck!

At the same time, Fuel and I will settle our heads-up match on PokerStars. He holds a 2-0 lead in the best of 5 series, but I'm not going to go down easy.

When to Bluff

Seldom do you know exactly where you stand in a contentious hand. Most postflop decisions can be characterized as an "either/or" situation. For example:

_ Way ahead-way behind:

You have a good but not great hand, while your opponent either has a lesser hand or a powerhouse that he's slowplaying. This kind of situation could come up when you have AA on a JJ8 board -- you probably have the best hand, but you could be toast against trip Jacks.

Conventional wisdom says you should be more likely to control the pot size and try to see a showdown in these situations. Bluffing big is usually a bad idea because you won't get the trips to fold.

_ Way ahead:

If you make a hidden nut straight, the board isn't paired and there's no flush draw out there, you don't have much much to worry about.

Your only guiding principle in this situation should be to try to get as much money into the pot as possible. Whether that's by playing fast or playing slow is circumstantial.

_ Way behind:

Durr. I guess you should fold. Stone-cold bluffs can be an option depending on the board texture and your opponent, but it's often better to have a backup draw.

_ A little ahead-way behind:

This is a bad spot that I find frequently comes up on the flop with two-pair hands or ignorant draws. It can be very dangerous when you hold a hand like JT on a JTQ board with two suited cards. Unless your opponent folds immediately, a conservative (but money-saving) way of playing this kind of two-pair hand is to wait for a safe card on the turn before putting in much more money. You need to be prepared to let go if the action gets too hot.

_ A little ahead-a little behind:

These are the kinds of hands where it seems like you have the best opportunity to make a big bluff. When you have a strong combination draw, you'll be close to even money anyway, and by playing strong you can take down the pot without a showdown. Even a gutshot draw combined with a backdoor flush draw and a pair can give you enough equity to make a legitimate play at the pot.

These kinds of moves are semi-bluffs, which are the best kind because "pure" bluffs can be suicidal if you run into the wrong hand.

I'm not sure how useful this is, but it can't hurt to think about these relative hand strength possibilities when deciding how you want the hand to develop. It makes Level 2 thinking a little easier.

Hawaii Weather

---

EasyE left a very useful comment on my post about attempts to make PokerAce HUD work faster when multitabling on Full Tilt (edited to insert updated link):

I have this same problem. With me, running PAHUD with Full Tilt was virtually unusable. But I have found the following helps greatly:

- surprisingly it is much quicker when I set "Flicker Free Drawing" to on. When I have this unchecked, it seems that the screen is forever redrawing, and this takes up a lot of resources. I know it's supposed to work better with this set to off, but on my PC it is SIGNIFICANTLY faster with this set on.
- running a freeware app called "Process Tamer", which you can get at http://tinyurl.com/mdhnp . You mentioned setting priorities for applications in the Windows Task Manager. Well this app let's you set rules and additional settings so that this is automatically taken care of each time FT and PAHUD are run. I've found that my system works well when I set an explicit rule so that Full Tilt is "Forced Realtime" and Poker Tracker is "Forced Below Normal". I actually don't change the settings for PAHUD.

Running it this way makes FT, PT and PAHUD very usable.

Give these a try, you might find it helps.

I tested his suggestions out, and I discovered that I really like Process Tamer. It seems to do the job very well! I didn't open more than four tables at a time tonight, but PokerAce ran much smoother. I also tried adjusting explicit rules for PokerAce, and it seems like "Forced Realtime" worked better than leaving it as the default. Thanks again to easyE.

---

I ran a big bluff a few days ago with AK in a 10/20 game, and I wanted to hear what some of you think.

UTG raises $55
VILLAIN calls $55
MP calls $55
HERO raises $250 from LP with Ah Kd (Standard raise here. I want to get money into the pot and thin the field)
UTG folds
VILLAIN calls $195 (OK, so now I know he cold called twice preflop. I put him on a mid pocket pair)
MP folds.
** Dealing Flop ** [ Js, 7h, 2c ]
VILLAIN checks.
HERO bets $400 (Obvious continuation bet that I will make every time in this spot)
VILLAIN calls $400 (Seems consistent with my suspicion that he might have a pocket pair. Maybe 88-TT. Or even 77 for a set, but I'm willing to accept that if he hit it. I also start to think he may have a Jack, but it seems unlikely given the action)
** Dealing Turn ** [ 8d ]
VILLAIN checks.
HERO is all-In for $1,358. (The pot size had grown over $1,400. I trusted my read that he had a pocket pair or a Jack. He couldn't call with many of the hands I put him on, especially since I'm representing AA or KK. Even if he called, I would still have six outs to make a better pair with an Ace or King on the river.)

