Tuesday, May 29, 2007

Going broke with top pair

Here's a hand where I went broke with top pair and I think it was a reasonable risk, contrary to the adage against it.

It was a 1/2 blind NL HE game with a $200 cap on the buyin. I don't usually by in for the max until I've been at the table a while. I bought in for $100 and lost a little. I had a little over $70 when this hand arose.

Six players at the table, a limp in front of me, I limp in the cutoff with QcJc, button calls, the big blind makes it $12. I don't really want to go up againswt a raise with this hand, but the player in front of me calls, so I go ahead and call, the button calls.

Flop is Qs 8c 3c. Top pair and a flush draw. Even a back door straight gut-shot.

Check-Check. I'm surprised at the check from the raiser. Doesn't seem normal. I'm suspecting a big hand of some sort. I'm thinking maybe AQ or AA. But maybe not. If he has me beat I have a flush draw. If he has a better draw then I have the best hand. Maybe he's got neither, maybe I have the best hand and he doesn't have a draw.

Anyway, the pot is almost $50 and I have a little over $60, so I just go allin. Button folds. He quickly moves allin for a total of about $100, the guy between us folds. Now I think I'm beat.

I turn over my hand. He doesn't. He's mister slowroll. But I'm still okay with my hand. I think he has an over-pair so I probably have about 15 outs, so I'm actually not beat.

Turn is a queen, river makes me a flush, he had flopped a set of 8's, his fullhouse wins.

Even against the worst case scenario I had 9 outs, after considering his redraw I had about 6 effective outs against a set. That's not great but it's only about a 3 to 1 dog at worst.

That's a key for considering whether a top pair is worth going broke with. Do you know you aren't drawing dead and at least have a few (more than 2 or 3) live outs? If so you have a lot more than top pair.


Saturday, May 26, 2007

Top pair revisited

The other day I made a post titled Don't fall in love with top pair. More recently Ed Miller has a post about Going Broke with One Pair. The two ideas are related, although not exactly the same. Falling in love with top pair often leads to going broke needlessly, but the converse is not so often true. There are plenty of circumstances besides inappropriately falling in love with top pair which might lead to going busted with top pair. Ed's post uses one of those other situations as an example to illustrate his thesis.

His thesis appears to be
Going broke with just a pair brings on a bevy of emotions, from guilt (for ignoring such a simple rule), to embarrassment (for losing so much with such a modest hand), to despair (as in, “Why the hell can’t I figure this game out?”).

The thing is, all that angst is often thoroughly misplaced. Sometimes it’s not only ok to go broke with one pair, but it’s the right thing to do.

I'm not sure that I'd say going broke is ever the right thing to do, although it might sometimes be a common result from doing the right thing.

Ed didn't mention my prior post in his, but making a reference to somebody elses blog isn't the sort of thing I expect from Ed anyway. He's just not that kind of guy.

Some of Ed's post is based on some misconceptions he has about poker history and the source of the phrase "Don't go broke with top pair" as an adage that is heavily adopted by many players. He doesn't seem to understand the motivation for the original adage.
I think the main thing that trips people up is a common poker fallacy. It goes like this: “I see bad players do that a lot, so it must be a bad thing to do.”

It’s similar for going broke with one pair. Bad players do it a lot. It’s part of what makes them bad. But that doesn’t mean that’s it’s always a thing to avoid.

That's not really the source of the adage. The source of the adage is that it's a solid truth in the context of the games that gave rise to the adage. Those games tended to be deep money cash games. In deep money games it's important to keep pots small with vulnerable hands. To relate it to some comments I've made on my mathandpoker blog, (I'm having some database errors on that blog, so that link might not work) what becomes important in deep money no limit games isn't EV, it's risk-adjusted EV. Risk-adjusted EV is a concept from mathematical finance that's based on mean/variance efficient frontiers.

The way to control risk in deep money no limit games is to keep the pot small enough so that you can easily get away from vulnerable hands if things go badly for you.

Ed gives an example of a short money game where the hero got all-in on a red flop of 566 with a pair of black queens. Flush draws, straight draws, three sixes, overcards, all kind of draws that put his hand at risk and at best he has a 2-card redraw if he's beat.

