Thinking in Strategies

One of the most useful things I’ve learned from poker is that it is often more helpful to think about a strategy, and how the current situation fits into it, than to try to grapple with the current situation in a vacuum.

For example, when you have a strong hand, your first inclination might be to bet; but then you remember that poker is a game of deception, and if you bet your opponent will surely know you have a good hand, so maybe you shouldn’t bet. In the heat of the moment this is quite a difficult knot to untangle. Many people place a high value on deception and end up checking the vast majority of their best hands. They don’t do it as part of a preconceived strategy, but approach the problem anew each time they hold a strong hand, and more often than not the desire to trick their opponents wins out and they check.

If we take a giant step back, how does their strategy look? When they have a good hand they hardly ever bet; and when they are betting they hardly ever have a good hand. Well, that can’t be right. Few would endorse such a strategy, but it is in fact how many people end up playing.

Rather than approaching each hand in a vacuum, it’s helpful to think about an overall strategy. Clearly our best hands are the ones we most want to bet with, since we want to play a big pot. But if we bet with only those hands, it will be obvious that we have a great hand whenever we bet and our opponents can simply fold. Some amount of deception does seem to be necessary. We could try to achieve it by checking our best hands, but then we can’t really bet anything else either, since then we’d never have anything when we bet. Unless we want our whole strategy to be passive, we need to bet some other hands in addition to our best hands. In broad strokes, a good strategy often involves betting most of your best hands, along with some bluffs and semi-bluffs.

I find this way of thinking to be helpful outside of poker as well. In the lead-up to the Iraq war, I found the cases for and against the war very confusing. They have weapons of mass destruction. Or maybe they don’t. Or maybe they do, but they don’t intend to use them against us. Saddam Hussein is a horrible tyrant. But is it our job to depose tyrants? They support terrorism. Or do they? Maybe only a little bit.

It seems to me more helpful to ask, what is our strategy for invading foreign countries? I’m not at all sure what our actual strategy is, but I have a sense it would be difficult to come up with a strategy that would have endorsed invading Iraq without also recommending the invasion of many other countries.



I just came across this old post by Bill Barnwell at Grantland about momentum, or as he calls it, nomentum, because he believes there’s no such thing. As is the case with the hot hand theory, which I wrote about before, there’s a striking disconnect between players, commentators, and fans, who seem to put a lot of stock in momentum, and stats guys, who flatly deny its existence.

I wonder if further research into momentum might follow a similar pattern as the hot hand theory: initial popular assumption that it’s real and important -> rudimentary research uncovers no evidence of the effect -> more nuanced research suggests that the effect is real, but less drastic than commonly believed, and offset by compensatory effects.

Part of the difficulty is that it’s not at all clear what momentum is. The word is used to describe a variety of different phenomena. In order to wrap my mind around momentum, I tried to nail down a definition. At its most basic level, momentum is the idea that what happened before is going to keep happening. But isn’t that just evidence-based reasoning? We all use the past to try to predict the future.

What makes momentum special is the extraordinarily high weight it puts on recent events. Again, this makes sense, up to a point. In trying to predict the result of the Super Bowl this weekend, we should clearly put more weight on the Patriot’s victory in the Conference Championship two weeks ago than on the team’s performance in 1974, which featured no players or coaches currently on the team. But how much more should we value the Conference Championship than the Patriots’ performance in week one of the regular season?

It seems to me that momentum isn’t really a unique idea, but a form of evidence-based reasoning that puts an especially high value on recent events. Therefore, a better question that “Is momentum real?” will be “How heavily should we weight recent events?” In most cases, I suspect momentum believers value recent events to a degree that can’t be justified.

Heads-up Limit Hold’em Solved

The University of Alberta’s Poker Research Group announced they have solved heads-up limit hold’em by creating an effectively unbeatable strategy.