Thoughts? I'll post the results in the comments soon.

Tax Accountant Z

Man, if you dig on zombie movies, I don't know how you can dislike "28 Weeks Later." It was fantastic.

I read one review that criticized it "for pretty pyrotechnics but defies all logic and human decency" as well as for having "a nasty spirit."

Um...yes. That's what I like in a zombie movie. See it in the theater.

---

As I was walking out of the tax accountant's office the other day, she mentioned that she had recently played poker at a CPA party. She said she busted out pretty quickly.

I gave her some easy advice for next time.

"Just fold a lot until you have a really good hand," I said.

She told me the folding was the problem!

"All the accountants played very conservatively," she said. "But the 12-year-olds in the game won it all. They just kept bluffing at every hand."

PokerAce Tip

I like Full Tilt, but their software has always caused some people problems, especially since an upgrade a few of months ago to include resizable tables.

This upgrade seems to have caused some players who use PokerAce HUD to experience lag if they open too many tables. If I open more than two tables at a time and have PT and PokerAce running, Full Tilt will slow to a crawl. Card animation is difficult to see, and sometimes I can't click the check, fold or raise buttons for several seconds while my computer thinks about it.

Maybe my computer is getting old (3 years), but it's still a problem that was created by a Full Tilt upgrade. The PokerAce programmer said it's nothing that he can fix.

So here are a couple of things you can do to moderately reduce lag on Full Tilt if you have this problem:

_ Turn off "Flicker Free Drawing" in PokerAce's preferences.

_ Set PokerAce to low priority in Windows Task Manger. Do this by pressing Control-Alt-Delete once, and then selecting the "Processes" tab in Task Manager. There should be two instances of "PAHud.exe." Right click on each of them, select "Set Priority" and then choose "Low." It helps a little.

In the long term, I think the solution will be for Full Tilt to either work on a software solution, or for me to buy a nice new computer. Maybe at the end of the year.

Tax Answers

After paying taxes this year, I quickly decided it was time for me to stop doing them by hand and find a tax accountant. Taxes are a pain, they're too expensive to risk making mistakes, and I had a lot of questions.

So I met with an accountant yesterday and had a great opportunity to ask her all about poker and taxes.

The first thing I wanted to know about was filing as a professional. As a professional, you can deduct many poker-related expenses, including travel, meals, expenses and lodging. The downside is that you have to pay self-employment taxes on your winnings of an additional 15.3 percent. The accountant ran the math, and it didn't result in any savings for me. Unless I spend tens of thousands in poker-related expenses, it makes more sense for me to file taxes as normal. Maybe someday, when I become a badass tourney player and tour the world. Right.

I also found out about how to pay estimated taxes, which I will have to do this year or else risk paying penalties. I have to pay quarterly estimated taxes because government withholdings from my paychecks don't include gambling income. Anyway, the way to do it this year is to base my estimated tax payments on my taxes last year. For example, if I owed $15,000 in taxes on April 15, I need to basically divide that number by four to figure out my quarterly responsibility, and then fill out form 1040-ES for the feds and another form for the state.

Because I owed a large amount in taxes last month, I had to make several withdrawals from poker sites in order to cover the bill. Those withdrawals temporarily inflated my bank account above $10,000 for the first time. I wondered whether that amount triggered federal reporting requirements. Fortunately, the accountant told me those requirements only apply to cash transactions. When it comes to checking accounts, she said there's no reporting requirement. That's nice to know.

Finally, I asked her the big question: Isn't there some way for me to pay less taxes? Unfortunately, she said there wasn't much I could do. All income is taxable, and we have to pay the taxman or risk getting caught.

WSOP: I'm in!

After sending a cashier's check for $1,500 to the WSOP folks, I received an e-mail confirming my payment for event No. 12, the 6-max NL on June 7. I guess this means I'm in!

Dear Gnome,

** This email notification is for informational purposes only.**
** Please do not reply to this email. **
** It was sent from an unattended mailbox, and replies are not reviewed. **
** See below for contact information. **

Gnome, your funds have been received. Please proceed to the World Series of Poker Cashier window upon your arrival at The Rio Hotel All-Suite Hotel and Casino, Las Vegas, NV to complete your registration. Please arrive at least one hour before your earliest event. Your funds maybe applied to event registration at that time or for any other use.