As a prelude to the hand history he says,
Sometimes one pair is more than enough to get all-in with, and if you go broke, you go broke. An example of this is today’s Q&A.

That's nuts.

It turns out that the villain had a black AJ and the QQ was far ahead. But with that flop, there's no way to put a typical villian on a black AJ unless you've shown a history of being willing to lay down pairs on drawy looking flops and he's shown an ability to overplay weak draws. Without that information (which I didn't see anywhere) this is not at all an example of when an ovepair is more than enough to get all-in with. Not even close.

While it turns out I actually agree with Ed that in the situation as given it probably is right for the hero to call a check-raise on the flop with all his chips (which is how he got all-in), the reason it's probably the right thing to do isn't because his hand is worth it, it's because he didn't have many chips.

There was $3.30 in the pot preflop, hero bet $2 and the villain goes all-in for $2.50 more. Sure call an extra $2.50 once the pot is over $7. But not because you have a hand to go busted with, becuase the money is short and you're getting a price.

The didn't go busted anyway when the villain rivered an Ace, he had the villain covered.

Ed seems to have completely missed the point. About the only time top pair (or an overpair) is a hand to go busted with is when you're short stacked and the pot has gotten big relative to what chips you have left. Or, as is the actual case in his example, when you're not really going broke.

Labels: , , ,

Saturday, May 19, 2007

Math versus psychology

Dichotomous Thinking
Mathematics v. psychology

One of the most prevalent instances of intellectual comfort food among poker players is the idea that limit poker is about mathematics and no-limit is about people and their psychology. Such thinking basically gives the weak player an out. If you’re not doing well in limit poker games then you can tell yourself that you’re just not mathematically oriented, that you’re more of a people person and should shift your game to no-limit. Well, good luck.

The false dichotomy appears to come from people who think poker related math begins and ends with calculating pot odds. It’s true that pot odds doesn’t really come into play in no-limit games as often as it does in limit – and that even when it does come into play it’s importance is often just marginal. But, there’s a lot more to the mathematics of poker than pot odds. The distribution of possible hands your opponents might hold is a mathematical concept. Balancing your action against your opponent’s likely reaction is mathematics.

Poker is a mathematical game. The kind of mathematics that might be useful depends on the situation, often depending a great deal on your opponents. The whole point of the game is to exploit the mistakes of your opponents. Mathematics is an important tool in both identifying what kind of mistakes your opponents make, and in developing strategic responses to exploit those errors. If your opponents are making gross errors it’s probably enough to just sit back and let the money fall into your lap. But, if they’re just making ordinary errors you usually have to actively go out and get the money.

If you can’t do that in a limit game then you probably won’t succeed in a no-limit game either. In a talk Chris Ferguson gave right after he won the WSOP he said, “If you don’t think mathematics is important in poker, then you just don’t know the right mathematics.” He was primarily talking about game theory. Game theory is in some ways the mathematics of rational people. This isn’t a game theory text, but I talk about it a little in the chapter on strategic thinking. Other mathematics topics I’ll get into some are optimization theory, bayesian analysis, decision theory, and artificial intelligence.


Friday, May 18, 2007

Popular Wisdom

02 Popular Wisdom

Before we get into strategic ideas about no-limit hold’em, let’s spend some time on popular wisdom about the game and why following popular or conventional wisdom isn’t always wise. Just because an idea sounds good does not make it a good idea. There are a lot of really bad ideas that sound good on the surface.

People tend to be attracted by simple ideas that tend to dichotomize complexity. You can see this effect strongly in political discourse. The popular ideas are the ones that can be expressed as a simple either/or television sound byte, even if the idea is based on absurd logic. It’s comforting to be able to divide things into either/or categories. It gives us a semblance of control, a sense of understanding. Simple assertions of faux truth are a form of comfort food for the brain. But while facing the complexity of reality won’t always bring you comfort, it’s usually the best way to win at poker.