What does this mean for poker players? Not much, at least in the short term. Heads-up limit hold’em had already largely died out. Heads-up (one-on-one) poker is generally not offered at all in casinos, and increasingly less popular online. Likewise, limit poker has largely given way to no limit or pot limit games. So heads-up limit hold’em is at this point a fairly obscure poker variant for human players.

Nonetheless, the achievement is a landmark for computer poker and has some interesting implications. I had been thinking recently about the question, why are computers better at chess than at poker? Arguably this new announcement calls into question whether that’s even the case, but I think it’s still safe to say that computers are indeed better at chess. Computers have been much better than the best human chess players for years now, while it is unclear if they are better than the best human players in many popular forms of poker.

I imagine many people’s first answer will be that poker rewards skills such as bluffing and reading opponents that computers are not good at. But in fact, computers bluff just fine, and while it is indeed difficult to teach a computer to read cues such as facial expressions, there is still no advantage there for a human adversary: the human can’t “read” the computer at all.

Maybe one reason computers have been bad at poker is that humans are so bad we don’t really know what to teach them. As with chess, computers are getting good at poker not by emulating humans, but by excelling in their own computer-y way. The Alberta team started with a program that bet completely at random, then re-evaluated its play and adjusted. Countless iterations of this process eventually produced an unbeatable strategy. In other words, they started with no preconceptions about how the machine “should” play. Poker is so strange and confusing that the best way to learn may turn out to be to teach computers to teach themselves so that they can teach us.

I’ve found that it is possible, more or less, to turn your brain into a chess machine. If you play and study enough you get to a point where the best moves often seem natural and obvious. This seems to be less true with poker. While experience will help you beat a human opponent (when you sense he’s uncomfortable, you raise), it may not help you much if you’re trying to play “optimal” poker, the kind you’ll need to beat a computer. In many cases, the best strategy involves mixing together different options. For example, maybe you bet 60% of the time and check 40%. This idea – that neither betting nor checking are right or wrong, but must be mixed in the right frequency to form an optimal strategy – is very difficult for humans to understand and implement.

The biggest reason that computers are better at chess is probably a boring one: people have been working on it for longer. Building a chess-playing machine was an early grail for computer programming, and many of computer science’s brightest lights worked on it at one time or another: Alan Turing, Claude Shannon, and many others. It is only much more recently that the same kind of attention has been paid to poker.

It’s natural to wonder if computers’ mastery of poker might eventually kill the game. This doesn’t seem to be happening in chess: if anything, computers have made chess more interesting for humans by improving analysis. But of course, in poker money is at stake, so there is more of a concern that players will use computers for a competitive advantage. My guess is that this will be a big problem in online poker, maybe eventually making it unviable, but won’t have much impact on live poker. Most people, it seems, play however they like, without much concern for theory.

The Storytelling Animal

I recently finished The Storytelling Animal by Jonathan Gottschall. This sentence struck me as being particularly important for poker:

The storytelling mind is a factory that churns out true stories when it can, but will churn out lies when it can’t.

A big part of being a poker pro, or succeeding in any area where luck plays a large roll, is constantly debunking the specious stories your mind “churns out.” To a beginner, poker seems to be all luck. Whoever has the best cards wins. As we get better, we start to see the ways to influence our luck, by getting maximum value when we have the best hand, getting away cheaply when we’re beat, bluffing judiciously, and so on. But many skillful players overshoot the mark in estimating the roll of skill. Poker pros try to strong-arm this chaotic game into something predictable. It’s true that if you play enough hands, and play skillfully enough, you have a very high chance of winning, but that doesn’t change the fact that, by any reasonable measure, poker is mostly luck.

Likewise many of the events we encounter in poker, which seem so redolent of meaning, probably come down to luck. “I can’t beat this guy.” Maybe he got lucky against you in a few hands. “I knew he was bluffing.” Maybe you were lucky he was bluffing this time. “That hand really turned my session around.” Maybe you were unlucky before, and lucky after, that hand. “I had a good feeling about this hand.” Really?

