Working towards the big picture

The ultimate "truth" of poker is the answer to the question, does your strategy defeat their strategy? (Or in other words: if you played forever, who would come out ahead?) The challenge is to work towards this truth using the hands you play as evidence. Steps in that direction:

1. Results

Let's take a hand as an example. You're playing 1/2 Hold'em with 50 big blind stacks. It's folded to you in the cutoff and you open KK to $6. Button and small blind fold and big blind raises to $18. You go all-in for $100 and he calls with JJ. He hits a Jack and wins the $201 pot (the $1 is from the small blind). You lose $100. Raw cash results aren't meaningless -- given enough hands, they will begin to approach your expected value in the games you play -- but "enough hands" here means many thousands. In the short term results can be, of course, very misleading.

2. Expected value-adjusted results

This is a simple way to account for one kind of luck. Whenever all the money goes in you calculate your expected value and consider that the result of the hand. In our example hand, all the money went in pre-flop. KK beats JJ 81.5% of the time, so our expected value is .815 * 201 = 163.8. Subtract the $100 we invested, and that means we made $63.80 on this hand. We've stripped away the luck element that kicks in after the money goes in the middle, but there's still a lot of luck in how the cards are dealt out to begin with. We were lucky to get dealt KK, the second-strongest starting hand, and even more lucky that our opponent held JJ, the fourth-strongest. If he had AA we would have gotten all the money in way behind; if he had 72 he would have folded and would have just won the blinds.

3. Our hand v. their range

The concept of a range is probably the most important idea in poker strategy. A range is all possible hands you can hold given your actions. In the example hand, the big blind had JJ, but let's say his range for raising and calling a shove there is pocket pairs tens and better, ace-king, and ace-queen. Our equity against that range is 67.6% -- still ahead, but not by as much. His range still includes JJ, as well as QQ and TT, all of which have only 18% against KK. But he can also have AQs (32%) or even AA (82%). (You can download a free tool for calculating these numbers at pokerstove.com). According to these numbers, our profit for the hand is .676 * 201 -100 = 35.88. Not surprising, given that we had such a good hand.

4. Our range v. their hand

Same concept, but flipped around. Now we'll calculate the equity of our range against his actual hand. Let's say our range for opening the cutoff then shoving over a raise is all pocket pairs, AJ+, and all suited aces. I won't get into the reasoning behind that range, or whether it represents a good strategy right now; but if you're wondering why our range includes so many more hands than the big blind's, it's because we pushed all-in, so our range includes bluffs, but he called an all-in bet, so he doesn't have any bluffs. Anyway, that range has 35.9% equity against JJ. According to this measure, our expected value from the hand is .359 * 201 - 100. So we lost 27.84 on the hand. This makes intuitive sense: in actuality we held KK, the second-strongest starting hand in Hold'em, but our range is comprised mostly of weaker hands. It also suggests something that will be no surprise to experienced players: his strategy of getting it in with jacks 50 big blinds deep is a winning play, even though it didn't appear to work out well in the actual hand.

5. Our range v. their range

Using the ranges described above, the equity of our range against his range is 39.3%. So when all the money goes in, we lose an average of .393 * 201 - 100 = -21. This still isn't the whole story though, because both sides had several opportunities to fold (or just call) along the way. In particular, he had to call our all-in bet to get to showdown. So while we are generally behind when all the money goes in, we should be making money on the hands that don't go to showdown because sometimes our bluffs will work and we'll take down the pot. Whether or not that compensates for the money we lose at showdown depends on just how often he's folding. If he's never folding, we should shrink our range to just the strongest hands. If he's folding a lot, we should expand our range to include more bluffs.

6. Reciprocality: a useful shortcut

This concept doesn't fit neatly into the hand range framework described above, but it can be useful for getting an idea of whether or not you're making money. (Reciprocality isn't a real word, but while reciprocity is, it doesn't mean the right thing, so there you go.) The basic idea is to ask what would happen if you and your opponent switched places. In the example hand, as long as we're both reasonable players, we're probably getting all-in here. Any time you would do the exact same thing with places reversed, no theoretical money changed hands, despite appearances. It's only when your strategy differs from your opponent's that you can make money.

Poker Sucks

I had half an hour to kill at the auto repair shop so I downloaded a poker app for my phone. It's been a long time since I played one table at a time with nothing at stake, and when played like that -- in other words, when played like most games are played all the time -- poker is incredibly boring. There's a huge amount of down time. When you do get a playable hand the cards fall one way or another and there's not much to do but shrug and move on.

Which isn't to say that I don't like poker. Parts of it are interesting: trying to construct an optimal strategy that your opponents can't beat even if they know what you're doing, and finding ways to adjust that strategy to exploit the mistakes they're making. But these things play out over thousands of hands. One hand at a time you're mostly seeing variance. Playing poker one hand at a time is like studying a great whale through a microscope. You won't have any sense of what you're really looking at unless you already have enough knowledge to recognize the whole from the smallest parts.

As a casual game it doesn't get much worse than Texas Hold'em, which makes me wonder about the allure of the home game. I guess it's mostly an excuse to drink beer and hang out with your friends, but even so, I'd rather do those things while playing Hearts, or Stratego, or Monopoly.

World Series

There's some guy who played Ultimate Frisbee for Michigan State who did pretty well in the World Series Main Event a few years ago. Now he travels around, plays Ultimate, and plays in a live poker tournament every now and then. People keep telling me about him, and it's kind of driving me crazy. The thing is, he's probably not even good.

Online players have a strange relationship with the World Series, while the World Series has a strange relationship with the poker world as a whole. I can't think of a competition in any other game or sport that occupies quite the same place as the World Series. Maybe the closest is the NBA All-Star Game -- a beloved spectacle, far from meaningless, but equally far from the sport's competitive heights.