The game of poker, and particularly no-limit poker, is not a simple game of either/or, black or white, win or lose. Almost everything that happens tends to occur on a graduated scale of some sort. And it’s seldom on a linear scale. It’s a dance. You have to constantly be weaving and dodging, setting traps for your opponents to fall into while evading the traps they’re setting for you. When you put an early position raiser on a hand it’s not enough to think either he has a big pair or he has AK. He might also have a pair of eights, or he might have a 67 suited. Those hands might not be as likely as a big pair or a big ace, but you ignore the possibility at your own peril.

It’s possible to rationally, even mathematically, analyze such a dance. It can get complex, but it’s certainly doable. But when forced with the need for a complex analysis, most people just let their eyes glaze over and they fall back on intuition. The problem is that when faced with complex, probabilistic situations our intuition almost always fails us.

This might seem to contradict some of the claims in the recent bestseller, Blink. But it really doesn’t. Blink is a book about first impressions. But it doesn’t claim that first impressions are always reliable. Sometimes they are, and sometimes they go very, very wrong. Your first impressions are important. But when the impressions are about a complex, probabilistic situation they probably aren’t reliable. Humans have some strong natural biases and blind spots when analyzing probabilistic events.


Thursday, May 17, 2007

TV, Tournaments, strategic thinking

Influence of TV

I wrote my first poker book in 1999 (it was published in 2001), long before the huge growth in poker triggered by television coverage of no limit Hold’Em poker tournaments. When I wrote my first book limit hold’em was the primary game, no limit games where very rare in cardrooms. So I didn’t devote a lot of space to no limit hold’em in that book. Most of the TV coverage has been of no limit hold’em tournaments, which has created a lot of interest in no limit hold’em among new players.

Limit games are still common, but small blind no limit games have become the predominant game being spread in many cardrooms these days and interest in the games is growing. A $50 or $100 buy in no limit game isn’t really all that hard to find. Three years ago it was almost impossible to find such a game in a cardroom.

It’s not just the TV coverage that’s spawned the growth in popularity of no limit hold’em – the internet has had a lot of influence also. The economics of an internet poker room allows them to spread penny-ante games. The marginal cost of them opening an extra game is essentially zero so they can profitably spread games that only rake pennies per hour – providing players an introduction to no limit hold’em that only requires them to put one or two dollars at risk.

Of course online poker rooms do face other costs, the risk of being faced with criminal sanctions from the US government is very real and unpredictable.

Of course TV coverage and the availability of internet games haven’t operated on the poker boom independently. The boom in both internet games and TV coverage was fueled by Chris Moneymaker’s win of the World Series of Poker (WSOP) in 2003. Interest skyrocketed when the internet laying accountant from Tennessee became an instant millionaire from winning the WSOP. Moneymaker had the effect of creating a bridge between the internet and TV as far as poker is concerned.

Tournament Strategy

Most of the TV coverage is of the final table of a large, multi-table event, the last 9 or 10 players of hundreds or thousands of players who started in the event. In the final stages of the event a poker tournament plays differently than a regular poker game. There are fundamental strategic differe3nces between tournament play and the play of regular poker games. Play is faster paced and more aggressive. There are at least four reasons for this: a structured payout schedule, limitations on time, a limit on total chips in play, and player fatigue.

The most important strategic reason tournaments are different from regular games is that tournaments don’t pay winner take all. When you buy in to a tournament you pay full value for your chips (there are some exceptions in re-buy events that I’ll get to later). But when you win a tournament you only get something like 30-50% of the original purchase value, usually towards the low end of that range. That’s because some of the money was paired out to losing players 2nd place got some, 3rd place got some, etc. You have to win all the chips to get 30% of the money. That mismatch in chips values makes for strategic differences between final table play in a large tournament and play in a regular game where you cash in any chips you win at face value and you can do so at any time. I’ll be pointing out some of the details of these strategic differences throughout the book.

Another factor that affects strategic play is time. Theoretically a cash game can last forever. Players leave, and new players sit down. After 24 hours it probably won’t be the same players, but the game can still be going. Tournaments don’t have new players arriving. And the old players can’t leave until they either go busted or win. So there has to be a device to ensure the end of a tournament. You could just have a tournament finish after a fixed amount of time, but tradition has settled on playing until one player has all the chips (even though he doesn’t get all the money).