Another poker pro, a winning player, told me, “I run bad with draws.” I imagine he missed some draws in big, memorable pots, but his storytelling mind turned that into a story that’s not true. A poker player can’t be bad at draws the way a basketball player is bad from three-point range. The cards are dealt randomly. The problem with false stories is that they’re likely to influence how you play. This player likely plays his draws too passively because he “knows” he won’t hit. If you believe all the stories your mind tells you, you’ll end up playing based on your history with luck, rather than your best guess at a sound strategy. You won’t, in fact, play well, unless random events align to teach you a good strategy. That would be very lucky indeed.

The Right Way to Slow Play

While I’m not usually a big fan of slow playing, it’s an important strategy to have in your arsenal. In this hand from the One Drop, Cristoph Vogelsang shows us the right way to do it:

He raises pocket aces, flops a full house on A33, and check-calls all the way. A good place to start thinking about this hand is to consider which would be a better slow play candidate on this board: aces or 43 suited.

I would argue that aces are a far better slow play, for a couple reasons. First, if you try to slow play 43, your opponent could hit a flush or a full house with something like 88, in which case you’ll lose a big pot. With aces, you actually want them to hit a strong second best hand, because you can still beat them. Second, 43 is a better betting hand, because your opponent will probably not fold a pair of aces, but he might not bet every street himself with a hand like A9. When you have AA yourself, it’s very hard for your opponent to have an ace.

So aces has two qualities that make for a good slow play:

Invulnerability: Your opponent is extremely unlikely to make a better hand. If he improves, it will be to a second best hand that you still beat.

Blocks calling hands: If you block the hands your opponent would call down with, betting becomes less valuable, which makes the alternative – slow playing – comparatively more valuable.

It’s important to note that Vogelsang does not take the betting lead at any point. He checks all the way. I see a lot of players check to the river, then suddenly spring into action with a bet. The whole point of this line is that you know your opponent likely has nothing at all and you’re giving him a chance to bluff. If you bet yourself, he can’t really call with nothing, but if you check, he can certainly bet with nothing.

That “bet with nothing” bit is important – this line loses much of its value if your opponent isn’t capable of bluffing his whole stack. It’s largely a way of protecting yourself, and your marginal hands, from an opponent who can do exactly that. If you know your opponent will never run a big bluff, you may as well bet and hope he somehow has something to call with.


In an act of unprecedented spite, Lebron James ignored his own self interest, confirmed tendencies, and the deepest longings of his soul to prove me wrong by returning to Cleveland.

What can I say? My world is in shambles.

Definitely not Cleveland

Now that Lebron has opted out of his contract with Miami, speculation runs rampant over where he’ll end up. New York? L.A.? Miami after all? I don’t know where he’ll land, but I do know where he WON’T go: Cleveland.

Ever since he left Cleveland, I’ve been puzzled by the persistent rumors that he might return. Not because of Dan Gilbert’s unhinged “open letter” – although that didn’t help any – but simply because of Lebron’s trajectory. He is a man bent on hegemony. He has no interest in glorifying his provincial birthplace. This doesn’t end with a heartwarming reunion, it ends with Lebron, high atop the mountain, alone. A shooting star doesn’t return to orbit. Lebron isn’t going back to Cleveland.

Brazil in the World Cup

With one of the best squads in the world and home field advantage, it’s no surprise that Brazil are the unanimous favorites in the World Cup. But by how much? Typical betting lines in Vegas had them around 3-to-1, indicating a roughly 25% chance of winning it all, but forecasts from some prominent analysts pegged them at near 50%. Nate Silver on FiveThirtyEight gives Brazil a 45.2% shot of winning it all, while a report from Goldman Sachs is even more bullish at 48.5%.

If you believe Silver and Sachs, you could walk into any Vegas sports book and make a handsomely profitable bet on Brazil. Yet it’s hard to figure how Brazil can really be even odds to win. In a 32-team field, if all the teams were equal, each would have only a little more than a 3% chance to win, so for one team to have nearly 50% indicates a massive advantage over the field. Given that, you’d expect Brazil to be regarded as the clear top team in the world, but they’re not. Currently they’re only number three in the FIFA rankings. While those FIFA rankings are suspect, and many do consider Brazil to be the world’s top team, it’s not by a landslide. Common opinion puts them on nearly even footing with a handful of other elite teams.