Nonetheless, after years of pitching the World Series as poker's ultimate championship, ESPN has made that perception into a sort of reality. The glamor and media coverage make the World Series a favorite of casual players, people who wouldn't put down 10k on any other poker tournament. Which means that, as compared to other poker tournaments with similar buy-ins, the Main Event is distinguished by the low level of competition. And you can turn on your TV at almost any hour of the day or night and see self-serious dorks in sunglasses playing awful poker.

That makes it seem like a great opportunity for good online players to make money, but it's counterbalanced by a number of other factors. First, you have to get yourself physically to Vegas. Second, the tournament features a grueling 12-day schedule. Even if you figured to be worth twice the buy-in (representative of a massive skill advantage), that's still 12 long days' work for 10k, not a spectacular wage by poker standards. Of course, if you bust out early you don't have to stay around for the full 12 days, but the fact remains that the tournament represents a large time commitment. And finally, no matter how good you are, by far the most likely outcome is that you'll walk away out 10k. Only about 10% of the field makes any money back.

Dan Harrington compared playing in big live tournaments to playing the lottery: "If you're bad, you don't have a ticket. If you're average, you have one ticket. If you're good, you have two tickets, and if you're great you have six tickets. But you're still in the lottery."

So I don't see the World Series as a great opportunity to make money. But people still ask me if I've played in it, and I kind of want to be able to say I have. Maybe at some point if my poker job goes well enough I'll be able to justify spending 10k on it.

Party Poker

Something strange and wonderful happened the other day. Pokerstars had a software glitch that caused the wait list feature to stop working. What's supposed to happen is that when a player leaves the table, the program alerts you and allows you to take your reserved seat. The glitch prevented you from sitting down, but left the seat reserved, blocking all other players from sitting there either. Most regulars play many tables and the easiest way to do this is to join a lot of waiting lists. When the glitch came up, the regulars mostly quit for the day.

But not the fish. They kept happily plugging away at one or two tables. So while finding a seat was more of a challenge than usual, it was well worth the effort. Over the past year I've worked my way up from $.05/$.10 to my standard game now, $1/$2. But after the software glitch the $1/$2 games played like $.05/$.10. It was a nostalgic throwback to those early days and a reminder of how far I've come. Back then, even when I knew my opponents were playing badly, I was often unnerved by the chaos of poker and unsure of my own plays. But now I felt confident, almost giddy. Whatever money they had on the table was mine, it was just a matter of time. As poker players say, it was like printing money.

It's hard to describe the difference between playing against fish and playing against regulars. Most regulars are going to play mostly the same as you do. They're familiar with the math of the game, with all the typical situations that have been endlessly discussed and analyzed. Getting an edge is about making subtle adjustments and counter-adjustments, tweaking your game here and there. But fish often make plays that donate large chunks of money with little effort or adjustment on your part. A typical thought process against a regular: "He's probably noticed that I'm 3betting him a lot, so he's probably adjusting by 4bet bluffing. I'll add some small pocket pairs to my 3betting range with the intention of shoving over his 4bets." A typical thought process against a fish: "I have a good hand. He never folds. Bet bet bet!"

Pros who have been playing for a long time look back fondly to the days of the poker boom, when the games were flooded with fish. They often call those the Party Poker days. Party Poker was the name of the most popular site then (which was later crippled by changes in US online gambling laws, but that's a different story), but it also refers to the general atmosphere of the period. Poker was easy, fun, and lucrative. I missed the Party Poker days, but I got a taste of them when the software broke. It didn't last long, of course -- they fixed the software within an hour. But it was fun while it lasted.

When the Numbers Say Go Nuts

After explaining what I do for a living, I've had several people ask if I just play "solid poker." What they seem to mean is playing what could be called an honest strategy: betting or raising good cards, checking or folding weak cards.

I'm not sure how I would define "solid poker," but a reasonable definition might be playing in a way that is difficult to exploit. In this sense an honest strategy is not solid because it's very easy to exploit. When they bet or raise, you fold unless you have a very strong hand. When they check, you bet. Their actions translate to reliable information about their hand that you can then act upon.

So while honest play isn't really solid, the association between the two ideas is common and stretches beyond poker. After Bill Belichick went for a controversial and risky fourth down conversion, Tony Dungy criticized the call on ESPN by saying "you have to play the percentages"...even though analysis of the percentages showed that Belichick made the right call by going for it. But to Dungy and many other commentators, "playing the percentages" was synonymous with playing conservatively. The numbers, they felt, would always point to conservative options, while aggressive strategies could only be motivated by emotion.

In poker the opposite often holds true: the numbers suggest a highly aggressive approach, but many players play too conservatively for emotional reasons. In The Mathematics of Poker by Bill Chen and Jerrod Ankenman, the authors find that a "high level of aggression is supported by analysis. When we study toy games [simplified games similar to poker] we are often surprised at how aggressive [the optimal] strategies are." While No Limit Hold'em has not been solved, analysis suggests that a mathematically "correct" strategy would appear to most players to be psychotically aggressive. Nonetheless, many players are reluctant to push their aggression because they're uncomfortable with the risk involved in going for a big bluff. In other words, emotional hangups prevent them from going for the mathematically correct play.

So why the persistent association between analysis and conservative approaches? It may be because the most visible and disastrous examples of under-analysis are often over-aggressive. In poker this would be the "maniac," a player who bets and raises compulsively with too many hands. Not only does this type of player often go broke, he does so with the full attention of everyone at the table. From the analytical point of view, an overly cautious approach is no more correct than a maniacal one, but it's far less conspicuous.

Sorry

So, yeah.