But if you have two players who are fairly evenly matched, both with a log of chips, it’s entirely possible that they could play for a lifetime, just trading a few chips back and forth. That wouldn’t be a good result.

To ensure that the game eventually terminates, tournaments are played with escalating blinds and antes. The blinds are forced bets that are required every hand. Money will get put in the pot whether there’s any players who want to play that hand or not, and somebody will always win something, insuring that chips get transferred among the players. The blinds just get bigger and bigger even though the total number of chips in play stay the same. This escalation of the ratio of blinds to chips puts pressure on all the players to get in and mix it up. You can play a sit and wait game for awhile. But you’ll eventually reach a point where you simply can’t do that anymore, when you’ll have to take a stand or go broke posting bigger and bigger blinds while you’re waiting.

This brings us to a limitation on chips in play and the subsequent limitation on stack sizes, the third factor that often drives strategy in tournaments. Stack size, how many chips you have relative to the other players and to the blinds, makes a difference in how you should play in various situations. Stack size situations aren’t unique to tournaments, they also arise in regular games, but such situations occur more frequently in tournaments because the playing structure calls for regular increases in blind sizes and you can’t add chips to your stack during the tournament (at least in the late stages).

You probably can’t bluff a player who only has one chip left. So, the stack sizes of you and your opponents can have a major strategic influence. Stack size mismatches can occur in either tournaments or regular games. But since players can just keep buying chips in cash games, stack size mismatches don’t occur automatically.

Since you can control your own stack size in regular games, the mismatches of primary interest in cash games are from the point of view of playing against short stacks or extremely large stacks. There’s no reason for you to ever play in a cash game with a short stack because it puts you at a distinct disadvantage and you always have the option of cashing out and coming back another day. But in tournaments you don’t want to give up just because you lost most of you chips, so playing a short stack is an important tournament skill, while playing against a short stack is an important skill in both tournaments and cash games.

The ultimate short stack story is the chip and a chair story of Jack Strauss. The year he won the WSOP he was all in at one point and lost that pot. Then he discovered a single $500 chip that had been covered by a napkin and into included in his bet. It turned out that he’d only thought he was all in. The ruling was that the chip played, he was still in the game. He parlayed that one chip into a first place finish.

The fourth reason is one that isn’t often discussed. People get tired. In cash games you should never play tired. Period. Go home. Take a nap. There will be another game tomorrow.

Even if everyone at the table is equally fatigued, any edge you might have had at the beginning is probably gone. Fatigue is a great equalizer. But in tournaments you sometimes have no choice but to remain at the table while battling fatigue. The ability to maintain mental alertness and avoiding fatigue is a much more important factor in tournaments than it is in cash games. You can avoid marathon cash games (and I recommend you do so). You can’t win a moderate sized tournament without finishing a marathon.

The payout schedule, the ratio of blinds to your stack, and the ratio of your stack to that of other players can all have a strong effect on strategic decisions. The only one of these situations that’s totally unique to tournaments is the payout schedule. You should never play short stacked in cash games. You should just quit if you get short-stacked and don’t have money to add to your stack. But even if you don’t get short-stacked yourself, you will encounter other players who get short-stacked. From a strategic point of view, knowing how your opponents will likely be playing is one of the most important inputs into your decision making process, if not the most important. So, knowing how an opponent with a short stack will likely respond is important even if you’ll never be short-stacked yourself.


Aliens from outer space

The readership on this blog isn't very high, so I tend to notice where visitors come from. Recently I've been getting readers who get here by clicking on a link at

But, it's not an ordinary blog. It's a secret society, some modern branch of the FreeMasons or something, invitation only blog.

Maybe this makes me weird, but I just think that's weird.


Friday, May 11, 2007

Variance, capped games, rest

I used to play a lot of no-limit (and spread limit with wide spreads) draw poker in California. Mostly San Bruno and San Jose.

The games in San Bruno where all no-limit games. San Jose had a city
ordinance capping any bets at $200,. so no limit wasn't legal. But, they had
spread limit games, mostly $4-$40 draw and sometimes $20-200 lowball. I played
in the lowball spread limit game sometimes when it was short-handed, but mostly
I played the spread limit draw there.