Below is a copy of the information you have provided us:

... (miscellaneous personal information) ...

Total Amount Received: $ 1500
Payment Type: CashiersCheck
Payment Status: Received Funds
Pre-Registration Confirmation #: XXXX

Participants will need to present proof of identity (passport, drivers license, state identification card or military identification card) in person at the Rio to complete the registration process and obtain his or her table and seat assignment.

Payment is a deposit only. You must complete pre-registration at The Rio, Las Vegas, NV for the events as set forth in the rules available at www.worldseriesofpoker.com. Your deposit may be applied to event registration at that time or for any other use.

If you have any questions about the WSOP Pre-Registration, please go to www.worldseriesofpoker.com "Frequently Asked Questions" for general information or contact our staff directly at 702-777-6777.

Sincerely,
------------------------------------
Jack Effel, WSOP Tournament Director
Robert Daily, WSOP Event Director

It's time to pay the price

OK, so seven random things about me, after being tagged by Scurvy and Glyph:

1. I've held a lot of jobs, including landscaping, Chick-Fil-A supervisor, Longhorn Steaks dishwasher, Macaroni Grill waiter, Toys 'R' Us cash register dude and reporter at 10 newspapers and bureaus.

2. If I hadn't burned my hand on a grill while working at Chick-Fil-A in high school, my life may have taken a very different path. That accident set off a chain reaction including drunkenness from a six-pack of Zima, a road trip to Texas and a need to find a job in college that eventually landed me in Hawaii.

3. I don't feel like I'm exceptionally good at poker, but I've had some success because I'm careful with my bankroll and I learned to stop overplaying high pocket pairs.

4. I've been skydiving twice, and it was awesome.

5. I used to hate Wil Wheaton because Wesley Crusher was such a terrible character on Star Trek. I always laughed when a friend of mine talked about how he needed to have a spoon beamed into his heart. ButWil is alright, even if he played a brown-nosing annoying cadet on TV.

6. I went through a phase when I would only use matches to light cigarettes. Ah, random neurosis.

7. If I had to choose between the Braves and UGA winning a championship, I would pick the Braves.

And now I tag you!:

Kuro
Sham
Surf
Slb
ZAPLAB (Heh -- no chance he'll do this)

Beating the game

Thought of the day that I don't want to write a whole post about:

Many losing players could beat online no limit hold 'em at low to mid limits with a formulaic strategy. They could win if they used good bankroll management, played tight, folded when behind, raised when ahead and thought about their actions before making them.

---

Here are some links!

Anatomy of the Continuation Bet

Blind Stealing

Summary of Voluntary Statistics Survey

April > March

"No one should rest. People who are doing that are setting themselves up for failure in the future."
--Taylor Caby

April was a great month -- in fact, I'm pretty sure it was my best ever as I won about nine 10/20 buy-ins. That's about the pace I always aim for. I want to win about 10 buy-ins a month because at that rate, my bankroll can grow pretty quickly.

I figure that if, on average, I win a buy-in 20 days a month and lose a buy-in 10 days a month, I'll come out way ahead.

My biggest hand of the month came when I flopped quad 7s against KK and a flopped boat. That'll pay off every time. That pot was worth about 3.5 buy-ins alone.

My worst hand of the month came just a few days ago when I turned a gutshot straight against a turned two-outer boat (55 on a 3345 board). I lost a full buy-in on that hand, and it would have been hard to get away from despite the paired board. The pot was already so large that I felt committed with what I thought was the best hand.

Mostly I tried to play consistently and smartly. I think the hit I took from paying a ridiculous amount to the IRS actually helped my mindset, in that I didn't feel as much pressure to build my bankroll to meet my $100K goal. Instead, I just went back to work. I'm still a couple of months away from my goal at this rate, but that's OK. You won't find me complaining.

My game continues to improve.

I realized that while I steal the blinds at a steady clip, I don't defend them quite as much as I should. I don't think that's a big flaw though.

I also figured out that I need to float in position more often and fold to continuation bets less.

Mostly though, I just played solid poker. Against calling stations, I kept the pot small until I had what I thought was the best hand. When I thought I had the best hand, I pushed hard. When I didn't, I folded. I know it's not always that easy, but when you're running good, sometimes it feels that way.

And if all else fails, I used my secret weapon: sucking out on the river.