The biggest reason the analysts love Brazil seems to be home field advantage. Not without reason: home teams have historically out-performed their abilities in the World Cup and no European team has ever won a World Cup held in the Americas. Whether you agree with the Vegas line makers or the quants comes down to how much stock you put in home field advantage. The Vegas line represents more of a common sense estimate in a level field, while the math models have a lot of respect for playing at home.

Betting on stuff that matters

Paul Sabin, a Yale historian, has just written a book about a famous wager between Paul Ehrlich and Julian Simon. Ehrlich, a biologist, predicted a looming environmental crisis, while Simon, an economist, believed that human ingenuity would compensate for the drain on natural resources. They put their views to the test with a bet on how the prices of various natural resources would change over ten years. Simon won the bet, causing Ehrlich to completely change his mind and renounce his lifelong advocacy for environmental protection.

No, wait, that second part didn’t happen. Like the guys who “decode” the Bible and predict an apocalypse, Ehrlich didn’t let the unabated existence of the world slow him down. In his support other scientists figured out that he would have won the bet in the majority of decades in the 20th century, so it could be he was right about the general trend and just got unlucky (or lucky, depending on how you look at it).

When it comes to environmental catastrophes, I wonder if a gradual trend is what we should really be looking for, anyway. In gambling we have a term, “fading,” that means avoiding a disaster. If you get all-in with top pair against a flush draw, you’re fading the flush. The fact that we’ve faded an environmental disaster so far doesn’t tell us how lucky we had to get to do so. According to some accounts JFK estimated the chance of nuclear war with the Soviet Union to be at least 50% during his presidency. Certainly, we’ve come close to destroying our whole world in one fell swoop. Every time I turn on public radio I learn about another facet of the environment that’s out of whack – ocean acidity, coral reefs, probably a hundred more I don’t know about. It’s kind of amazing the planet still works as well as it does.

But back to bets. It’s quite unusual for two public figures to bet on something important. During the last presidential election Nate Silver wanted to bet Joe Scarborough that Obama would win. Silver had predicted a comfortable advantage for Obama, while Scarborough opined, “Anybody that thinks that this race is anything but a tossup right now is such an ideologue, they should be kept away from typewriters, computers, laptops and microphones for the next 10 days, because they’re jokes.” Scarborough was apparently operating on the principle that any time there are two possible outcomes, they are equally likely, which works pretty well in PLO, but not so much elsewhere. When Obama won, a parade was thrown for Silver and Scarborough was stoned in the public square.

Oops, that also didn’t happen. Scarborough went right on hosting his political commentary show and no one thought anything of it. What Silver didn’t understand is that Joe Scarborough isn’t in the business of being right. His actual business is harder to pin down. Looking a certain way…sounding a certain way…a bit of trolling now and then. That’s all part of it. But making accurate predictions doesn’t seem to have anything to do with it.

When habitual bettors offer a wager to non-bettors and are refused, they think they’ve proven their point: I put my money where my mouth is and he doesn’t. More likely, they’ve just bullied someone who’s not comfortable throwing money around. But more fundamentally, offering a bet implies that what counts is who’s right, and for most people most of the time, it’s not.

Perhaps I was wrong

Well, it would have to happen the day after I wrote about that, wouldn’t it? It got checked through on the flop and turn and the river brought a straight. Player A bets 50, player B raises to 175, player C cold calls, player A re-raises to 500, player B goes all-in for 1500, player C calls, and player A calls. Players A and B roll the nuts. Player C checks his cards and his face falls.

For my part, I still won’t be raising in this spot, because I think I’m more likely to misread my hand than my opponents. I have some strong suits, but knowing my hand isn’t one of them.