The standard structure for the first betting round required that you raise the blinds, you couldn't limp in by calling the blinds. San Bruno was mostly $4 to go (4 to go means 4 is the minimum bet) no-limit, with $2 winner blind (winner blind means the winner of each pot must put in an out of position blind the next hand), to mostly $4-$40 with 1-1-2 blinds also was part of the reason for an increase in earn when I moved from mostly San Bruno games to mostly San Jose games -- the
spread limit started out with bigger pots and was really a bigger game, plus it
kept the bankroll fluctuations more stable. The $40 bet cap meant that one bad call wouldn't destroy me. And, San Jose had fewer cheats. I think the biggest reason I did better in the San Jose games though was my session habits.

I lived in San Francisco at the time. So travel time did enter into my decisions about session length.

I used to keep real detailed records. I'd even make a list of the players at
the table every hour. I don't do that anymore. But, back when I did I noticed
a big difference in results by length of session. My win rate in the first
hour was bad. In hours 2, 3, 4 it was very good. After 4 hours I started
taking a bath. My win in hours 2-4 was so good that I was actually losing
money after 4 hours but would still end up a 10 hour session ahead.

Anyway, before I noticed that I was just playing once a day, pretty much every
day, and playing anywhere from 6-12 hours a day. I'd bought into the silly
idea that every hour of play was an earn.

After I noticed the way my results fluctuated, I changed the way I scheduled

I quit playing every day. I had an RV. I'd just play in chunks of a few days
at a time, parking my RV in the parking lot (Garden City security guards made
me park it down the street). But, I'd play 4 hour sessions. After 4 hours I'd
cash out and leave the room. I'd eat, (I didn't eat in the room) or go rent a
hot tub for an hour (that's where I'd shower, it was right across the street
from GC), or take a nap, or just have a cup of coffee and read the paper. I'd
stay gone at least an hour.

After my meal, or nap, or whatever, I'd go back and play another 4 hours. If
the game was bad I'd leave early, but I'd never play longer than 4 hours. I'd
do that for 3-4 days, just immersing myself in poker, but only in spurts, then
go home for 3-4 days. I was still playing 12 hours a day, but not long

My income tripled when I started doing that, even though I was playing slightly
fewer hours a week. (it was close to the same)

Back then gambling was my only source of income. It's not anymore and I again
often just play all night and piss away chips. I need to stop that.

Monday, May 07, 2007

Flopping a straight

Flopping a straight can sometimes be problematic. It's not always clear how strong that hand is, straights can be pretty iffy hand, vulnerable when they're getting action.

You just never can be sure. If you're getting heavy action it might be from two pair, which tends to happen often when a potential straight is on the board because of players playing suited connectors. If that's the case you're in good shape, they're drawing pretty thin. But flush draws and draws to better straights aren't drawing quite so thin.

There was a hand discussed on rgp a while back that I think illustrates some of the problems that can crop up with flopped straights. Not so much in terms of how the hand actually played out, but in terms of the things you need to think about with such hands.

It was a 2/5 game, with most stacks about $500, one aggresive player had about $1,000. This hand put that big stack in mid position. He opened for $20, one caller, our hero has a T9 of spades and calls from late position. The button and the big blind call after him.

I think the preflop call is pretty automatic. If the stacks had been shorter it's a pretty easy fold. I think a raise is out of the question here.


It's checked to the original raiser, who bets $25 into an $80 pot. What the hell is that all about? Our hero makes a minimum raise, the other two guys fold back to the original raiser who calls.

I don't know what's going on here. I'd have just called the flop or made a more substantial raise. Our hero said he made the small raise as an attempt to fish for a
re-raise. I don't like fishing for a re-raise when it's not clear whether anybody actually has a hand to re-raise with or not. The $25 bet by the aggressor doesn't look like a big hand to me, not with that flop. It looks like AK to me (but things always look like AK to me).

I like calling here. I think you're going to be more likely to get an overcall by a call than a re-raise by a weenie raise. With my hand and this flop I don't really mind continuing on to the turn with players behind me, I don't feel any need to raise to by myself the button or anything.

If the flop had been two-suited I'd be thinking very differently. I don't like just calling unless I'm fishing for an overcall. I also don't like just calling when somebody might be drawing to a flush.

A 10D hit the turn, possibly counterfieting the straight, possibly giving an AK a flush draw, possibly giving the other guy a better straight, although that's somewhat unlikely.

The hands that I might put the original raiser on that are helped by that TD are AKD, 9 9 or 10 10. I think it's real doubtful he has Q 9, so I'll only worry about that hand a little bit. If the turn card had been a 9D I'd worry a little about a Q 10, but I'm just not going to worry about the Q 9.75

The anti-hero checks. At this point our hero bets $75. He commented that his after thought is that $75 is a terrible bet. I'm not so sure it's terrible. I made have bet a little more, but I think I'd want a call here. I like our hero's hand at this point. Although he's a little more vulnarable after that ten fell than he had been on the flop, I don't see any reason to not think he doesn't still have the best. There are some possible scare cards on the river -- cards like a jack, a nine, or a diamond might slow me down quite a bit, but the most likely river card doesn't include any of those cards. He said he made the bet out of fear, but I don't know what he's afraid of. The anti-hero calls quickly.

The river brings 3D, putting three diamonds on the board. The anti-hero moves all in -- our hero has $350 left, getting about 5/2 on a call.

I think he has to call here. The anti-hero can't put him on a backdoor flush draw so has to think the hero will worry about a flush when he goes all-in on that river card. He could very well be overplaying an overpair here, hoping the hero will lay down two pair.

He did call, the anti-hero had 4D 5D for the flush.

I wouldn't have put him on that specific hand.

Should the hero have bet more on the turn? I think a little more, I'd probbably have bet more like $120, maybe even $175. But I don't think it would have changed the outcome. I think he'd have been called unless he made a huge overbet on the turn. And, I don't see any strong reason to do that, he's ahead enough on the turn that I just don't see the problem with betting as much as you think the anti-hero will call.

But, then again, I'm writing for a living, not making TV appearances, so what do I know?


Sunday, May 06, 2007

Big pots in small games

Karol of I had Outs has a quote from the author of Hunting Fish: A Cross-Country Search for America's Worst Poker Players
It’s $2-$5 and we’re playing very deep. At the start of the hand I have about $1,900 in my stack, and two people at the table have me covered, including one of the principles in this hand.

A fairly loose, rather aggressive player with about 3k in his stack, open-raises for $35. He’s been taking some liberties, I think, and when I see A-K, I decide to try and isolate. I raise to $125. FOUR PEOPLE call $125 cold. What book prepares you for a $500 preflop pot in a $2-$5 game?

While that's not typical in a 2/5 game, I'm don't think it's all that unusual, I think he needs to get out more.

I'm reminded of one pot in a 1/2 game at Gold Strike in Tunica. Four of us get all-in preflop, two with about $1,000 and the other two with about $500. Three pros and a land developer from Memphis. Three of us had AK. One of the pros had a 57 and he spiked a 7 to take down most of the pot.

That was a pretty big pot.

Another night in the same game the pot was over 3k preflop, heads up with AA (me) and AQs (the winner).


Don't fall in love with top pair

I ran across this hand on the internet.

Our hero is in a 50c/$1 game (I think) with slightly over $100 and brings it in for $3 with JTh. Button makes it $6. He calls, everyone else folds. Flop is jack high with 1 heart and two diamonds, he checks, button bets $3, our hero makes it $10.

I don't like the check/raise for so many reasons I'm not sure where to start. A bet would have been fine. A check/call would have been fine. But his hand just isn't strong enough for the check/raise. A mediocre top pair with a mediocre kicker with a player behind who had re-raised preflop is not a strong hand.

But that's what he did, I think setting himself up for big trouble. The turn is a 7h, putting a pair on the board. He bets $15, the button goes all in, raising about $70 more.

Now he just has to give it up. He's shown much more strength than his had warrents, and the other guy doesn't seem to care how strong he thinks he is. He's already lost more money than he should, there's no need to go broke here.